diff --git a/.github/workflows/CompatHelper.yml b/.github/workflows/CompatHelper.yml
new file mode 100644
index 0000000..f05a64a
--- /dev/null
+++ b/.github/workflows/CompatHelper.yml
@@ -0,0 +1,13 @@
+name: CompatHelper
+on:
+  schedule:
+    - cron: 0 0 * * *
+  workflow_dispatch:
+jobs:
+  CompatHelper:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: JuliaRegistries/compathelper-action@v1
+        with:
+          token: ${{ secrets.GITHUB_TOKEN }}
+          ssh: ${{ secrets.DOCUMENTER_KEY }}
diff --git a/.github/workflows/TagBot.yml b/.github/workflows/TagBot.yml
index f49313b..f389611 100644
--- a/.github/workflows/TagBot.yml
+++ b/.github/workflows/TagBot.yml
@@ -4,6 +4,11 @@ on:
     types:
       - created
   workflow_dispatch:
+    inputs:
+      lookback:
+        default: 3
+permissions:
+  contents: write
 jobs:
   TagBot:
     if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot'
diff --git a/.github/workflows/runtests.yml b/.github/workflows/ci.yml
similarity index 60%
rename from .github/workflows/runtests.yml
rename to .github/workflows/ci.yml
index 24406d7..47976f9 100644
--- a/.github/workflows/runtests.yml
+++ b/.github/workflows/ci.yml
@@ -1,11 +1,7 @@
 name: CI
 on:
-  push:
-    branches:
-      - master
-  pull_request:
-    branches:
-      - master
+  - pull_request
+  - push
 jobs:
   test:
     name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }}
@@ -22,21 +18,31 @@ jobs:
           - windows-latest
         arch:
           - x64
+        allow_failures:
+          - julia: nightly
       fail-fast: false
-
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v3
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.version }}
           arch: ${{ matrix.arch }}
+      - uses: actions/cache@v3
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
       - uses: julia-actions/julia-buildpkg@latest
       - uses: julia-actions/julia-runtest@latest
       - uses: julia-actions/julia-processcoverage@v1
-      - uses: codecov/codecov-action@v1
+      - uses: codecov/codecov-action@v2
         with:
           file: ./lcov.info
           flags: unittests
           name: codecov-umbrella
           fail_ci_if_error: false
-          token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/Project.toml b/Project.toml
index 93f0e92..d9251fa 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "Groups"
 uuid = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
 authors = ["Marek Kaluba <kalmar@amu.edu.pl>"]
-version = "0.7.3"
+version = "0.7.4"
 
 [deps]
 Folds = "41a02a25-b8f0-4f67-bc48-60067656b558"
@@ -16,7 +16,7 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 [compat]
 Folds = "0.2.7"
 GroupsCore = "0.4"
-KnuthBendix = "0.3"
+KnuthBendix = "0.4"
 OrderedCollections = "1"
 PermutationGroups = "0.3"
 StaticArrays = "1"
diff --git a/README.md b/README.md
index 79523ed..b2fc191 100644
--- a/README.md
+++ b/README.md
@@ -10,25 +10,25 @@ The package implements `AbstractFPGroup` with three concrete types: `FreeGroup`,
 julia> using Groups, GroupsCore
 
 julia> A = Alphabet([:a, :A, :b, :B, :c, :C], [2, 1, 4, 3, 6, 5])
-Alphabet of Symbol:
-        1.      :a = (:A)⁻¹
-        2.      :A = (:a)⁻¹
-        3.      :b = (:B)⁻¹
-        4.      :B = (:b)⁻¹
-        5.      :c = (:C)⁻¹
-        6.      :C = (:c)⁻¹
+Alphabet of Symbol
+  1. a   (inverse of: A)
+  2. A   (inverse of: a)
+  3. b   (inverse of: B)
+  4. B   (inverse of: b)
+  5. c   (inverse of: C)
+  6. C   (inverse of: c)
 
 julia> F = FreeGroup(A)
 free group on 3 generators
 
 julia> a,b,c = gens(F)
-3-element Vector{FPGroupElement{FreeGroup{Symbol}, KnuthBendix.Word{UInt8}}}:
+3-element Vector{FPGroupElement{FreeGroup{Symbol, KnuthBendix.LenLex{Symbol}}, …}}:
  a
  b
  c
 
 julia> a*inv(a)
-(empty word)
+(id)
 
 julia> (a*b)^2
 a*b*a*b
@@ -40,65 +40,75 @@ julia> x = a*b; y = inv(b)*a;
 
 julia> x*y
 a^2
-
 ```
+
+## FPGroup
 Let's create a quotient of the free group above:
 ```julia
-julia> ε = one(F);
-
-julia> G = FPGroup(F, [a^2 => ε, b^3=> ε, (a*b)^7=>ε, (a*b*a*inv(b))^6 => ε, commutator(a, c) => ε, commutator(b, c) => ε ])
-┌ Warning: Maximum number of rules (100) reached. The rewriting system may not be confluent.
-│     You may retry `knuthbendix` with a larger `maxrules` kwarg.
-└ @ KnuthBendix ~/.julia/packages/KnuthBendix/i93Np/src/kbs.jl:6
-⟨a, b, c | a^2 => (empty word), b^3 => (empty word), a*b*a*b*a*b*a*b*a*b*a*b*a*b => (empty word), a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B => (empty word), A*C*a*c => (empty word), B*C*b*c => (empty word)⟩
+julia> ε = one(F)
+(id)
 
+julia> G = FPGroup(F, [a^2 => ε, b^3=> ε, (a*b)^7=>ε, (a*b*a*inv(b))^6 => ε, commutator(a, c) => ε, commutator(b, c) => ε ], max_rules=100)
+┌ Warning: Maximum number of rules (100) reached.
+│ The rewriting system may not be confluent.
+│ You may retry `knuthbendix` with a larger `max_rules` kwarg.
+└ @ KnuthBendix ~/.julia/packages/KnuthBendix/6ME1b/src/knuthbendix_base.jl:8
+Finitely presented group generated by:
+        { a  b  c },
+subject to relations:
+                                             a^2 => (id)
+                                             b^3 => (id)
+                     a*b*a*b*a*b*a*b*a*b*a*b*a*b => (id)
+ a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B => (id)
+                                         A*C*a*c => (id)
+                                         B*C*b*c => (id)
 ```
-As you can see from the warning, the Knuth-Bendix procedure has not completed successfully. This means that we only are able to approximate the word problem in `G`, i.e. if the equality (`==`) of two group elements may return `false` even if group elements are equal. Let us try with a larger maximal number of rules in the underlying rewriting system.
+As you can see from the warning, the Knuth-Bendix procedure has not completed successfully. This means that we only are able to **approximate the word problem** in `G`, i.e. if the equality (`==`) of two group elements may return `false` even if group elements are equal. Let us try with a larger maximal number of rules in the underlying rewriting system.
 
 ```julia
-julia> G = FPGroup(F, [a^2 => ε, b^3=> ε, (a*b)^7=>ε, (a*b*a*inv(b))^6 => ε, commutator(a, c) => ε, commutator(b, c) => ε ], maxrules=500)
-⟨a, b, c | a^2 => (empty word), b^3 => (empty word), a*b*a*b*a*b*a*b*a*b*a*b*a*b => (empty word), a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B => (empty word), A*C*a*c => (empty word), B*C*b*c => (empty word)⟩
+julia> G = FPGroup(F, [a^2 => ε, b^3=> ε, (a*b)^7=>ε, (a*b*a*inv(b))^6 => ε, commutator(a, c) => ε, commutator(b, c) => ε ], max_rules=500)
+Finitely presented group generated by:
+        { a  b  c },
+subject to relations:
+                                             a^2 => (id)
+                                             b^3 => (id)
+                     a*b*a*b*a*b*a*b*a*b*a*b*a*b => (id)
+ a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B*a*b*a*B => (id)
+                                         A*C*a*c => (id)
+                                         B*C*b*c => (id)
 
 ```
-This time there was no warning, i.e. Knuth-Bendix completion was successful and we may treat the equality (`==`) as true mathematical equality. Note that `G` is the direct product of `ℤ = ⟨ c ⟩` and a quotient of van Dyck `(2,3,7)`-group. Let's create a random word and reduce it as an element of `G`.
+This time there was no warning, i.e. Knuth-Bendix completion was successful and we may treat the equality (`==`) as the **true mathematical equality**. Note that `G` is the direct product of `ℤ = ⟨ c ⟩` and a quotient of van Dyck `(2,3,7)`-group. Let's create a random word and reduce it as an element of `G`.
 ```julia
-julia> using Random; Random.seed!(1); w = Groups.Word(rand(1:length(A), 16))
-KnuthBendix.Word{UInt16}: 4·6·1·1·1·6·5·1·5·2·3·6·2·4·2·6
+julia> using Random; Random.seed!(1); w = Groups.Word(rand(1:length(A), 16));
 
-julia> F(w) # freely reduced w
-B*C*a^4*c*A*b*C*A*B*A*C
+julia> length(w), w # word of itself
+(16, 1·3·5·4·6·2·5·5·5·2·4·3·2·1·4·4)
 
-julia> G(w) # w as an element of G
-B*a*b*a*B*a*C^2
+julia> f = F(w) # freely reduced w
+a*b*c*B*C*A*c^3*A*B^2
 
-julia> F(w) # freely reduced w
-B*C*a^4*c*A*b*C*A*B*A*C
+julia> length(word(f)), word(f) # the underlying word in F
+(12, 1·3·5·4·6·2·5·5·5·2·4·4)
 
-julia> word(ans) # the underlying word in A
-KnuthBendix.Word{UInt8}: 4·6·1·1·1·1·5·2·3·6·2·4·2·6
-
-julia> G(w) # w as an element of G
-B*a*b*a*B*a*C^2
-
-julia> word(ans) # the underlying word in A
-KnuthBendix.Word{UInt8}: 4·1·3·1·4·1·6·6
+julia> g = G(w) # w as an element of G
+a*b*c^3
 
+julia> length(word(g)), word(g) # the underlying word in G
+(5, 1·3·5·5·5)
 ```
 As we can see the underlying words change according to where they are reduced.
-Note that a word `w` (of type `Word <: AbstractWord`) is just a sequence of numbers -- pointers to letters of an `Alphabet`. Without the alphabet `w` has no meaning.
+Note that a word `w` (of type `Word <: AbstractWord`) is just a sequence of numbers -- indices of letters of an `Alphabet`. Without the alphabet `w` has no intrinsic meaning.
 
-### Automorphism Groups
+## Automorphism Groups
 
-Relatively complete is the support for the automorphisms of free groups, as given by Gersten presentation:
+Relatively complete is the support for the automorphisms of free groups generated by transvections (or Nielsen generators):
 ```julia
-julia> saut = SpecialAutomorphismGroup(F, maxrules=100)
-┌ Warning: Maximum number of rules (100) reached. The rewriting system may not be confluent.
-│     You may retry `knuthbendix` with a larger `maxrules` kwarg.
-└ @ KnuthBendix ~/.julia/packages/KnuthBendix/i93Np/src/kbs.jl:6
+julia> saut = SpecialAutomorphismGroup(F, max_rules=1000)
 automorphism group of free group on 3 generators
 
 julia> S = gens(saut)
-12-element Vector{Automorphism{FreeGroup{Symbol},…}}:
+12-element Vector{Automorphism{FreeGroup{Symbol, KnuthBendix.LenLex{Symbol}}, …}}:
  ϱ₁.₂
  ϱ₁.₃
  ϱ₂.₁
@@ -114,17 +124,15 @@ julia> S = gens(saut)
 
 julia> x, y, z = S[1], S[12], S[6];
 
-julia> f = x*y*inv(z)
-ϱ₁.₂*λ₃.₂*ϱ₃.₂^-1
+julia> f = x*y*inv(z);
 
-julia> g = inv(z)*y*x
-ϱ₃.₂^-1*ϱ₁.₂*λ₃.₂
+julia> g = inv(z)*y*x;
 
 julia> word(f), word(g)
-(KnuthBendix.Word{UInt8}: 1·12·18, KnuthBendix.Word{UInt8}: 18·1·12)
+(1·23·12, 12·23·1)
 
 ```
-Even though Knuth-Bendix did not finish successfully in automorphism groups we have another ace in our sleeve to solve the word problem: evaluation.
+Even though there is no known finite, confluent rewriting system for automorphism groupsof the free group (so Knuth-Bendix did not finish successfully) we have another ace in our sleeve to solve the word problem: evaluation.
 Lets have a look at the images of generators under those automorphisms:
 ```julia
 julia> evaluate(f) # or to be more verbose...
@@ -147,7 +155,7 @@ This is what is happening behind the scenes:
  2. if resulting words are equal `true` is returned
  3. if they are not equal `Groups.equality_data` is computed for each argument (here: the images of generators) and the result of comparison is returned.
 
