#9153 ⟨a, b | aa=a, abba=abb⟩

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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. ac ⇒ c
  3. ab ⇒ c
  4. cba ⇒ cb
  5. cb2 ⇒ cbc 
# ab:aa=a,abba=abb acb ab=c frequency:2/1
aa=a
ac=c
ab=c
cba=cb
cbb=cbc

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.

2 total

Σ#PresentationMapping
1125163⟨a, b | aa=a, aabba=abb⟩φ(a) = a, φ(b) = b
1125677⟨a, b | aa=a, abba=aabb⟩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.

1 total

Σ#PresentationMapping
1125166⟨a, b | aa=a, aabba=bba⟩φ(a) = a, φ(b) = b