#1186 ⟨a, b | aa=1, abab=bb⟩

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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. bab ⇒ ab2 
# ab:aa=1,abab=bb ab
aa=1
bab=abb

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.

9 total

Σ#PresentationMapping
81251⟨a, b | aa=1, bab=abb⟩φ(a) = a, φ(b) = b
109950⟨a, b | aa=1, aaabab=bb⟩φ(a) = a, φ(b) = b
109989⟨a, b | aa=1, abaaab=bb⟩φ(a) = a, φ(b) = b
1010227⟨a, b | aa=1, aaabb=bab⟩φ(a) = a, φ(b) = b
1010239⟨a, b | aa=1, aabab=abb⟩φ(a) = a, φ(b) = b
1010265⟨a, b | aa=1, abaab=bab⟩φ(a) = a, φ(b) = b
1010307⟨a, b | aa=1, baaab=abb⟩φ(a) = a, φ(b) = b
1010484⟨a, b | aa=1, abab=aabb⟩φ(a) = a, φ(b) = b
1010506⟨a, b | aa=1, baab=abab⟩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.

6 total

Σ#PresentationMapping
109966⟨a, b | aa=1, aababa=bb⟩φ(a) = a, φ(b) = b
1010242⟨a, b | aa=1, aabab=bba⟩φ(a) = a, φ(b) = b
1010249⟨a, b | aa=1, aabba=bab⟩φ(a) = a, φ(b) = b
1010271⟨a, b | aa=1, ababa=abb⟩φ(a) = a, φ(b) = b
1010490⟨a, b | aa=1, abba=abab⟩φ(a) = a, φ(b) = b
1010509⟨a, b | aa=1, baba=aabb⟩φ(a) = a, φ(b) = b