-Moreover we try to amortize the cost of computing those images. That is a hash of `equality_daata` is lazily stored  in each group element and used as needed. Essentially only if `true` is returned, but comparison of words returns `false` recomputation of images is needed (to guard against hash collisions).
+Moreover we try to amortize the cost of computing those images. That is a hash of `equality_daata` is lazily stored in each group element and used as needed. Essentially only if `true` is returned, but comparison of words returns `false` recomputation of images is needed (to guard against hash collisions).
 
 ----
 This package was developed for computations in [1712.07167](https://arxiv.org/abs/1712.07167) and in [1812.03456](https://arxiv.org/abs/1812.03456). If you happen to use this package please cite either of them.
diff --git a/src/Groups.jl b/src/Groups.jl
index 7c97e77..f34a7b7 100644
--- a/src/Groups.jl
+++ b/src/Groups.jl
@@ -10,7 +10,7 @@ import OrderedCollections: OrderedSet
 
 import KnuthBendix
 import KnuthBendix: AbstractWord, Alphabet, Word
-import KnuthBendix: alphabet
+import KnuthBendix: alphabet, ordering
 
 export MatrixGroups
 
diff --git a/src/abelianize.jl b/src/abelianize.jl
index e059feb..4f47f0f 100644
--- a/src/abelianize.jl
+++ b/src/abelianize.jl
@@ -1,7 +1,7 @@
 function _abelianize(
     i::Integer,
     source::AutomorphismGroup{<:FreeGroup},
-    target::MatrixGroups.SpecialLinearGroup{N, T}) where {N, T}
+    target::MatrixGroups.SpecialLinearGroup{N,T}) where {N,T}
     n = ngens(object(source))
     @assert n == N
     aut = alphabet(source)[i]
@@ -10,10 +10,10 @@ function _abelianize(
         # Automorphisms act on the right which corresponds to action on
         # the columns in the matrix case
         eij = MatrixGroups.ElementaryMatrix{N}(
-                aut.j,
-                aut.i,
-                ifelse(aut.inv, -one(T), one(T))
-            )
+            aut.j,
+            aut.i,
+            ifelse(aut.inv, -one(T), one(T))
+        )
         k = alphabet(target)[eij]
         return word_type(target)([k])
     else
@@ -24,7 +24,7 @@ end
 function _abelianize(
     i::Integer,
     source::AutomorphismGroup{<:Groups.SurfaceGroup},
-    target::MatrixGroups.SpecialLinearGroup{N, T}) where {N, T}
+    target::MatrixGroups.SpecialLinearGroup{N,T}) where {N,T}
     n = ngens(Groups.object(source))
     @assert n == N
     g = alphabet(source)[i].autFn_word
@@ -39,8 +39,8 @@ end
 function Groups._abelianize(
     i::Integer,
     source::AutomorphismGroup{<:Groups.SurfaceGroup},
-    target::MatrixGroups.SymplecticGroup{N, T}
-) where {N, T}
+    target::MatrixGroups.SymplecticGroup{N,T}
+) where {N,T}
     @assert iseven(N)
     As = alphabet(source)
     At = alphabet(target)
@@ -53,7 +53,7 @@ function Groups._abelianize(
     ab = Groups.Homomorphism(Groups._abelianize, source, SlN, check=false)
 
     matrix_spn_map = let S = gens(target)
-        Dict(MatrixGroups.matrix_repr(g)=> word(g) for g in union(S, inv.(S)))
+        Dict(MatrixGroups.matrix_repr(g) => word(g) for g in union(S, inv.(S)))
     end
 
     # renumeration:
@@ -63,7 +63,7 @@ function Groups._abelianize(
     p = [reverse(2:2:N); reverse(1:2:N)]
 
     g = source([i])
-    Mg = MatrixGroups.matrix_repr(ab(g))[p,p]
+    Mg = MatrixGroups.matrix_repr(ab(g))[p, p]
 
     return matrix_spn_map[Mg]
 end
diff --git a/src/aut_groups/gersten_relations.jl b/src/aut_groups/gersten_relations.jl
index 79014b8..d91a8ef 100644
--- a/src/aut_groups/gersten_relations.jl
+++ b/src/aut_groups/gersten_relations.jl
@@ -1,4 +1,4 @@
-function gersten_alphabet(n::Integer; commutative::Bool = true)
+function gersten_alphabet(n::Integer; commutative::Bool=true)
     indexing = [(i, j) for i in 1:n for j in 1:n if i ≠ j]
     S = [ϱ(i, j) for (i, j) in indexing]
 
@@ -6,7 +6,7 @@ function gersten_alphabet(n::Integer; commutative::Bool = true)
         append!(S, [λ(i, j) for (i, j) in indexing])
     end
 
-    return Alphabet(S)
+    return Alphabet(mapreduce(x -> [x, inv(x)], union, S))
 end
 
 function _commutation_rule(
@@ -41,12 +41,12 @@ function _hexagonal_rule(
 end
 
 gersten_relations(n::Integer; commutative) =
-    gersten_relations(Word{UInt8}, n, commutative = commutative)
+    gersten_relations(Word{UInt8}, n, commutative=commutative)
 
 function gersten_relations(::Type{W}, n::Integer; commutative) where {W<:AbstractWord}
     @assert n > 1 "Gersten relations are defined only for n>1, got n=$n"
-    A = gersten_alphabet(n, commutative = commutative)
-    @assert length(A) <= KnuthBendix._max_alphabet_length(W) "Type $W can not represent words over alphabet with $(length(A)) letters."
+    A = gersten_alphabet(n, commutative=commutative)
+    @assert length(A) <= typemax(eltype(W)) "Type $W can not represent words over alphabet with $(length(A)) letters."
 
     rels = Pair{W,W}[]
 
@@ -96,7 +96,7 @@ function gersten_relations(::Type{W}, n::Integer; commutative) where {W<:Abstrac
             if i ≠ j
                 push!(rels, _hexagonal_rule(W, A, ϱ(i, j), ϱ(j, i), λ(i, j), λ(j, i)))
                 w = W([A[ϱ(i, j)], A[ϱ(j, i)^-1], A[λ(i, j)]])
-                push!(rels, w^2 => inv(A, w)^2)
+                push!(rels, w^2 => inv(w, A)^2)
             end
         end
     end
diff --git a/src/aut_groups/mcg.jl b/src/aut_groups/mcg.jl
index 5d9041f..1fc6286 100644
--- a/src/aut_groups/mcg.jl
+++ b/src/aut_groups/mcg.jl
@@ -1,9 +1,9 @@
-struct SurfaceGroup{T, S, R} <: AbstractFPGroup
+struct SurfaceGroup{T,S,RW} <: AbstractFPGroup
     genus::Int
     boundaries::Int
     gens::Vector{T}
     relations::Vector{<:Pair{S,S}}
-    rws::R
+    rw::RW
 end
 
 include("symplectic_twists.jl")
@@ -17,7 +17,7 @@ function Base.show(io::IO, S::SurfaceGroup)
     end
 end
 
-function SurfaceGroup(genus::Integer, boundaries::Integer)
+function SurfaceGroup(genus::Integer, boundaries::Integer, W=Word{Int16})
     @assert genus > 1
 
     # The (confluent) rewriting systems comes from
@@ -30,15 +30,15 @@ function SurfaceGroup(genus::Integer, boundaries::Integer)
 
     ltrs = String[]
     for i in 1:genus
-        subscript = join('₀'+d for d in reverse(digits(i)))
+        subscript = join('₀' + d for d in reverse(digits(i)))
         append!(ltrs, ["A" * subscript, "a" * subscript, "B" * subscript, "b" * subscript])
     end
     Al = Alphabet(reverse!(ltrs))
 
     for i in 1:genus
-        subscript = join('₀'+d for d in reverse(digits(i)))
-        KnuthBendix.set_inversion!(Al, "a" * subscript, "A" * subscript)
-        KnuthBendix.set_inversion!(Al, "b" * subscript, "B" * subscript)
+        subscript = join('₀' + d for d in reverse(digits(i)))
+        KnuthBendix.setinverse!(Al, "a" * subscript, "A" * subscript)
+        KnuthBendix.setinverse!(Al, "b" * subscript, "B" * subscript)
     end
 
     if boundaries == 0
@@ -46,43 +46,44 @@ function SurfaceGroup(genus::Integer, boundaries::Integer)
 
         for i in reverse(1:genus)
             x = 4 * i
-            append!(word, [x, x-2, x-1, x-3])
+            append!(word, [x, x - 2, x - 1, x - 3])
         end
-        comms = Word(word)
-        word_rels = [ comms => one(comms) ]
+        comms = W(word)
+        word_rels = [comms => one(comms)]
 
-        rws = KnuthBendix.RewritingSystem(word_rels, KnuthBendix.RecursivePathOrder(Al))
-        KnuthBendix.knuthbendix!(rws)
+        rws = let R = KnuthBendix.RewritingSystem(word_rels, KnuthBendix.Recursive(Al))
+            KnuthBendix.IndexAutomaton(KnuthBendix.knuthbendix(R))
+        end
     elseif boundaries == 1
-        S = typeof(one(Word(Int[])))
-        word_rels = Pair{S, S}[]
-        rws = RewritingSystem(word_rels, KnuthBendix.LenLex(Al))
+        word_rels = Pair{W,W}[]
+        rws = let R = RewritingSystem(word_rels, KnuthBendix.LenLex(Al))
+            KnuthBendix.IndexAutomaton(KnuthBendix.knuthbendix(R))
+        end
     else
-        throw("Not Implemented")
+        throw("Not Implemented for MCG with $boundaryies boundary components")
     end
 
-    F = FreeGroup(alphabet(rws))
-    rels = [F(lhs)=>F(rhs) for (lhs,rhs) in word_rels]
+    F = FreeGroup(Al)
+    rels = [F(lhs) => F(rhs) for (lhs, rhs) in word_rels]
 
-    return SurfaceGroup(genus, boundaries, KnuthBendix.letters(Al)[2:2:end], rels, rws)
+    return SurfaceGroup(genus, boundaries, [Al[i] for i in 2:2:length(Al)], rels, rws)
 end
 
-rewriting(S::SurfaceGroup) = S.rws
-KnuthBendix.alphabet(S::SurfaceGroup) = alphabet(rewriting(S))
+rewriting(S::SurfaceGroup) = S.rw
 relations(S::SurfaceGroup) = S.relations
 
 function symplectic_twists(π₁Σ::SurfaceGroup)
     g = genus(π₁Σ)
 
-    saut = SpecialAutomorphismGroup(FreeGroup(2g), maxrules=100)
+    saut = SpecialAutomorphismGroup(FreeGroup(2g), max_rules=1000)
 
