#1119 ⟨a, b | aa=1, abbab=b⟩

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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 ⇒ 1
  2. b3 ⇒ b
  3. b2ab ⇒ ab 
# ab:aa=1,abbab=b ab
aa=1
bbb=b
bbab=ab

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.

7 total

Σ#PresentationMapping
109683⟨a, b | aa=1, aaabbab=b⟩φ(a) = a, φ(b) = b
109723⟨a, b | aa=1, abaabab=b⟩φ(a) = a, φ(b) = b
109741⟨a, b | aa=1, abbaaab=b⟩φ(a) = a, φ(b) = b
109975⟨a, b | aa=1, aabbab=ab⟩φ(a) = a, φ(b) = b
1010036⟨a, b | aa=1, baabab=ab⟩φ(a) = a, φ(b) = b
1010283⟨a, b | aa=1, abbab=aab⟩φ(a) = a, φ(b) = b
1010286⟨a, b | aa=1, abbab=baa⟩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.

8 total

Σ#PresentationMapping
81199⟨a, b | aa=1, babb=ba⟩φ(a) = a, φ(b) = b
109699⟨a, b | aa=1, aababba=b⟩φ(a) = a, φ(b) = b
109969⟨a, b | aa=1, aababb=ba⟩φ(a) = a, φ(b) = b
1010002⟨a, b | aa=1, ababba=ab⟩φ(a) = a, φ(b) = b
1010033⟨a, b | aa=1, baaabb=ba⟩φ(a) = a, φ(b) = b
1010276⟨a, b | aa=1, ababb=aba⟩φ(a) = a, φ(b) = b
1010514⟨a, b | aa=1, babb=aaba⟩φ(a) = a, φ(b) = b
1010520⟨a, b | aa=1, babb=baaa⟩φ(a) = a, φ(b) = b