#241 ⟨a, b | aa=a, abb=a⟩

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Properties

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. a2 ⇒ a
  2. ab2 ⇒ a 
# ab:aa=a,abb=a ab
aa=a
abb=a

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

23 total

Σ#PresentationMapping
8886⟨a, b | aa=a, aabb=a⟩φ(a) = a, φ(b) = b
8962⟨a, b | aa=a, abb=aa⟩φ(a) = a, φ(b) = b
91624⟨a, b | aab=ab, abb=a⟩φ(a) = a, φ(b) = b
92862⟨a, b | aa=a, aaabb=a⟩φ(a) = a, φ(b) = b
93011⟨a, b | aa=a, aabb=aa⟩φ(a) = a, φ(b) = b
93139⟨a, b | aa=a, abb=aaa⟩φ(a) = a, φ(b) = b
105028⟨a, b | aaa=aa, aabb=a⟩φ(a) = a, φ(b) = b
105132⟨a, b | aab=ab, aabb=a⟩φ(a) = a, φ(b) = b
108574⟨a, b | aa=a, aaaabb=a⟩φ(a) = a, φ(b) = b
108851⟨a, b | aa=a, aaabb=aa⟩φ(a) = a, φ(b) = b
109115⟨a, b | aa=a, aaaa=abb⟩φ(a) = a, φ(b) = b
109134⟨a, b | aa=a, aabb=aaa⟩φ(a) = a, φ(b) = b
1114671⟨a, b | aabb=a, aaabb=a⟩φ(a) = a, φ(b) = b
1114677⟨a, b | aabb=a, aabba=a⟩φ(a) = a, φ(b) = b
1114689⟨a, b | aabb=a, abbaa=a⟩φ(a) = a, φ(b) = b
1114799⟨a, b | abba=a, aaabb=a⟩φ(a) = a, φ(b) = b
1115407⟨a, b | aaa=aa, aaabb=a⟩φ(a) = a, φ(b) = b
1115615⟨a, b | aab=ab, aaabb=a⟩φ(a) = a, φ(b) = b
1124050⟨a, b | aa=a, aaaaabb=a⟩φ(a) = a, φ(b) = b
1124599⟨a, b | aa=a, aaaabb=aa⟩φ(a) = a, φ(b) = b
1125119⟨a, b | aa=a, aaaaa=abb⟩φ(a) = a, φ(b) = b
1125138⟨a, b | aa=a, aaabb=aaa⟩φ(a) = a, φ(b) = b
1125663⟨a, b | aa=a, aabb=aaaa⟩φ(a) = a, φ(b) = b

Other anti-isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

17 total

Σ#PresentationMapping
92059⟨a, b | aab=b, aabb=b⟩φ(a) = b, φ(b) = a
92071⟨a, b | aab=b, baab=b⟩φ(a) = b, φ(b) = a
105150⟨a, b | aab=ab, bbaa=a⟩φ(a) = a, φ(b) = b
1112245⟨a, b | aaab=ab, aabb=b⟩φ(a) = b, φ(b) = a
1112379⟨a, b | aaba=ba, aabb=b⟩φ(a) = b, φ(b) = a
1112391⟨a, b | aaba=ba, baab=b⟩φ(a) = b, φ(b) = a
1112564⟨a, b | abba=aa, bbaa=a⟩φ(a) = a, φ(b) = b
1115657⟨a, b | aab=ab, bbaaa=a⟩φ(a) = a, φ(b) = b
1118967⟨a, b | aab=b, aaaabb=b⟩φ(a) = b, φ(b) = a
1118979⟨a, b | aab=b, aabaab=b⟩φ(a) = b, φ(b) = a
1119027⟨a, b | aab=b, baaaab=b⟩φ(a) = b, φ(b) = a
1119511⟨a, b | aab=b, aaaab=bb⟩φ(a) = b, φ(b) = a
1119517⟨a, b | aab=b, aaabb=ab⟩φ(a) = b, φ(b) = a
1119541⟨a, b | aab=b, abaab=ab⟩φ(a) = b, φ(b) = a
1120059⟨a, b | aab=b, aaab=abb⟩φ(a) = b, φ(b) = a
1120073⟨a, b | aab=b, aabb=aab⟩φ(a) = b, φ(b) = a
1120121⟨a, b | aab=b, baab=aab⟩φ(a) = b, φ(b) = a