-    Aij  = [SymplecticMappingClass(saut, :A, i, j) for i in 1:g for j in 1:g if i≠j]
+    Aij = [SymplecticMappingClass(saut, :A, i, j) for i in 1:g for j in 1:g if i ≠ j]
 
-    Bij  = [SymplecticMappingClass(saut, :B, i, j) for i in 1:g for j in 1:g if i≠j]
+    Bij = [SymplecticMappingClass(saut, :B, i, j) for i in 1:g for j in 1:g if i ≠ j]
 
-    mBij = [SymplecticMappingClass(saut, :B, i, j, minus=true) for i in 1:g for j in 1:g if i≠j]
+    mBij = [SymplecticMappingClass(saut, :B, i, j, minus=true) for i in 1:g for j in 1:g if i ≠ j]
 
-    Bii  = [SymplecticMappingClass(saut, :B, i, i) for i in 1:g]
+    Bii = [SymplecticMappingClass(saut, :B, i, i) for i in 1:g]
 
     mBii = [SymplecticMappingClass(saut, :B, i, i, minus=true) for i in 1:g]
 
@@ -98,6 +99,6 @@ function AutomorphismGroup(π₁Σ::SurfaceGroup; kwargs...)
     # this is to fix the definitions of symplectic twists:
     # with i->gens(π₁Σ, i) the corresponding automorphisms return
     # reversed words
-    domain = ntuple(i->inv(gens(π₁Σ, i)), 2genus(π₁Σ))
+    domain = ntuple(i -> inv(gens(π₁Σ, i)), 2genus(π₁Σ))
     return AutomorphismGroup(π₁Σ, S, A, domain)
 end
diff --git a/src/aut_groups/sautFn.jl b/src/aut_groups/sautFn.jl
index 4e86a37..b0805fa 100644
--- a/src/aut_groups/sautFn.jl
+++ b/src/aut_groups/sautFn.jl
@@ -1,25 +1,25 @@
 include("transvections.jl")
 include("gersten_relations.jl")
 
-function SpecialAutomorphismGroup(F::FreeGroup; ordering = KnuthBendix.LenLex, kwargs...)
+function SpecialAutomorphismGroup(F::FreeGroup; ordering=KnuthBendix.LenLex, kwargs...)
 
     n = length(alphabet(F)) ÷ 2
-    A, rels = gersten_relations(n, commutative = false)
-    S = KnuthBendix.letters(A)[1:2(n^2-n)]
+    A, rels = gersten_relations(n, commutative=false)
+    S = [A[i] for i in 1:2:length(A)]
 
-    maxrules = 1000*n
+    max_rules = 1000 * n
 
-    rws = KnuthBendix.RewritingSystem(rels, ordering(A))
-    Logging.with_logger(Logging.NullLogger()) do
+    rws = Logging.with_logger(Logging.NullLogger()) do
+        rws = KnuthBendix.RewritingSystem(rels, ordering(A))
         # the rws is not confluent, let's suppress warning about it
-        KnuthBendix.knuthbendix!(rws; maxrules=maxrules, kwargs...)
+        KnuthBendix.knuthbendix(rws, KnuthBendix.Settings(; max_rules=max_rules, kwargs...))
     end
-    return AutomorphismGroup(F, S, rws, ntuple(i -> gens(F, i), n))
-end
 
-KnuthBendix.alphabet(G::AutomorphismGroup{<:FreeGroup}) = alphabet(rewriting(G))
+    idxA = KnuthBendix.IndexAutomaton(rws)
+    return AutomorphismGroup(F, S, idxA, ntuple(i -> gens(F, i), n))
+end
 
 function relations(G::AutomorphismGroup{<:FreeGroup})
     n = length(alphabet(object(G))) ÷ 2
-    return last(gersten_relations(n, commutative = false))
+    return last(gersten_relations(n, commutative=false))
 end
diff --git a/src/aut_groups/symplectic_twists.jl b/src/aut_groups/symplectic_twists.jl
index f9f36dd..7a48233 100644
--- a/src/aut_groups/symplectic_twists.jl
+++ b/src/aut_groups/symplectic_twists.jl
@@ -25,7 +25,7 @@ function Te_diagonal(λ::Groups.ΡΛ, ϱ::Groups.ΡΛ, i::Integer)
 
     if i == n
         τ = rotation_element(λ, ϱ)
-        return inv(A, τ) * Te_diagonal(λ, ϱ, 1) * τ
+        return inv(τ, A) * Te_diagonal(λ, ϱ, 1) * τ
     end
 
     @assert 1 <= i < n
@@ -37,32 +37,32 @@ function Te_diagonal(λ::Groups.ΡΛ, ϱ::Groups.ΡΛ, i::Integer)
 
     g = one(Word(Int[]))
     g *= λ[NJ, NI]                    # β ↦ α*β
-    g *= λ[NI, I] * inv(A, ϱ[NI, J])  # α ↦ a*α*b^-1
-    g *= inv(A, λ[NJ, NI])            # β ↦ b*α^-1*a^-1*α*β
-    g *= λ[J, NI] * inv(A, λ[J, I])   # b ↦ α
-    g *= inv(A, λ[J, NI])             # b ↦ b*α^-1*a^-1*α
-    g *= inv(A, ϱ[J, NI]) * ϱ[J, I]   # b ↦ b*α^-1*a^-1*α*b*α^-1
+    g *= λ[NI, I] * inv(ϱ[NI, J], A)  # α ↦ a*α*b^-1
+    g *= inv(λ[NJ, NI], A)            # β ↦ b*α^-1*a^-1*α*β
+    g *= λ[J, NI] * inv(λ[J, I], A)   # b ↦ α
+    g *= inv(λ[J, NI], A)             # b ↦ b*α^-1*a^-1*α
+    g *= inv(ϱ[J, NI], A) * ϱ[J, I]   # b ↦ b*α^-1*a^-1*α*b*α^-1
     g *= ϱ[J, NI]                     # b ↦ b*α^-1*a^-1*α*b*α^-1*a*α*b^-1
 
     return g
 end
 
 function Te_lantern(A::Alphabet, b₀::T, a₁::T, a₂::T, a₃::T, a₄::T, a₅::T) where {T}
-    a₀ = (a₁ * a₂ * a₃)^4 * inv(A, b₀)
+    a₀ = (a₁ * a₂ * a₃)^4 * inv(b₀, A)
     X = a₄ * a₅ * a₃ * a₄ # from Primer
-    b₁ = inv(A, X) * a₀ * X # from Primer
+    b₁ = inv(X, A) * a₀ * X # from Primer
     Y = a₂ * a₃ * a₁ * a₂
-    return inv(A, Y) * b₁ * Y # b₂ from Primer
+    return inv(Y, A) * b₁ * Y # b₂ from Primer
 end
 
 function Ta(λ::Groups.ΡΛ, i::Integer)
-    @assert λ.id == :λ;
-    return λ[mod1(λ.N-2i+1, λ.N), mod1(λ.N-2i+2, λ.N)]
+    @assert λ.id == :λ
+    return λ[mod1(λ.N - 2i + 1, λ.N), mod1(λ.N - 2i + 2, λ.N)]
 end
 
 function Tα(λ::Groups.ΡΛ, i::Integer)
-    @assert λ.id == :λ;
-    return inv(λ.A, λ[mod1(λ.N-2i+2, λ.N), mod1(λ.N-2i+1, λ.N)])
+    @assert λ.id == :λ
+    return inv(λ[mod1(λ.N - 2i + 2, λ.N), mod1(λ.N - 2i + 1, λ.N)], λ.A)
 end
 
 function Te(λ::ΡΛ, ϱ::ΡΛ, i, j)
@@ -73,7 +73,7 @@ function Te(λ::ΡΛ, ϱ::ΡΛ, i, j)
     @assert λ.id == :λ && ϱ.id == :ϱ
 
     @assert iseven(λ.N)
-    genus = λ.N÷2
+    genus = λ.N ÷ 2
     i = mod1(i, genus)
     j = mod1(j, genus)
 
@@ -85,16 +85,16 @@ function Te(λ::ΡΛ, ϱ::ΡΛ, i, j)
     if mod(j - (i + 1), genus) == 0
         return Te_diagonal(λ, ϱ, i)
     else
-        return inv(A, Te_lantern(
-            A,
-            # Our notation:               # Primer notation:
-            inv(A, Ta(λ, i + 1)),         # b₀
-            inv(A, Ta(λ, i)),             # a₁
-            inv(A, Tα(λ, i)),             # a₂
-            inv(A, Te_diagonal(λ, ϱ, i)), # a₃
-            inv(A, Tα(λ, i + 1)),         # a₄
-            inv(A, Te(λ, ϱ, i + 1, j)),   # a₅
-        ))
+        return inv(Te_lantern(
+                A,
+                # Our notation:               # Primer notation:
+                inv(Ta(λ, i + 1), A),         # b₀
+                inv(Ta(λ, i), A),             # a₁
+                inv(Tα(λ, i), A),             # a₂
+                inv(Te_diagonal(λ, ϱ, i), A), # a₃
+                inv(Tα(λ, i + 1), A),         # a₄
+                inv(Te(λ, ϱ, i + 1, j), A),   # a₅
+            ), A)
     end
 end
 
@@ -118,29 +118,29 @@ end
 
 function rotation_element(λ::ΡΛ, ϱ::ΡΛ)
     @assert iseven(λ.N)
-    genus = λ.N÷2
+    genus = λ.N ÷ 2
     A = λ.A
 
     halftwists = map(1:genus-1) do i
         j = i + 1
-        x = Ta(λ, j) * inv(A, Ta(λ, i)) * Tα(λ, j) * Te_diagonal(λ, ϱ, i)
-        δ = x * Tα(λ, i) * inv(A, x)
+        x = Ta(λ, j) * inv(Ta(λ, i), A) * Tα(λ, j) * Te_diagonal(λ, ϱ, i)
+        δ = x * Tα(λ, i) * inv(x, A)
         c =
-            inv(A, Ta(λ, j)) *
+            inv(Ta(λ, j), A) *
             Te(λ, ϱ, i, j) *
             Tα(λ, i)^2 *
-            inv(A, δ) *
-            inv(A, Ta(λ, j)) *
+            inv(δ, A) *
+            inv(Ta(λ, j), A) *
             Ta(λ, i) *
             δ
         z =
             Te_diagonal(λ, ϱ, i) *
-            inv(A, Ta(λ, i)) *
+            inv(Ta(λ, i), A) *
             Tα(λ, i) *
             Ta(λ, i) *
-            inv(A, Te_diagonal(λ, ϱ, i))
+            inv(Te_diagonal(λ, ϱ, i), A)
 
-        Ta(λ, i) * inv(A, Ta(λ, j) * Tα(λ, j))^6 * (Ta(λ, j) * Tα(λ, j) * z)^4 * c
+        Ta(λ, i) * inv(Ta(λ, j) * Tα(λ, j), A)^6 * (Ta(λ, j) * Tα(λ, j) * z)^4 * c
     end
 
     τ = (Ta(λ, 1) * Tα(λ, 1))^6 * prod(halftwists)
@@ -168,7 +168,7 @@ function mcg_twists(G::AutomorphismGroup{<:FreeGroup})
     return Tas, Tαs, Tes
 end
 
-struct SymplecticMappingClass{T, F} <: GSymbol
+struct SymplecticMappingClass{T,F} <: GSymbol
     id::Symbol # :A, :B
     i::UInt
     j::UInt
@@ -187,13 +187,13 @@ function SymplecticMappingClass(
     id::Symbol,
     i::Integer,
     j::Integer;
-    minus = false,
-    inverse = false,
+    minus=false,
+    inverse=false
 )
     @assert i > 0 && j > 0
     id === :A && @assert i ≠ j
     @assert iseven(ngens(object(sautFn)))
-    genus = ngens(object(sautFn))÷2
+    genus = ngens(object(sautFn)) ÷ 2
 
