#888 ⟨a, b | aa=a, abab=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. aba ⇒ ab
  3. ab2 ⇒ a 
# ab:aa=a,abab=a ab
aa=a
aba=ab
abb=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.

45 total

Σ#PresentationMapping
91666⟨a, b | aba=ab, abb=a⟩φ(a) = a, φ(b) = b
92866⟨a, b | aa=a, aabab=a⟩φ(a) = a, φ(b) = b
92872⟨a, b | aa=a, abaab=a⟩φ(a) = a, φ(b) = b
93015⟨a, b | aa=a, abab=aa⟩φ(a) = a, φ(b) = b
105030⟨a, b | aaa=aa, abab=a⟩φ(a) = a, φ(b) = b
105136⟨a, b | aab=ab, abab=a⟩φ(a) = a, φ(b) = b
105248⟨a, b | aba=ab, aabb=a⟩φ(a) = a, φ(b) = b
105252⟨a, b | aba=ab, abab=a⟩φ(a) = a, φ(b) = b
105254⟨a, b | aba=ab, abba=a⟩φ(a) = a, φ(b) = b
108578⟨a, b | aa=a, aaabab=a⟩φ(a) = a, φ(b) = b
108584⟨a, b | aa=a, aabaab=a⟩φ(a) = a, φ(b) = b
108598⟨a, b | aa=a, abaaab=a⟩φ(a) = a, φ(b) = b
108858⟨a, b | aa=a, aabab=aa⟩φ(a) = a, φ(b) = b
108870⟨a, b | aa=a, abaab=aa⟩φ(a) = a, φ(b) = b
109142⟨a, b | aa=a, abab=aaa⟩φ(a) = a, φ(b) = b
1112432⟨a, b | aabb=aa, abab=a⟩φ(a) = a, φ(b) = b
1114683⟨a, b | aabb=a, abaab=a⟩φ(a) = a, φ(b) = b
1114735⟨a, b | abab=a, aaabb=a⟩φ(a) = a, φ(b) = b
1114739⟨a, b | abab=a, aabab=a⟩φ(a) = a, φ(b) = b
1114741⟨a, b | abab=a, aabba=a⟩φ(a) = a, φ(b) = b
1114747⟨a, b | abab=a, abaab=a⟩φ(a) = a, φ(b) = b
1114749⟨a, b | abab=a, ababa=a⟩φ(a) = a, φ(b) = b
1114753⟨a, b | abab=a, abbaa=a⟩φ(a) = a, φ(b) = b
1114803⟨a, b | abba=a, aabab=a⟩φ(a) = a, φ(b) = b
1114809⟨a, b | abba=a, abaab=a⟩φ(a) = a, φ(b) = b
1115411⟨a, b | aaa=aa, aabab=a⟩φ(a) = a, φ(b) = b
1115417⟨a, b | aaa=aa, abaab=a⟩φ(a) = a, φ(b) = b
1115619⟨a, b | aab=ab, aabab=a⟩φ(a) = a, φ(b) = b
1115627⟨a, b | aab=ab, abaab=a⟩φ(a) = a, φ(b) = b
1115847⟨a, b | aba=ab, aaabb=a⟩φ(a) = a, φ(b) = b
1115851⟨a, b | aba=ab, aabab=a⟩φ(a) = a, φ(b) = b
1115853⟨a, b | aba=ab, aabba=a⟩φ(a) = a, φ(b) = b
1115859⟨a, b | aba=ab, abaab=a⟩φ(a) = a, φ(b) = b
1115861⟨a, b | aba=ab, ababa=a⟩φ(a) = a, φ(b) = b
1115865⟨a, b | aba=ab, abbaa=a⟩φ(a) = a, φ(b) = b
1124054⟨a, b | aa=a, aaaabab=a⟩φ(a) = a, φ(b) = b
1124062⟨a, b | aa=a, aaabaab=a⟩φ(a) = a, φ(b) = b
1124076⟨a, b | aa=a, aabaaab=a⟩φ(a) = a, φ(b) = b
1124104⟨a, b | aa=a, abaaaab=a⟩φ(a) = a, φ(b) = b
1124607⟨a, b | aa=a, aaabab=aa⟩φ(a) = a, φ(b) = b
1124619⟨a, b | aa=a, aabaab=aa⟩φ(a) = a, φ(b) = b
1124646⟨a, b | aa=a, abaaab=aa⟩φ(a) = a, φ(b) = b
1125152⟨a, b | aa=a, aabab=aaa⟩φ(a) = a, φ(b) = b
1125176⟨a, b | aa=a, abaab=aaa⟩φ(a) = a, φ(b) = b
1125669⟨a, b | aa=a, abab=aaaa⟩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.

5 total

Σ#PresentationMapping
105146⟨a, b | aab=ab, baba=a⟩φ(a) = a, φ(b) = b
1112560⟨a, b | abba=aa, baba=a⟩φ(a) = a, φ(b) = b
1112628⟨a, b | baba=aa, bbaa=a⟩φ(a) = a, φ(b) = b
1115645⟨a, b | aab=ab, baaba=a⟩φ(a) = a, φ(b) = b
1115649⟨a, b | aab=ab, babaa=a⟩φ(a) = a, φ(b) = b