#239 ⟨a, b | aa=a, aba=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 ⇒ a 
# ab:aa=a,aba=a ab
aa=a
aba=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
8884⟨a, b | aa=a, aaba=a⟩φ(a) = a, φ(b) = b
8959⟨a, b | aa=a, aba=aa⟩φ(a) = a, φ(b) = b
91622⟨a, b | aab=ab, aba=a⟩φ(a) = a, φ(b) = b
92088⟨a, b | aba=a, aaba=a⟩φ(a) = a, φ(b) = b
92860⟨a, b | aa=a, aaaba=a⟩φ(a) = a, φ(b) = b
92864⟨a, b | aa=a, aabaa=a⟩φ(a) = a, φ(b) = b
93007⟨a, b | aa=a, aaba=aa⟩φ(a) = a, φ(b) = b
93137⟨a, b | aa=a, aba=aaa⟩φ(a) = a, φ(b) = b
105026⟨a, b | aaa=aa, aaba=a⟩φ(a) = a, φ(b) = b
105130⟨a, b | aab=ab, aaba=a⟩φ(a) = a, φ(b) = b
105134⟨a, b | aab=ab, abaa=a⟩φ(a) = a, φ(b) = b
108572⟨a, b | aa=a, aaaaba=a⟩φ(a) = a, φ(b) = b
108576⟨a, b | aa=a, aaabaa=a⟩φ(a) = a, φ(b) = b
108847⟨a, b | aa=a, aaaba=aa⟩φ(a) = a, φ(b) = b
108855⟨a, b | aa=a, aabaa=aa⟩φ(a) = a, φ(b) = b
109114⟨a, b | aa=a, aaaa=aba⟩φ(a) = a, φ(b) = b
109126⟨a, b | aa=a, aaba=aaa⟩φ(a) = a, φ(b) = b
1112328⟨a, b | aaba=aa, abaa=a⟩φ(a) = a, φ(b) = b
1112526⟨a, b | abab=ab, babb=b⟩φ(a) = b, φ(b) = a
1112529⟨a, b | abab=ab, bbab=b⟩φ(a) = b, φ(b) = a
1114541⟨a, b | aaba=a, aaaba=a⟩φ(a) = a, φ(b) = b
1114545⟨a, b | aaba=a, aabaa=a⟩φ(a) = a, φ(b) = b
1114553⟨a, b | aaba=a, abaaa=a⟩φ(a) = a, φ(b) = b
1115405⟨a, b | aaa=aa, aaaba=a⟩φ(a) = a, φ(b) = b
1115409⟨a, b | aaa=aa, aabaa=a⟩φ(a) = a, φ(b) = b
1115613⟨a, b | aab=ab, aaaba=a⟩φ(a) = a, φ(b) = b
1115617⟨a, b | aab=ab, aabaa=a⟩φ(a) = a, φ(b) = b
1115625⟨a, b | aab=ab, abaaa=a⟩φ(a) = a, φ(b) = b
1119106⟨a, b | aba=a, aababa=a⟩φ(a) = a, φ(b) = b
1119120⟨a, b | aba=a, abaaba=a⟩φ(a) = a, φ(b) = b
1119651⟨a, b | aba=a, aabab=ab⟩φ(a) = a, φ(b) = b
1119663⟨a, b | aba=a, abaab=ab⟩φ(a) = a, φ(b) = b
1119666⟨a, b | aba=a, ababa=aa⟩φ(a) = a, φ(b) = b
1120192⟨a, b | aba=a, aaba=aba⟩φ(a) = a, φ(b) = b
1120207⟨a, b | aba=a, abab=aab⟩φ(a) = a, φ(b) = b
1120232⟨a, b | aba=a, baab=bab⟩φ(a) = a, φ(b) = b
1124048⟨a, b | aa=a, aaaaaba=a⟩φ(a) = a, φ(b) = b
1124052⟨a, b | aa=a, aaaabaa=a⟩φ(a) = a, φ(b) = b
1124060⟨a, b | aa=a, aaabaaa=a⟩φ(a) = a, φ(b) = b
1124595⟨a, b | aa=a, aaaaba=aa⟩φ(a) = a, φ(b) = b
1124603⟨a, b | aa=a, aaabaa=aa⟩φ(a) = a, φ(b) = b
1125118⟨a, b | aa=a, aaaaa=aba⟩φ(a) = a, φ(b) = b
1125130⟨a, b | aa=a, aaaba=aaa⟩φ(a) = a, φ(b) = b
1125146⟨a, b | aa=a, aabaa=aaa⟩φ(a) = a, φ(b) = b
1125661⟨a, b | aa=a, aaba=aaaa⟩φ(a) = a, φ(b) = b