     A = alphabet(sautFn)
     λ = ΡΛ(:λ, A, 2genus)
@@ -201,24 +201,24 @@ function SymplecticMappingClass(
 
     w = if id === :A
         Te(λ, ϱ, i, j) *
-        inv(A, Ta(λ, i)) *
+        inv(Ta(λ, i), A) *
         Tα(λ, i) *
         Ta(λ, i) *
-        inv(A, Te(λ, ϱ, i, j)) *
-        inv(A, Tα(λ, i)) *
-        inv(A, Ta(λ, j))
+        inv(Te(λ, ϱ, i, j), A) *
+        inv(Tα(λ, i), A) *
+        inv(Ta(λ, j), A)
     elseif id === :B
         if !minus
             if i ≠ j
-                x = Ta(λ, j) * inv(A, Ta(λ, i)) * Tα(λ, j) * Te(λ, ϱ, i, j)
-                δ = x * Tα(λ, i) * inv(A, x)
-                Tα(λ, i) * Tα(λ, j) * inv(A, δ)
+                x = Ta(λ, j) * inv(Ta(λ, i), A) * Tα(λ, j) * Te(λ, ϱ, i, j)
+                δ = x * Tα(λ, i) * inv(x, A)
+                Tα(λ, i) * Tα(λ, j) * inv(δ, A)
             else
-                inv(A, Tα(λ, i))
+                inv(Tα(λ, i), A)
             end
         else
             if i ≠ j
-                Ta(λ, i) * Ta(λ, j) * inv(A, Te(λ, ϱ, i, j))
+                Ta(λ, i) * Ta(λ, j) * inv(Te(λ, ϱ, i, j), A)
             else
                 Ta(λ, i)
             end
@@ -241,7 +241,7 @@ end
 
 function Base.show(io::IO, smc::SymplecticMappingClass)
     smc.minus && print(io, 'm')
-    if  smc.i < 10 && smc.j < 10
+    if smc.i < 10 && smc.j < 10
         print(io, smc.id, subscriptify(smc.i), subscriptify(smc.j))
     else
         print(io, smc.id, subscriptify(smc.i), ".", subscriptify(smc.j))
diff --git a/src/aut_groups/transvections.jl b/src/aut_groups/transvections.jl
index ce6238b..63c9717 100644
--- a/src/aut_groups/transvections.jl
+++ b/src/aut_groups/transvections.jl
@@ -4,7 +4,7 @@ struct Transvection <: GSymbol
     j::UInt16
     inv::Bool
 
-    function Transvection(id::Symbol, i::Integer, j::Integer, inv = false)
+    function Transvection(id::Symbol, i::Integer, j::Integer, inv=false)
         @assert id in (:ϱ, :λ)
         return new(id, i, j, inv)
     end
@@ -33,7 +33,7 @@ Base.hash(t::Transvection, h::UInt) = hash(hash(t.id, hash(t.i)), hash(t.j, hash
 Base.@propagate_inbounds @inline function evaluate!(
     v::NTuple{T,N},
     t::Transvection,
-    tmp = one(first(v)),
+    tmp=one(first(v)),
 ) where {T,N}
     i, j = t.i, t.j
     @assert 1 ≤ i ≤ length(v) && 1 ≤ j ≤ length(v)
@@ -45,9 +45,9 @@ Base.@propagate_inbounds @inline function evaluate!(
             if !t.inv
                 append!(word(v[i]), word(v[j]))
             else
-                # append!(word(v[i]), inv(A, word(v[j])))
+                # append!(word(v[i]), inv(word(v[j]), A))
                 for l in Iterators.reverse(word(v[j]))
-                    push!(word(v[i]), inv(A, l))
+                    push!(word(v[i]), inv(l, A))
                 end
             end
         else # if t.id === :λ
@@ -57,9 +57,9 @@ Base.@propagate_inbounds @inline function evaluate!(
                     pushfirst!(word(v[i]), l)
                 end
             else
-                # prepend!(word(v[i]), inv(A, word(v[j])))
+                # prepend!(word(v[i]), inv(word(v[j]), A))
                 for l in word(v[j])
-                    pushfirst!(word(v[i]), inv(A, l))
+                    pushfirst!(word(v[i]), inv(l, A))
                 end
             end
         end
@@ -92,4 +92,4 @@ Base.inv(p::PermRightAut) = PermRightAut(invperm(p.perm))
 Base.:(==)(p::PermRightAut, q::PermRightAut) = p.perm == q.perm
 Base.hash(p::PermRightAut, h::UInt) = hash(p.perm, hash(PermRightAut, h))
 
-evaluate!(v::NTuple{T,N}, p::PermRightAut, tmp = nothing) where {T,N} = v[p.perm]
+evaluate!(v::NTuple{T,N}, p::PermRightAut, tmp=nothing) where {T,N} = v[p.perm]
diff --git a/src/autgroups.jl b/src/autgroups.jl
index 696270a..c255b47 100644
--- a/src/autgroups.jl
+++ b/src/autgroups.jl
@@ -4,15 +4,15 @@ function KnuthBendix.Alphabet(S::AbstractVector{<:GSymbol})
     return Alphabet(S, inversions)
 end
 
-struct AutomorphismGroup{G<:Group,T,R,S} <: AbstractFPGroup
+struct AutomorphismGroup{G<:Group,T,RW,S} <: AbstractFPGroup
     group::G
     gens::Vector{T}
-    rws::R
+    rw::RW
     domain::S
 end
 
 object(G::AutomorphismGroup) = G.group
-rewriting(G::AutomorphismGroup) = G.rws
+rewriting(G::AutomorphismGroup) = G.rw
 
 function equality_data(f::AbstractFPGroupElement{<:AutomorphismGroup})
     imf = evaluate(f)
@@ -104,8 +104,8 @@ evaluate(f::AbstractFPGroupElement{<:AutomorphismGroup}) = evaluate!(domain(f),
 function evaluate!(
     t::NTuple{N,T},
     f::AbstractFPGroupElement{<:AutomorphismGroup{<:Group}},
-    tmp = one(first(t)),
-) where {N, T<:FPGroupElement}
+    tmp=one(first(t)),
+) where {N,T<:FPGroupElement}
     A = alphabet(f)
     for idx in word(f)
         t = @inbounds evaluate!(t, A[idx], tmp)::NTuple{N,T}
@@ -113,12 +113,12 @@ function evaluate!(
     return t
 end
 
-evaluate!(t::NTuple{N, T}, s::GSymbol, tmp=nothing) where {N, T} = throw("you need to implement `evaluate!(::$(typeof(t)), ::$(typeof(s)), ::Alphabet, tmp=one(first(t)))`")
+evaluate!(t::NTuple{N,T}, s::GSymbol, tmp=nothing) where {N,T} = throw("you need to implement `evaluate!(::$(typeof(t)), ::$(typeof(s)), ::Alphabet, tmp=one(first(t)))`")
 
 # forward evaluate by substitution
 
-struct LettersMap{T, A}
-    indices_map::Dict{Int, T}
+struct LettersMap{T,A}
+    indices_map::Dict{Int,T}
     A::A
 end
 
@@ -144,11 +144,11 @@ end
 
 function Base.getindex(lm::LettersMap, i::Integer)
     # here i is an index of an alphabet
-    @boundscheck 1 ≤ i ≤ length(KnuthBendix.letters(lm.A))
+    @boundscheck 1 ≤ i ≤ length(lm.A)
 
     if !haskey(lm.indices_map, i)
-        img = if haskey(lm.indices_map, inv(lm.A, i))
-            inv(lm.A, lm.indices_map[inv(lm.A, i)])
+        img = if haskey(lm.indices_map, inv(i, lm.A))
+            inv(lm.indices_map[inv(i, lm.A)], lm.A)
         else
             @warn "LetterMap: neither $i nor its inverse has assigned value"
             one(valtype(lm.indices_map))
@@ -193,7 +193,7 @@ function generated_evaluate(a::FPGroupElement{<:AutomorphismGroup})
                 push!(args[idx].args, :(d[$k]))
                 continue
             end
-            k = findfirst(==(inv(A, l)), first_ltrs)
+            k = findfirst(==(inv(l, A)), first_ltrs)
             if k !== nothing
                 push!(args[idx].args, :(inv(d[$k])))
                 continue
@@ -201,13 +201,14 @@ function generated_evaluate(a::FPGroupElement{<:AutomorphismGroup})
             throw("Letter $l doesn't seem to be mapped anywhere!")
         end
     end
-    locals = Dict{Expr, Symbol}()
+    locals = Dict{Expr,Symbol}()
     locals_counter = 0
-    for (i,v) in enumerate(args)
+    for (i, v) in enumerate(args)
         @assert length(v.args) >= 2
         if length(v.args) > 2
             for (j, a) in pairs(v.args)
-                if a isa Expr &&  a.head == :call "$a"
+                if a isa Expr && a.head == :call
+                    "$a"
                     @assert a.args[1] == :inv
                     if !(a in keys(locals))
                         locals[a] = Symbol("var_#$locals_counter")
@@ -222,7 +223,7 @@ function generated_evaluate(a::FPGroupElement{<:AutomorphismGroup})
     end
 
     q = quote
-        $([:(local $v = $k) for (k,v) in locals]...)
+        $([:(local $v = $k) for (k, v) in locals]...)
     end
 
     # return args, locals
diff --git a/src/constructions/direct_power.jl b/src/constructions/direct_power.jl
index 7ecfd2b..25ffb4f 100644
--- a/src/constructions/direct_power.jl
+++ b/src/constructions/direct_power.jl
@@ -30,7 +30,7 @@ function Base.iterate(G::DirectPower)
     res = iterate(itr)
     @assert res !== nothing
     elt = DirectPowerElement(first(res), G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.iterate(G::DirectPower, state)
@@ -38,7 +38,7 @@ function Base.iterate(G::DirectPower, state)
     res = iterate(itr, st)
     res === nothing && return nothing
     elt = DirectPowerElement(first(res), G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.IteratorSize(::Type{<:DirectPower{Gr,N}}) where {Gr,N}
@@ -52,7 +52,7 @@ Base.size(G::DirectPower) = ntuple(_ -> length(G.group), _nfold(G))
 GroupsCore.order(::Type{I}, G::DirectPower) where {I<:Integer} =
     convert(I, order(I, G.group)^_nfold(G))
 
-GroupsCore.ngens(G::DirectPower) = _nfold(G)*ngens(G.group)
+GroupsCore.ngens(G::DirectPower) = _nfold(G) * ngens(G.group)
 
 function GroupsCore.gens(G::DirectPower, i::Integer)
     k = ngens(G.group)
@@ -66,7 +66,7 @@ end
 function GroupsCore.gens(G::DirectPower)
     N = _nfold(G)
     S = gens(G.group)
-    tups = [ntuple(j->(i == j ? s : one(s)), N) for i in 1:N for s in S]
+    tups = [ntuple(j -> (i == j ? s : one(s)), N) for i in 1:N for s in S]
 
     return [DirectPowerElement(elts, G) for elts in tups]
 end
@@ -99,7 +99,7 @@ function Base.:(*)(g::DirectPowerElement, h::DirectPowerElement)
 end
 
 GroupsCore.order(::Type{I}, g::DirectPowerElement) where {I<:Integer} =
-    convert(I, reduce(lcm, (order(I, h) for h in g.elts), init = one(I)))
+    convert(I, reduce(lcm, (order(I, h) for h in g.elts), init=one(I)))
 
