#322 ⟨a, b | aa=1, aaab=b

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 ⇒ 1
  2. abb
# ab:aa=1,aaab=b ab
aa=1
ab=b

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.

24 total

Σ#PresentationMapping
7359a, b | aa=1, aab=abφ(a) = a, φ(b) = b
93339a, b | aa=1, aaaaab=bφ(a) = a, φ(b) = b
93345a, b | aa=1, aaabaa=bφ(a) = a, φ(b) = b
93476a, b | aa=1, aaaab=abφ(a) = a, φ(b) = b
93481a, b | aa=1, aaaba=baφ(a) = a, φ(b) = b
93488a, b | aa=1, aabaa=abφ(a) = a, φ(b) = b
93615a, b | aa=1, aaab=aabφ(a) = a, φ(b) = b
93618a, b | aa=1, aaab=baaφ(a) = a, φ(b) = b
93624a, b | aa=1, aaba=abaφ(a) = a, φ(b) = b
1126443a, b | aa=1, aaaaaaab=bφ(a) = a, φ(b) = b
1126449a, b | aa=1, aaaaabaa=bφ(a) = a, φ(b) = b
1126972a, b | aa=1, aaaaaab=abφ(a) = a, φ(b) = b
1126977a, b | aa=1, aaaaaba=baφ(a) = a, φ(b) = b
1126984a, b | aa=1, aaaabaa=abφ(a) = a, φ(b) = b
1127503a, b | aa=1, aaaaab=aabφ(a) = a, φ(b) = b
1127506a, b | aa=1, aaaaab=baaφ(a) = a, φ(b) = b
1127512a, b | aa=1, aaaaba=abaφ(a) = a, φ(b) = b
1127527a, b | aa=1, aaabaa=aabφ(a) = a, φ(b) = b
1127530a, b | aa=1, aaabaa=baaφ(a) = a, φ(b) = b
1128035a, b | aa=1, aaaab=aaabφ(a) = a, φ(b) = b
1128038a, b | aa=1, aaaab=abaaφ(a) = a, φ(b) = b
1128052a, b | aa=1, aaaba=aabaφ(a) = a, φ(b) = b
1128058a, b | aa=1, aaaba=baaaφ(a) = a, φ(b) = b
1128083a, b | aa=1, aabaa=aaabφ(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.

24 total

Σ#PresentationMapping
7324a, b | aa=1, aaba=bφ(a) = a, φ(b) = b
7360a, b | aa=1, aab=baφ(a) = a, φ(b) = b
7363a, b | aa=1, aba=abφ(a) = a, φ(b) = b
93341a, b | aa=1, aaaaba=bφ(a) = a, φ(b) = b
93477a, b | aa=1, aaaab=baφ(a) = a, φ(b) = b
93480a, b | aa=1, aaaba=abφ(a) = a, φ(b) = b
93616a, b | aa=1, aaab=abaφ(a) = a, φ(b) = b
93623a, b | aa=1, aaba=aabφ(a) = a, φ(b) = b
93626a, b | aa=1, aaba=baaφ(a) = a, φ(b) = b
1126445a, b | aa=1, aaaaaaba=bφ(a) = a, φ(b) = b
1126457a, b | aa=1, aaaabaaa=bφ(a) = a, φ(b) = b
1126973a, b | aa=1, aaaaaab=baφ(a) = a, φ(b) = b
1126976a, b | aa=1, aaaaaba=abφ(a) = a, φ(b) = b
1126985a, b | aa=1, aaaabaa=baφ(a) = a, φ(b) = b
1127000a, b | aa=1, aaabaaa=abφ(a) = a, φ(b) = b
1127504a, b | aa=1, aaaaab=abaφ(a) = a, φ(b) = b
1127511a, b | aa=1, aaaaba=aabφ(a) = a, φ(b) = b
1127514a, b | aa=1, aaaaba=baaφ(a) = a, φ(b) = b
1127528a, b | aa=1, aaabaa=abaφ(a) = a, φ(b) = b
1128036a, b | aa=1, aaaab=aabaφ(a) = a, φ(b) = b
1128042a, b | aa=1, aaaab=baaaφ(a) = a, φ(b) = b
1128051a, b | aa=1, aaaba=aaabφ(a) = a, φ(b) = b
1128054a, b | aa=1, aaaba=abaaφ(a) = a, φ(b) = b
1128084a, b | aa=1, aabaa=aabaφ(a) = a, φ(b) = b