#3383 ⟨a, b | aa=1, abbbab=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. b4 ⇒ b
  3. b3ab ⇒ ab 
# ab:aa=1,abbbab=b ab
aa=1
bbbb=b
bbbab=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.

8 total

Σ#PresentationMapping
1126497⟨a, b | aa=1, aaabbbab=b⟩φ(a) = a, φ(b) = b
1126575⟨a, b | aa=1, abaabbab=b⟩φ(a) = a, φ(b) = b
1126607⟨a, b | aa=1, abbaabab=b⟩φ(a) = a, φ(b) = b
1126623⟨a, b | aa=1, abbbaaab=b⟩φ(a) = a, φ(b) = b
1127073⟨a, b | aa=1, aabbbab=ab⟩φ(a) = a, φ(b) = b
1127191⟨a, b | aa=1, baabbab=ab⟩φ(a) = a, φ(b) = b
1127675⟨a, b | aa=1, abbbab=aab⟩φ(a) = a, φ(b) = b
1127678⟨a, b | aa=1, abbbab=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.

9 total

Σ#PresentationMapping
93536⟨a, b | aa=1, babbb=ba⟩φ(a) = a, φ(b) = b
1126527⟨a, b | aa=1, aababbba=b⟩φ(a) = a, φ(b) = b
1127055⟨a, b | aa=1, aababbb=ba⟩φ(a) = a, φ(b) = b
1127123⟨a, b | aa=1, ababbba=ab⟩φ(a) = a, φ(b) = b
1127181⟨a, b | aa=1, baaabbb=ba⟩φ(a) = a, φ(b) = b
1127200⟨a, b | aa=1, babaabb=ba⟩φ(a) = a, φ(b) = b
1127652⟨a, b | aa=1, ababbb=aba⟩φ(a) = a, φ(b) = b
1128262⟨a, b | aa=1, babbb=aaba⟩φ(a) = a, φ(b) = b
1128268⟨a, b | aa=1, babbb=baaa⟩φ(a) = a, φ(b) = b