 Base.isone(g::DirectPowerElement) = all(isone, g.elts)
 
diff --git a/src/constructions/direct_product.jl b/src/constructions/direct_product.jl
index 2f6db67..0ea6dfe 100644
--- a/src/constructions/direct_product.jl
+++ b/src/constructions/direct_product.jl
@@ -25,7 +25,7 @@ function Base.iterate(G::DirectProduct)
     res = iterate(itr)
     @assert res !== nothing
     elt = DirectProductElement(first(res), G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.iterate(G::DirectProduct, state)
@@ -33,7 +33,7 @@ function Base.iterate(G::DirectProduct, state)
     res = iterate(itr, st)
     res === nothing && return nothing
     elt = DirectProductElement(first(res), G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.IteratorSize(::Type{<:DirectProduct{Gt,Ht}}) where {Gt,Ht}
diff --git a/src/constructions/wreath_product.jl b/src/constructions/wreath_product.jl
index 41ad021..aa61198 100644
--- a/src/constructions/wreath_product.jl
+++ b/src/constructions/wreath_product.jl
@@ -52,7 +52,7 @@ function Base.iterate(G::WreathProduct)
     res = iterate(itr)
     @assert res !== nothing
     elt = WreathProductElement(first(res)..., G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.iterate(G::WreathProduct, state)
@@ -60,7 +60,7 @@ function Base.iterate(G::WreathProduct, state)
     res = iterate(itr, st)
     res === nothing && return nothing
     elt = WreathProductElement(first(res)..., G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.IteratorSize(::Type{<:WreathProduct{DP,PGr}}) where {DP,PGr}
diff --git a/src/homomorphisms.jl b/src/homomorphisms.jl
index f241ba0..d045d47 100644
--- a/src/homomorphisms.jl
+++ b/src/homomorphisms.jl
@@ -58,8 +58,8 @@ true
 ```
 
 """
-struct Homomorphism{Gr1, Gr2, I, W}
-    gens_images::Dict{I, W}
+struct Homomorphism{Gr1,Gr2,I,W}
+    gens_images::Dict{I,W}
     source::Gr1
     target::Gr2
 
@@ -70,11 +70,11 @@ struct Homomorphism{Gr1, Gr2, I, W}
         check=true
     )
         A = alphabet(source)
-        dct = Dict(i=>convert(word_type(target), f(i, source, target))
-            for i in 1:length(A))
+        dct = Dict(i => convert(word_type(target), f(i, source, target))
+                   for i in 1:length(A))
         I = eltype(word_type(source))
         W = word_type(target)
-        hom = new{typeof(source), typeof(target), I, W}(dct, source, target)
+        hom = new{typeof(source),typeof(target),I,W}(dct, source, target)
 
         if check
             @assert hom(one(source)) == one(target)
@@ -83,12 +83,12 @@ struct Homomorphism{Gr1, Gr2, I, W}
                 @assert hom(x^-1) == hom(x)^-1
 
                 for y in gens(source)
-                    @assert hom(x*y) == hom(x)*hom(y)
-                    @assert hom(x*y)^-1 == hom(y^-1)*hom(x^-1)
+                    @assert hom(x * y) == hom(x) * hom(y)
+                    @assert hom(x * y)^-1 == hom(y^-1) * hom(x^-1)
                 end
             end
             for (lhs, rhs) in relations(source)
-                relator = lhs*inv(alphabet(source), rhs)
+                relator = lhs * inv(rhs, alphabet(source))
                 im_r = hom.target(hom(relator))
                 @assert isone(im_r) "Map does not define a homomorphism: h($relator) = $(im_r) ≠ $(one(target))."
             end
diff --git a/src/iteration.jl b/src/iteration.jl
index 04ce088..210289b 100644
--- a/src/iteration.jl
+++ b/src/iteration.jl
@@ -1,4 +1,4 @@
-mutable struct FPGroupIter{S, T, GEl}
+mutable struct FPGroupIter{S,T,GEl}
     seen::S
     seen_iter_state::T
     current::GEl
diff --git a/src/matrix_groups/SLn.jl b/src/matrix_groups/SLn.jl
index c4a1f04..5a783fa 100644
--- a/src/matrix_groups/SLn.jl
+++ b/src/matrix_groups/SLn.jl
@@ -1,12 +1,12 @@
 include("eltary_matrices.jl")
 
-struct SpecialLinearGroup{N, T, R, A, S} <: MatrixGroup{N,T}
+struct SpecialLinearGroup{N,T,R,A,S} <: MatrixGroup{N,T}
     base_ring::R
     alphabet::A
     gens::S
 
-    function SpecialLinearGroup{N}(base_ring) where N
-        S = [ElementaryMatrix{N}(i,j, one(base_ring)) for i in 1:N for j in 1:N if i≠j]
+    function SpecialLinearGroup{N}(base_ring) where {N}
+        S = [ElementaryMatrix{N}(i, j, one(base_ring)) for i in 1:N for j in 1:N if i ≠ j]
         alphabet = Alphabet(S)
 
         return new{
@@ -19,16 +19,16 @@ struct SpecialLinearGroup{N, T, R, A, S} <: MatrixGroup{N,T}
     end
 end
 
-GroupsCore.ngens(SL::SpecialLinearGroup{N}) where N = N^2 - N
+GroupsCore.ngens(SL::SpecialLinearGroup{N}) where {N} = N^2 - N
 
-Base.show(io::IO, SL::SpecialLinearGroup{N, T}) where {N, T} =
+Base.show(io::IO, SL::SpecialLinearGroup{N,T}) where {N,T} =
     print(io, "special linear group of $N×$N matrices over $T")
 
 function Base.show(
     io::IO,
     ::MIME"text/plain",
     sl::Groups.AbstractFPGroupElement{<:SpecialLinearGroup{N}}
-) where N
+) where {N}
 
     Groups.normalform!(sl)
 
diff --git a/src/matrix_groups/Spn.jl b/src/matrix_groups/Spn.jl
index 4287773..6d98bae 100644
--- a/src/matrix_groups/Spn.jl
+++ b/src/matrix_groups/Spn.jl
@@ -1,11 +1,11 @@
 include("eltary_symplectic.jl")
 
-struct SymplecticGroup{N, T, R, A, S} <: MatrixGroup{N,T}
+struct SymplecticGroup{N,T,R,A,S} <: MatrixGroup{N,T}
     base_ring::R
     alphabet::A
     gens::S
 
-    function SymplecticGroup{N}(base_ring) where N
+    function SymplecticGroup{N}(base_ring) where {N}
         S = symplectic_gens(N, eltype(base_ring))
         alphabet = Alphabet(S)
 
@@ -21,7 +21,7 @@ end
 
 GroupsCore.ngens(Sp::SymplecticGroup) = length(Sp.gens)
 
-Base.show(io::IO, ::SymplecticGroup{N}) where N = print(io, "group of $N×$N symplectic matrices")
+Base.show(io::IO, ::SymplecticGroup{N}) where {N} = print(io, "group of $N×$N symplectic matrices")
 
 function Base.show(
     io::IO,
@@ -35,15 +35,15 @@ function Base.show(
     Base.print_array(io, matrix_repr(sp))
 end
 
-_offdiag_idcs(n) = ((i,j) for i in 1:n for j in 1:n if i ≠ j)
+_offdiag_idcs(n) = ((i, j) for i in 1:n for j in 1:n if i ≠ j)
 
 function symplectic_gens(N, T=Int8)
     iseven(N) || throw(ArgumentError("N needs to be even!"))
-    n = N÷2
+    n = N ÷ 2
 
-    a_ijs = [ElementarySymplectic{N}(:A, i,j, one(T)) for (i,j) in _offdiag_idcs(n)]
-    b_is =  [ElementarySymplectic{N}(:B, n+i,i, one(T)) for i in 1:n]
-    c_ijs = [ElementarySymplectic{N}(:B, n+i,j, one(T)) for (i,j) in _offdiag_idcs(n)]
+    a_ijs = [ElementarySymplectic{N}(:A, i, j, one(T)) for (i, j) in _offdiag_idcs(n)]
+    b_is = [ElementarySymplectic{N}(:B, n + i, i, one(T)) for i in 1:n]
+    c_ijs = [ElementarySymplectic{N}(:B, n + i, j, one(T)) for (i, j) in _offdiag_idcs(n)]
 
     S = [a_ijs; b_is; c_ijs]
 
@@ -53,18 +53,18 @@ function symplectic_gens(N, T=Int8)
 end
 
 function _std_symplectic_form(m::AbstractMatrix)
-    r,c = size(m)
+    r, c = size(m)
     r == c || return false
     iseven(r) || return false
 
-    n = r÷2
+    n = r ÷ 2
     𝕆 = zeros(eltype(m), n, n)
-    𝕀 = one(eltype(m))*LinearAlgebra.I
+    𝕀 = one(eltype(m)) * LinearAlgebra.I
     Ω = [𝕆 -𝕀
-         𝕀  𝕆]
+        𝕀 𝕆]
     return Ω
 end
 
-function issymplectic(mat::M, Ω = _std_symplectic_form(mat)) where M <: AbstractMatrix
+function issymplectic(mat::M, Ω=_std_symplectic_form(mat)) where {M<:AbstractMatrix}
     return Ω == transpose(mat) * Ω * mat
 end
diff --git a/src/matrix_groups/abstract.jl b/src/matrix_groups/abstract.jl
index 1a4cf1f..1da2228 100644
--- a/src/matrix_groups/abstract.jl
+++ b/src/matrix_groups/abstract.jl
@@ -1,17 +1,17 @@
-abstract type MatrixGroup{N, T} <: Groups.AbstractFPGroup end
-const MatrixGroupElement{N, T} = Groups.AbstractFPGroupElement{<:MatrixGroup{N, T}}
+abstract type MatrixGroup{N,T} <: Groups.AbstractFPGroup end
+const MatrixGroupElement{N,T} = Groups.AbstractFPGroupElement{<:MatrixGroup{N,T}}
 
-Base.isone(g::MatrixGroupElement{N, T}) where {N, T} =
+Base.isone(g::MatrixGroupElement{N,T}) where {N,T} =
     isone(word(g)) || matrix_repr(g) == LinearAlgebra.I
 
-function Base.:(==)(m1::M1, m2::M2) where {M1<:MatrixGroupElement, M2<:MatrixGroupElement}
+function Base.:(==)(m1::M1, m2::M2) where {M1<:MatrixGroupElement,M2<:MatrixGroupElement}
     parent(m1) === parent(m2) || return false
     word(m1) == word(m2) && return true
     return matrix_repr(m1) == matrix_repr(m2)
 end
 
-Base.size(m::MatrixGroupElement{N}) where N = (N, N)
-Base.eltype(m::MatrixGroupElement{N, T}) where {N, T} = T
+Base.size(m::MatrixGroupElement{N}) where {N} = (N, N)
+Base.eltype(m::MatrixGroupElement{N,T}) where {N,T} = T
 
 # three structural assumptions about matrix groups
 Groups.word(sl::MatrixGroupElement) = sl.word
@@ -22,9 +22,9 @@ Groups.rewriting(M::MatrixGroup) = alphabet(M)
 Base.hash(sl::MatrixGroupElement, h::UInt) =
     hash(matrix_repr(sl), hash(parent(sl), h))
 
-function matrix_repr(m::MatrixGroupElement{N, T}) where {N, T}
+function matrix_repr(m::MatrixGroupElement{N,T}) where {N,T}
     if isone(word(m))
-        return StaticArrays.SMatrix{N, N, T}(LinearAlgebra.I)
+        return StaticArrays.SMatrix{N,N,T}(LinearAlgebra.I)
     end
     A = alphabet(parent(m))
     return prod(matrix_repr(A[l]) for l in word(m))
@@ -33,7 +33,7 @@ end
 function Base.rand(
     rng::Random.AbstractRNG,
