#890 ⟨a, b | aa=a, abba=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. ab2a ⇒ a 
# ab:aa=a,abba=a ab
aa=a
abba=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.

17 total

Σ#PresentationMapping
92868⟨a, b | aa=a, aabba=a⟩φ(a) = a, φ(b) = b
93019⟨a, b | aa=a, abba=aa⟩φ(a) = a, φ(b) = b
105138⟨a, b | aab=ab, abba=a⟩φ(a) = a, φ(b) = b
108580⟨a, b | aa=a, aaabba=a⟩φ(a) = a, φ(b) = b
108590⟨a, b | aa=a, aabbaa=a⟩φ(a) = a, φ(b) = b
108862⟨a, b | aa=a, aabba=aa⟩φ(a) = a, φ(b) = b
109150⟨a, b | aa=a, abba=aaa⟩φ(a) = a, φ(b) = b
1114805⟨a, b | abba=a, aabba=a⟩φ(a) = a, φ(b) = b
1115413⟨a, b | aaa=aa, aabba=a⟩φ(a) = a, φ(b) = b
1115621⟨a, b | aab=ab, aabba=a⟩φ(a) = a, φ(b) = b
1115633⟨a, b | aab=ab, abbaa=a⟩φ(a) = a, φ(b) = b
1124056⟨a, b | aa=a, aaaabba=a⟩φ(a) = a, φ(b) = b
1124068⟨a, b | aa=a, aaabbaa=a⟩φ(a) = a, φ(b) = b
1124611⟨a, b | aa=a, aaabba=aa⟩φ(a) = a, φ(b) = b
1124631⟨a, b | aa=a, aabbaa=aa⟩φ(a) = a, φ(b) = b
1125160⟨a, b | aa=a, aabba=aaa⟩φ(a) = a, φ(b) = b
1125674⟨a, b | aa=a, abba=aaaa⟩φ(a) = a, φ(b) = b