#5048 ⟨a, b | aaa=ab, aabb=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. a6 ⇒ a
  2. ab ⇒ a3 
# ab:aaa=ab,aabb=a a/b
aaaaaa=a
ab=aaa

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.

12 total

Σ#PresentationMapping
105052⟨a, b | aaa=ab, abab=a⟩φ(a) = a, φ(b) = b
105054⟨a, b | aaa=ab, abba=a⟩φ(a) = a, φ(b) = b
1114667⟨a, b | aabb=a, aaaab=a⟩φ(a) = a, φ(b) = b
1114731⟨a, b | abab=a, aaaab=a⟩φ(a) = a, φ(b) = b
1114733⟨a, b | abab=a, aaaba=a⟩φ(a) = a, φ(b) = b
1114737⟨a, b | abab=a, aabaa=a⟩φ(a) = a, φ(b) = b
1114745⟨a, b | abab=a, abaaa=a⟩φ(a) = a, φ(b) = b
1114795⟨a, b | abba=a, aaaab=a⟩φ(a) = a, φ(b) = b
1115443⟨a, b | aaa=ab, aaaab=a⟩φ(a) = a, φ(b) = b
1115445⟨a, b | aaa=ab, aaaba=a⟩φ(a) = a, φ(b) = b
1115449⟨a, b | aaa=ab, aabaa=a⟩φ(a) = a, φ(b) = b
1115457⟨a, b | aaa=ab, abaaa=a⟩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.

2 total

Σ#PresentationMapping
1112301⟨a, b | aaab=bb, aabb=b⟩φ(a) = b, φ(b) = a
1112305⟨a, b | aaab=bb, abab=b⟩φ(a) = b, φ(b) = a