     rs::Random.SamplerTrivial{<:MatrixGroup},
-    )
+)
     Mgroup = rs[]
     S = gens(Mgroup)
     return prod(g -> rand(Bool) ? g : inv(g), rand(S, rand(1:30)))
diff --git a/src/matrix_groups/eltary_matrices.jl b/src/matrix_groups/eltary_matrices.jl
index 947faca..6e3ed48 100644
--- a/src/matrix_groups/eltary_matrices.jl
+++ b/src/matrix_groups/eltary_matrices.jl
@@ -1,9 +1,9 @@
-struct ElementaryMatrix{N, T} <: Groups.GSymbol
+struct ElementaryMatrix{N,T} <: Groups.GSymbol
     i::Int
     j::Int
     val::T
-    ElementaryMatrix{N}(i, j, val=1) where N =
-        (@assert i≠j; new{N, typeof(val)}(i, j, val))
+    ElementaryMatrix{N}(i, j, val=1) where {N} =
+        (@assert i ≠ j; new{N,typeof(val)}(i, j, val))
 end
 
 function Base.show(io::IO, e::ElementaryMatrix)
@@ -11,18 +11,18 @@ function Base.show(io::IO, e::ElementaryMatrix)
     !isone(e.val) && print(io, "^$(e.val)")
 end
 
-Base.:(==)(e::ElementaryMatrix{N}, f::ElementaryMatrix{N}) where N =
+Base.:(==)(e::ElementaryMatrix{N}, f::ElementaryMatrix{N}) where {N} =
     e.i == f.i && e.j == f.j && e.val == f.val
 
 Base.hash(e::ElementaryMatrix, h::UInt) =
     hash(typeof(e), hash((e.i, e.j, e.val), h))
 
-Base.inv(e::ElementaryMatrix{N}) where N =
+Base.inv(e::ElementaryMatrix{N}) where {N} =
     ElementaryMatrix{N}(e.i, e.j, -e.val)
 
-function matrix_repr(e::ElementaryMatrix{N, T}) where {N, T}
-    m = StaticArrays.MMatrix{N, N, T}(LinearAlgebra.I)
+function matrix_repr(e::ElementaryMatrix{N,T}) where {N,T}
+    m = StaticArrays.MMatrix{N,N,T}(LinearAlgebra.I)
     m[e.i, e.j] = e.val
-    x = StaticArrays.SMatrix{N, N}(m)
+    x = StaticArrays.SMatrix{N,N}(m)
     return x
 end
diff --git a/src/matrix_groups/eltary_symplectic.jl b/src/matrix_groups/eltary_symplectic.jl
index c1d3d68..0640e6b 100644
--- a/src/matrix_groups/eltary_symplectic.jl
+++ b/src/matrix_groups/eltary_symplectic.jl
@@ -1,18 +1,18 @@
-struct ElementarySymplectic{N, T} <: Groups.GSymbol
+struct ElementarySymplectic{N,T} <: Groups.GSymbol
     symbol::Symbol
     i::Int
     j::Int
     val::T
-    function ElementarySymplectic{N}(s::Symbol, i::Integer, j::Integer, val=1) where N
+    function ElementarySymplectic{N}(s::Symbol, i::Integer, j::Integer, val=1) where {N}
         @assert s ∈ (:A, :B)
         @assert iseven(N)
-        n = N÷2
+        n = N ÷ 2
         if s === :A
             @assert 1 ≤ i ≤ n && 1 ≤ j ≤ n && i ≠ j
         elseif s === :B
             @assert xor(1 ≤ i ≤ n, 1 ≤ j ≤ n) && xor(n < i ≤ N, n < j ≤ N)
         end
-        return new{N, typeof(val)}(s, i, j, val)
+        return new{N,typeof(val)}(s, i, j, val)
     end
 end
 
@@ -22,12 +22,12 @@ function Base.show(io::IO, s::ElementarySymplectic)
     !isone(s.val) && print(io, "^$(s.val)")
 end
 
-_ind(s::ElementarySymplectic{N}) where N = (s.i, s.j)
-_local_ind(N_half::Integer, i::Integer) = ifelse(i<=N_half, i, i-N_half)
-function _dual_ind(s::ElementarySymplectic{N}) where N
+_ind(s::ElementarySymplectic{N}) where {N} = (s.i, s.j)
+_local_ind(N_half::Integer, i::Integer) = ifelse(i <= N_half, i, i - N_half)
+function _dual_ind(s::ElementarySymplectic{N}) where {N}
     if s.symbol === :A && return _ind(s)
     else#if s.symbol === :B
-        return _dual_ind(N÷2, s.i, s.j)
+        return _dual_ind(N ÷ 2, s.i, s.j)
     end
 end
 
@@ -41,7 +41,7 @@ function _dual_ind(N_half, i, j)
     return i, j
 end
 
-function Base.:(==)(s::ElementarySymplectic{N}, t::ElementarySymplectic{M}) where {N, M}
+function Base.:(==)(s::ElementarySymplectic{N}, t::ElementarySymplectic{M}) where {N,M}
     N == M || return false
     s.symbol == t.symbol || return false
     s.val == t.val || return false
@@ -51,18 +51,18 @@ end
 Base.hash(s::ElementarySymplectic, h::UInt) =
     hash(Set([_ind(s); _dual_ind(s)]), hash(s.symbol, hash(s.val, h)))
 
-LinearAlgebra.transpose(s::ElementarySymplectic{N}) where N =
+LinearAlgebra.transpose(s::ElementarySymplectic{N}) where {N} =
     ElementarySymplectic{N}(s.symbol, s.j, s.i, s.val)
 
-Base.inv(s::ElementarySymplectic{N}) where N =
+Base.inv(s::ElementarySymplectic{N}) where {N} =
     ElementarySymplectic{N}(s.symbol, s.i, s.j, -s.val)
 
-function matrix_repr(s::ElementarySymplectic{N, T}) where {N, T}
+function matrix_repr(s::ElementarySymplectic{N,T}) where {N,T}
     @assert iseven(N)
     n = div(N, 2)
-    m = StaticArrays.MMatrix{N, N, T}(LinearAlgebra.I)
-    i,j = _ind(s)
-    m[i,j] = s.val
+    m = StaticArrays.MMatrix{N,N,T}(LinearAlgebra.I)
+    i, j = _ind(s)
+    m[i, j] = s.val
     if s.symbol === :A
         m[n+j, n+i] = -s.val
     else#if s.symbol === :B
@@ -72,5 +72,5 @@ function matrix_repr(s::ElementarySymplectic{N, T}) where {N, T}
             m[j-n, i+n] = s.val
         end
     end
-    return StaticArrays.SMatrix{N, N}(m)
+    return StaticArrays.SMatrix{N,N}(m)
 end
diff --git a/src/normalform.jl b/src/normalform.jl
index 0b799e3..7b7742c 100644
--- a/src/normalform.jl
+++ b/src/normalform.jl
@@ -42,5 +42,5 @@ Defaults to the rewriting in the free group.
 """
 @inline function normalform!(res::AbstractWord, g::AbstractFPGroupElement)
     isone(res) && isnormalform(g) && return append!(res, word(g))
-    return KnuthBendix.rewrite_from_left!(res, word(g), rewriting(parent(g)))
+    return KnuthBendix.rewrite!(res, word(g), rewriting(parent(g)))
 end
diff --git a/src/types.jl b/src/types.jl
index a96e5dc..bbe332f 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -3,15 +3,18 @@
 """
     AbstractFPGroup
 
-An Abstract type representing finitely presented groups. Every instance `` must implement
+An Abstract type representing finitely presented groups. Every instance must implement
  * `KnuthBendix.alphabet(G::MyFPGroup)`
  * `rewriting(G::MyFPGroup)` : return the rewriting object which must implement
- > `KnuthBendix.rewrite_from_left!(u, v, rewriting(G))`.
-By default `alphabet(G)` is returned, which amounts to free rewriting in `G`.
+ > `KnuthBendix.rewrite!(u, v, rewriting(G))`.
+ E.g. for `G::FreeGroup` `alphabet(G)` is returned, which amounts to free rewriting.
+ * `ordering(G::MyFPGroup)[ = KnuthBendix.ordering(rewriting(G))]` : return the
+ (implicit) ordering for the alphabet of `G`.
  * `relations(G::MyFPGroup)` : return a set of defining relations.
 
-AbstractFPGroup may also override `word_type(::Type{MyFPGroup}) = Word{UInt16}`,
-which controls the word type used for group elements. If a group has more than `255` generators you need to define e.g.
+AbstractFPGroup may also override `word_type(::Type{MyFPGroup}) = Word{UInt8}`,
+which controls the word type used for group elements.
+If a group has more than `255` generators you need to define e.g.
 > `word_type(::Type{MyFPGroup}) = Word{UInt16}`
 """
 abstract type AbstractFPGroup <: GroupsCore.Group end
@@ -22,22 +25,25 @@ word_type(::Type{<:AbstractFPGroup}) = Word{UInt8}
 
 """
     rewriting(G::AbstractFPGroup)
-Return a "rewriting object" for elements of `G`. The rewriting object must must implement
-    KnuthBendix.rewrite_from_left!(
-        u::AbstractWord,
-        v::AbstractWord,
-        rewriting(G)
-    )
+Return a "rewriting object" for elements of `G`.
 
-For example if `G` is a `FreeGroup` then `alphabet(G)` is returned which results in free rewriting. For `FPGroup` a rewriting system is returned which may (or may not) rewrite word `v` to its normal form.
+The rewriting object must must implement
+    KnuthBendix.rewrite!(u::AbstractWord, v::AbstractWord, rewriting(G))
+
+For example if `G` is a `FreeGroup` then `alphabet(G)` is returned which results
+in free rewriting. For `FPGroup` a rewriting system is returned which may
+(or may not) rewrite word `v` to its normal form (depending on e.g. its confluence).
 """
 function rewriting end
 
+KnuthBendix.ordering(G::AbstractFPGroup) = ordering(rewriting(G))
+KnuthBendix.alphabet(G::AbstractFPGroup) = alphabet(ordering(G))
+
 Base.@propagate_inbounds function (G::AbstractFPGroup)(
     word::AbstractVector{<:Integer},
 )
     @boundscheck @assert all(
-        l -> 1 <= l <= length(KnuthBendix.alphabet(G)),
+        l -> 1 <= l <= length(alphabet(G)),
         word,
     )
     return FPGroupElement(word_type(G)(word), G)
@@ -90,7 +96,7 @@ mutable struct FPGroupElement{Gr<:AbstractFPGroup,W<:AbstractWord} <:
     FPGroupElement(
         word::W,
         G::AbstractFPGroup,
-        hash::UInt = UInt(0),
+        hash::UInt=UInt(0),
     ) where {W<:AbstractWord} = new{typeof(G),W}(word, hash, G)
 
     FPGroupElement{Gr,W}(word::AbstractWord, G::Gr) where {Gr,W} =
@@ -128,7 +134,7 @@ end
 
 function Base.inv(g::GEl) where {GEl<:AbstractFPGroupElement}
     G = parent(g)
-    return GEl(inv(alphabet(G), word(g)), G)
+    return GEl(inv(word(g), alphabet(G)), G)
 end
 
 function Base.:(*)(g::GEl, h::GEl) where {GEl<:AbstractFPGroupElement}
@@ -153,8 +159,7 @@ struct FreeGroup{T,O} <: AbstractFPGroup
 
     function FreeGroup(gens, ordering::KnuthBendix.WordOrdering)
         @assert length(gens) == length(unique(gens))
-        L = KnuthBendix.letters(alphabet(ordering))
-        @assert all(l -> l in L, gens)
+        @assert all(l -> l in alphabet(ordering), gens)
         return new{eltype(gens),typeof(ordering)}(gens, ordering)
     end
 end
@@ -163,15 +168,14 @@ FreeGroup(gens, A::Alphabet) = FreeGroup(gens, KnuthBendix.LenLex(A))
 
 function FreeGroup(A::Alphabet)
     @boundscheck @assert all(
-        KnuthBendix.hasinverse(l, A) for l in KnuthBendix.letters(A)
+        KnuthBendix.hasinverse(l, A) for l in A
     )
-    ltrs = KnuthBendix.letters(A)
-    gens = Vector{eltype(ltrs)}()
-    invs = Vector{eltype(ltrs)}()
-    for l in ltrs
+    gens = Vector{eltype(A)}()
+    invs = Vector{eltype(A)}()
+    for l in A
         l ∈ invs && continue
         push!(gens, l)
-        push!(invs, inv(A, l))
+        push!(invs, inv(l, A))
     end
 
     return FreeGroup(gens, A)
@@ -193,10 +197,9 @@ Base.show(io::IO, F::FreeGroup) =
     print(io, "free group on $(ngens(F)) generators")
 
 # mandatory methods:
-relations(F::FreeGroup) = Pair{eltype(F)}[]
 KnuthBendix.ordering(F::FreeGroup) = F.ordering
-KnuthBendix.alphabet(F::FreeGroup) = alphabet(KnuthBendix.ordering(F))
-rewriting(F::FreeGroup) = alphabet(F)
+rewriting(F::FreeGroup) = alphabet(F) # alphabet(F) = alphabet(ordering(F))
+relations(F::FreeGroup) = Pair{eltype(F),eltype(F)}[]
 
 # GroupsCore interface:
 # these are mathematically correct
@@ -207,22 +210,20 @@ GroupsCore.isfiniteorder(g::AbstractFPGroupElement{<:FreeGroup}) =
 
 ## FP Groups
 
-struct FPGroup{T,R,S} <: AbstractFPGroup
+struct FPGroup{T,RW,S} <: AbstractFPGroup
     gens::Vector{T}
     relations::Vector{Pair{S,S}}
-    rws::R
+    rw::RW
 end
 
 relations(G::FPGroup) = G.relations
-rewriting(G::FPGroup) = G.rws
-KnuthBendix.ordering(G::FPGroup) = KnuthBendix.ordering(rewriting(G))
-KnuthBendix.alphabet(G::FPGroup) = alphabet(KnuthBendix.ordering(G))
+rewriting(G::FPGroup) = G.rw
 
 function FPGroup(
     G::AbstractFPGroup,
     rels::AbstractVector{<:Pair{GEl,GEl}};
-    ordering = KnuthBendix.ordering(G),
-    kwargs...,
+    ordering=KnuthBendix.ordering(G),
+    kwargs...
 ) where {GEl<:FPGroupElement}
     for (lhs, rhs) in rels
         @assert parent(lhs) === parent(rhs) === G
@@ -230,9 +231,9 @@ function FPGroup(
     word_rels = [word(lhs) => word(rhs) for (lhs, rhs) in [relations(G); rels]]
     rws = KnuthBendix.RewritingSystem(word_rels, ordering)
 
-    KnuthBendix.knuthbendix!(rws; kwargs...)
+    rws = KnuthBendix.knuthbendix(rws, KnuthBendix.Settings(; kwargs...))
 
-    return FPGroup(G.gens, rels, rws)
+    return FPGroup(G.gens, rels, KnuthBendix.IndexAutomaton(rws))
 end
 
 function Base.show(io::IO, ::MIME"text/plain", G::FPGroup)
diff --git a/src/wl_ball.jl b/src/wl_ball.jl
index 69fce79..18645cb 100644
--- a/src/wl_ball.jl
+++ b/src/wl_ball.jl
@@ -1,20 +1,31 @@
 """
     wlmetric_ball(S::AbstractVector{<:GroupElem}
-        [, center=one(first(S)); radius=2, op=*])
+        [, center=one(first(S)); radius=2, op=*, threading=true])
 Compute metric ball as a list of elements of non-decreasing length, given the
 word-length metric on the group generated by `S`. The ball is centered at `center`
 (by default: the identity element). `radius` and `op` keywords specify the
 radius and multiplication operation to be used.
 """
-function wlmetric_ball_serial(S::AbstractVector{T}, center::T=one(first(S)); radius = 2, op = *) where {T}
+function wlmetric_ball(
+    S::AbstractVector{T},
+    center::T=one(first(S));
+    radius=2,
+    op=*,
+    threading=true
+) where {T}
+    threading && return wlmetric_ball_thr(S, center, radius=radius, op=op)
+    return wlmetric_ball_serial(S, center, radius=radius, op=op)
+end
+
+function wlmetric_ball_serial(S::AbstractVector{T}, center::T=one(first(S)); radius=2, op=*) where {T}
     @assert radius >= 1
-    old = union!([center], [center*s for s in S])
+    old = union!([center], [center * s for s in S])
     return _wlmetric_ball(S, old, radius, op, collect, unique!)
 end
 
-function wlmetric_ball_thr(S::AbstractVector{T}, center::T=one(first(S)); radius = 2, op = *) where {T}
+function wlmetric_ball_thr(S::AbstractVector{T}, center::T=one(first(S)); radius=2, op=*) where {T}
     @assert radius >= 1
-    old = union!([center], [center*s for s in S])
+    old = union!([center], [center * s for s in S])
     return _wlmetric_ball(S, old, radius, op, Folds.collect, Folds.unique)
 end
 
@@ -26,6 +37,7 @@ function _wlmetric_ball(S, old, radius, op, collect, unique)
                 (g = op(o, s); hash(g); g)
                 for o in @view(old[sizes[end-1]:end]) for s in S
             )
+
             append!(old, new)
             unique(old)
         end
@@ -34,13 +46,3 @@ function _wlmetric_ball(S, old, radius, op, collect, unique)
     return old, sizes[2:end]
 end
 
-function wlmetric_ball(
-    S::AbstractVector{T},
-    center::T = one(first(S));
-    radius = 2,
-    op = *,
-    threading = true,
-) where {T}
-    threading && return wlmetric_ball_thr(S, center, radius = radius, op = op)
-    return wlmetric_ball_serial(S, center, radius = radius, op = op)
-end
diff --git a/test/AutFn.jl b/test/AutFn.jl
index 8c566ea..c3f035b 100644
--- a/test/AutFn.jl
+++ b/test/AutFn.jl
@@ -29,57 +29,57 @@
     end
 
     A4 = Alphabet(
-    [:a,:A,:b,:B,:c,:C,:d,:D],
-    [ 2, 1, 4, 3, 6, 5, 8, 7]
+        [:a, :A, :b, :B, :c, :C, :d, :D],
+        [2, 1, 4, 3, 6, 5, 8, 7]
     )
 
     A5 = Alphabet(
-    [:a,:A,:b,:B,:c,:C,:d,:D,:e,:E],
-    [ 2, 1, 4, 3, 6, 5, 8, 7,10, 9]
+        [:a, :A, :b, :B, :c, :C, :d, :D, :e, :E],
+        [2, 1, 4, 3, 6, 5, 8, 7, 10, 9]
     )
 
     F4 = FreeGroup([:a, :b, :c, :d], A4)
-    a,b,c,d = gens(F4)
-    D = ntuple(i->gens(F4, i), 4)
+    a, b, c, d = gens(F4)
+    D = ntuple(i -> gens(F4, i), 4)
 
     @testset "Transvection action correctness" begin
-        i,j = 1,2
-        r = Groups.Transvection(:ϱ,i,j)
-        l = Groups.Transvection(:λ,i,j)
+        i, j = 1, 2
+        r = Groups.Transvection(:ϱ, i, j)
+        l = Groups.Transvection(:λ, i, j)
 
         (t::Groups.Transvection)(v::Tuple) = Groups.evaluate!(v, t)
 
-        @test      r(deepcopy(D)) == (a*b,   b, c, d)
-        @test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d)
-        @test      l(deepcopy(D)) == (b*a,   b, c, d)
-        @test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d)
+        @test r(deepcopy(D)) == (a * b, b, c, d)
+        @test inv(r)(deepcopy(D)) == (a * b^-1, b, c, d)
+        @test l(deepcopy(D)) == (b * a, b, c, d)
+        @test inv(l)(deepcopy(D)) == (b^-1 * a, b, c, d)
 
-        i,j = 3,1
-        r = Groups.Transvection(:ϱ,i,j)
-        l = Groups.Transvection(:λ,i,j)
-        @test      r(deepcopy(D)) == (a, b, c*a,   d)
-        @test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d)
-        @test      l(deepcopy(D)) == (a, b, a*c,   d)
-        @test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d)
+        i, j = 3, 1
+        r = Groups.Transvection(:ϱ, i, j)
+        l = Groups.Transvection(:λ, i, j)
+        @test r(deepcopy(D)) == (a, b, c * a, d)
+        @test inv(r)(deepcopy(D)) == (a, b, c * a^-1, d)
+        @test l(deepcopy(D)) == (a, b, a * c, d)
+        @test inv(l)(deepcopy(D)) == (a, b, a^-1 * c, d)
 
-        i,j = 4,3
-        r = Groups.Transvection(:ϱ,i,j)
-        l = Groups.Transvection(:λ,i,j)
-        @test      r(deepcopy(D)) == (a, b, c, d*c)
-        @test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1)
-        @test      l(deepcopy(D)) == (a, b, c, c*d)
-        @test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d)
+        i, j = 4, 3
+        r = Groups.Transvection(:ϱ, i, j)
+        l = Groups.Transvection(:λ, i, j)
+        @test r(deepcopy(D)) == (a, b, c, d * c)
+        @test inv(r)(deepcopy(D)) == (a, b, c, d * c^-1)
+        @test l(deepcopy(D)) == (a, b, c, c * d)
+        @test inv(l)(deepcopy(D)) == (a, b, c, c^-1 * d)
 
-        i,j = 2,4
-        r = Groups.Transvection(:ϱ,i,j)
-        l = Groups.Transvection(:λ,i,j)
-        @test      r(deepcopy(D)) == (a, b*d,   c, d)
-        @test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d)
-        @test      l(deepcopy(D)) == (a, d*b,   c, d)
-        @test inv(l)(deepcopy(D)) == (a, d^-1*b,c, d)
+        i, j = 2, 4
+        r = Groups.Transvection(:ϱ, i, j)
+        l = Groups.Transvection(:λ, i, j)
+        @test r(deepcopy(D)) == (a, b * d, c, d)
+        @test inv(r)(deepcopy(D)) == (a, b * d^-1, c, d)
+        @test l(deepcopy(D)) == (a, d * b, c, d)
+        @test inv(l)(deepcopy(D)) == (a, d^-1 * b, c, d)
     end
 
-    A = SpecialAutomorphismGroup(F4, maxrules=1000)
+    A = SpecialAutomorphismGroup(F4, max_rules=1000)
 
     @testset "AutomorphismGroup constructors" begin
         @test A isa Groups.AbstractFPGroup
@@ -91,33 +91,33 @@
 
     @testset "Automorphisms: hash and evaluate" begin
         @test Groups.domain(gens(A, 1)) == D
-        g, h = gens(A, 1), gens(A, 8)
+        g, h = gens(A, 1), gens(A, 8) # (ϱ₁.₂, ϱ₃.₂)
 
-        @test evaluate(g*h) == evaluate(h*g)
-        @test (g*h).savedhash == zero(UInt)
+        @test evaluate(g * h) == evaluate(h * g)
+        @test (g * h).savedhash == zero(UInt)
 
-        @test sprint(show, typeof(g)) == "Automorphism{FreeGroup{Symbol, KnuthBendix.LenLex{Symbol}}, …}"
+        @test contains(sprint(show, typeof(g)), "Automorphism{FreeGroup{Symbol")
 
-        a = g*h
-        b = h*g
+        a = g * h
+        b = h * g
         @test hash(a) != zero(UInt)
         @test hash(a) == hash(b)
         @test a.savedhash == b.savedhash
 
-        @test length(unique([a,b])) == 1
-        @test length(unique([g*h, h*g])) == 1
+        @test length(unique([a, b])) == 1
+        @test length(unique([g * h, h * g])) == 1
 
         # Not so simple arithmetic: applying starting on the left:
         # ϱ₁₂*ϱ₂₁⁻¹*λ₁₂*ε₂ == σ₂₁₃₄
 
         g = gens(A, 1)
         x1, x2, x3, x4 = Groups.domain(g)
-        @test evaluate(g) == (x1*x2, x2, x3, x4)
+        @test evaluate(g) == (x1 * x2, x2, x3, x4)
 
-        g = g*inv(gens(A, 4)) # ϱ₂₁
-        @test evaluate(g) == (x1*x2, x1^-1, x3, x4)
+        g = g * inv(gens(A, 4)) # ϱ₂₁
+        @test evaluate(g) == (x1 * x2, x1^-1, x3, x4)
 
-        g = g*gens(A, 13)
+        g = g * gens(A, 13)
         @test evaluate(g) == (x2, x1^-1, x3, x4)
     end
 
@@ -128,7 +128,7 @@
         S = gens(G)
         @test S isa Vector{<:FPGroupElement{<:AutomorphismGroup{<:FreeGroup}}}
 
-        @test length(S) == 2*N*(N-1)
+        @test length(S) == 2 * N * (N - 1)
         @test length(unique(S)) == length(S)
 
         S_sym = [S; inv.(S)]
@@ -136,12 +136,12 @@
 
         pushfirst!(S_sym, one(G))
 
-        B_2 = [i*j for (i,j) in Base.product(S_sym, S_sym)]
+        B_2 = [i * j for (i, j) in Base.product(S_sym, S_sym)]
         @test length(B_2) == 2401
         @test length(unique(B_2)) == 1777
 
-        @test all(g->isone(inv(g)*g), B_2)
-        @test all(g->isone(g*inv(g)), B_2)
+        @test all(g -> isone(inv(g) * g), B_2)
+        @test all(g -> isone(g * inv(g)), B_2)
     end
 
     @testset "Forward evaluate" begin
@@ -153,7 +153,7 @@
 
         f = gens(F)
 
-        @test a(f[1]) == f[1]*f[2]
+        @test a(f[1]) == f[1] * f[2]
         @test all(a(f[i]) == f[i] for i in 2:length(f))
 
         S = let s = gens(G)
diff --git a/test/AutSigma3.jl b/test/AutSigma3.jl
index 475fb57..8905342 100644
--- a/test/AutSigma3.jl
+++ b/test/AutSigma3.jl
@@ -3,22 +3,24 @@
 
     π₁Σ = Groups.SurfaceGroup(genus, 0)
 
+    @test contains(sprint(print, π₁Σ), "surface")
+
     Groups.PermRightAut(p::Perm) = Groups.PermRightAut(p.d)
     # Groups.PermLeftAut(p::Perm) = Groups.PermLeftAut(p.d)
     autπ₁Σ = let autπ₁Σ = AutomorphismGroup(π₁Σ)
         pauts = let p = perm"(1,3,5)(2,4,6)"
             [Groups.PermRightAut(p^i) for i in 0:2]
         end
-        T = eltype(KnuthBendix.letters(alphabet(autπ₁Σ)))
+        T = eltype(alphabet(autπ₁Σ))
         S = eltype(pauts)
 
-        A = Alphabet(Union{T,S}[KnuthBendix.letters(alphabet(autπ₁Σ)); pauts])
+        A = Alphabet(Union{T,S}[alphabet(autπ₁Σ)...; pauts])
 
         autG = AutomorphismGroup(
             π₁Σ,
             autπ₁Σ.gens,
             A,
-            ntuple(i->inv(gens(π₁Σ, i)), 2Groups.genus(π₁Σ))
+            ntuple(i -> inv(gens(π₁Σ, i)), 2Groups.genus(π₁Σ))
         )
 
         autG
@@ -27,9 +29,7 @@
     Al = alphabet(autπ₁Σ)
     S = [gens(autπ₁Σ); inv.(gens(autπ₁Σ))]
 
-    sautFn = let ltrs = KnuthBendix.letters(Al)
-        parent(first(ltrs).autFn_word)
-    end
+    sautFn = parent(Al[1].autFn_word)
 
     τ = Groups.rotation_element(sautFn)
 
@@ -38,7 +38,7 @@
         λ = Groups.ΡΛ(:λ, A, 2genus)
         ϱ = Groups.ΡΛ(:ϱ, A, 2genus)
         @test sautFn(Groups.Te_diagonal(λ, ϱ, 1)) ==
-            conj(sautFn(Groups.Te_diagonal(λ, ϱ, 2)), τ)
+              conj(sautFn(Groups.Te_diagonal(λ, ϱ, 2)), τ)
 
         @test sautFn(Groups.Te_diagonal(λ, ϱ, 3)) == sautFn(Groups.Te(λ, ϱ, 3, 1))
     end
diff --git a/test/fp_groups.jl b/test/fp_groups.jl
index e06f165..5e98dd5 100644
--- a/test/fp_groups.jl
+++ b/test/fp_groups.jl
@@ -1,5 +1,5 @@
 @testset "FPGroups" begin
-    A = Alphabet([:a, :A, :b, :B, :c, :C], [2,1,4,3,6,5])
+    A = Alphabet([:a, :A, :b, :B, :c, :C], [2, 1, 4, 3, 6, 5])
 
     @test FreeGroup(A) isa FreeGroup
     @test sprint(show, FreeGroup(A)) == "free group on 3 generators"
@@ -7,26 +7,26 @@
     F = FreeGroup([:a, :b, :c], A)
     @test sprint(show, F) == "free group on 3 generators"
 
-    a,b,c = gens(F)
-    @test c*b*a isa FPGroupElement
+    a, b, c = gens(F)
+    @test c * b * a isa FPGroupElement
 
     # quotient of F:
-    G = FPGroup(F, [a*b=>b*a, a*c=>c*a, b*c=>c*b])
+    G = FPGroup(F, [a * b => b * a, a * c => c * a, b * c => c * b])
 
     @test G isa FPGroup
     @test sprint(show, G) == "⟨ a  b  c | \n\t  a*b => b*a  a*c => c*a  b*c => c*b ⟩"
     @test rand(G) isa FPGroupElement
 
-    f = a*c*b
+    f = a * c * b
     @test word(f) isa Word{UInt8}
 
-    aG,bG,cG = gens(G)
+    aG, bG, cG = gens(G)
 
     @test aG isa FPGroupElement
     @test_throws AssertionError aG == a
     @test word(aG) == word(a)
 
-    g = aG*cG*bG
+    g = aG * cG * bG
 
     @test_throws AssertionError f == g
     @test word(f) == word(g)
@@ -34,21 +34,21 @@
     Groups.normalform!(g)
     @test word(g) == [1, 3, 5]
 
-    let g = aG*cG*bG
+    let g = aG * cG * bG
         # test that we normalize g before printing
         @test sprint(show, g) == "a*b*c"
     end
 
     # quotient of G
-    H = FPGroup(G, [aG^2=>cG, bG*cG=>aG], maxrules=200)
+    H = FPGroup(G, [aG^2 => cG, bG * cG => aG], max_rules=200)
 
     h = H(word(g))
 
     @test h isa FPGroupElement
     @test_throws AssertionError h == g
-    @test_throws MethodError h*g
+    @test_throws MethodError h * g
 
-    H′ = FPGroup(G, [aG^2=>cG, bG*cG=>aG], maxrules=200)
+    H′ = FPGroup(G, [aG^2 => cG, bG * cG => aG], max_rules=200)
     @test_throws AssertionError one(H) == one(H′)
 
     Groups.normalform!(h)
diff --git a/test/matrix_groups.jl b/test/matrix_groups.jl
index 316ab8c..ef27c9d 100644
--- a/test/matrix_groups.jl
+++ b/test/matrix_groups.jl
@@ -4,23 +4,25 @@ using Groups.MatrixGroups
     @testset "SL(n, ℤ)" begin
         SL3Z = SpecialLinearGroup{3}(Int8)
 
-        S = gens(SL3Z); union!(S, inv.(S))
+        S = gens(SL3Z)
+        union!(S, inv.(S))
 
-        E, sizes = Groups.wlmetric_ball(S, radius=4)
+        _, sizes = Groups.wlmetric_ball(S, radius=4)
 
         @test sizes == [13, 121, 883, 5455]
 
-        E(i,j) = SL3Z([A[MatrixGroups.ElementaryMatrix{3}(i,j, Int8(1))]])
+        E(i, j) = SL3Z([A[MatrixGroups.ElementaryMatrix{3}(i, j, Int8(1))]])
 
         A = alphabet(SL3Z)
-        w = E(1,2)
-        r = E(2,3)^-3
-        s = E(1,3)^2*E(3,2)^-1
+        w = E(1, 2)
+        r = E(2, 3)^-3
+        s = E(1, 3)^2 * E(3, 2)^-1
 
-        S = [w,r,s]; S = unique([S; inv.(S)]);
-        _, sizes = Groups.wlmetric_ball(S, radius=4);
+        S = [w, r, s]
+        S = unique([S; inv.(S)])
+        _, sizes = Groups.wlmetric_ball(S, radius=4)
         @test sizes == [7, 33, 141, 561]
-        _, sizes = Groups.wlmetric_ball_serial(S, radius=4);
+        _, sizes = Groups.wlmetric_ball_serial(S, radius=4)
         @test sizes == [7, 33, 141, 561]
 
         Logging.with_logger(Logging.NullLogger()) do
@@ -34,10 +36,10 @@ using Groups.MatrixGroups
         end
 
 
-        x = w*inv(w)*r
+        x = w * inv(w) * r
 
         @test length(word(x)) == 5
-        @test size(x) == (3,3)
+        @test size(x) == (3, 3)
         @test eltype(x) == Int8
 
         @test contains(sprint(print, SL3Z), "special linear group of 3×3")
@@ -50,12 +52,14 @@ using Groups.MatrixGroups
     @testset "Sp(6, ℤ)" begin
         Sp6 = MatrixGroups.SymplecticGroup{6}(Int8)
 
-        @testset "GroupsCore conformance" begin
-            test_Group_interface(Sp6)
-            g = Sp6(rand(1:length(alphabet(Sp6)), 10))
-            h = Sp6(rand(1:length(alphabet(Sp6)), 10))
+        Logging.with_logger(Logging.NullLogger()) do
+            @testset "GroupsCore conformance" begin
+                test_Group_interface(Sp6)
+                g = Sp6(rand(1:length(alphabet(Sp6)), 10))
+                h = Sp6(rand(1:length(alphabet(Sp6)), 10))
 
-            test_GroupElement_interface(g, h)
+                test_GroupElement_interface(g, h)
+            end
         end
 
         @test contains(sprint(print, Sp6), "group of 6×6 symplectic matrices")
@@ -64,7 +68,7 @@ using Groups.MatrixGroups
         x *= inv(x) * gens(Sp6, 2)
 
         @test length(word(x)) == 3
-        @test size(x) == (6,6)
+        @test size(x) == (6, 6)
         @test eltype(x) == Int8
 
         @test contains(sprint(show, MIME"text/plain"(), x), "6×6 symplectic matrix:")
diff --git a/test/runtests.jl b/test/runtests.jl
index 061fac8..afe48a4 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -24,7 +24,7 @@ include(joinpath(pathof(GroupsCore), "..", "..", "test", "conformance_test.jl"))
     _, t = @timed include("homomorphisms.jl")
     @info "homomorphisms.jl took $(round(t, digits=2))s"
 
-    if haskey(ENV, "CI")
+    if !haskey(ENV, "CI")
         _, t = @timed include("AutSigma_41.jl")
         @info "AutSigma_41 took $(round(t, digits=2))s"
         _, t = @timed include("AutSigma3.jl")
@@ -36,5 +36,5 @@ include(joinpath(pathof(GroupsCore), "..", "..", "test", "conformance_test.jl"))
 end
 
 if !haskey(ENV, "CI")
-   include("benchmarks.jl")
+    include("benchmarks.jl")
 end