#368 ⟨a, b | aa=1, abb=bb⟩

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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 ⇒ 1
  2. ab2 ⇒ b2 
# ab:aa=1,abb=bb ab
aa=1
abb=bb

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.

25 total

Σ#PresentationMapping
93486⟨a, b | aa=1, aaabb=bb⟩φ(a) = a, φ(b) = b
93505⟨a, b | aa=1, abaab=bb⟩φ(a) = a, φ(b) = b
93633⟨a, b | aa=1, aabb=abb⟩φ(a) = a, φ(b) = b
93643⟨a, b | aa=1, abab=bab⟩φ(a) = a, φ(b) = ab
93663⟨a, b | aa=1, baab=abb⟩φ(a) = a, φ(b) = b
1126982⟨a, b | aa=1, aaaaabb=bb⟩φ(a) = a, φ(b) = b
1127005⟨a, b | aa=1, aaabaab=bb⟩φ(a) = a, φ(b) = b
1127017⟨a, b | aa=1, aaabbaa=bb⟩φ(a) = a, φ(b) = b
1127087⟨a, b | aa=1, abaaaab=bb⟩φ(a) = a, φ(b) = b
1127521⟨a, b | aa=1, aaaabb=abb⟩φ(a) = a, φ(b) = b
1127539⟨a, b | aa=1, aaabab=bab⟩φ(a) = a, φ(b) = ab
1127548⟨a, b | aa=1, aaabba=bba⟩φ(a) = a, φ(b) = b
1127561⟨a, b | aa=1, aabaab=abb⟩φ(a) = a, φ(b) = b
1127585⟨a, b | aa=1, aabbaa=abb⟩φ(a) = a, φ(b) = b
1127617⟨a, b | aa=1, abaaab=bab⟩φ(a) = a, φ(b) = ab
1127699⟨a, b | aa=1, baaaab=abb⟩φ(a) = a, φ(b) = b
1128069⟨a, b | aa=1, aaabb=aabb⟩φ(a) = a, φ(b) = b
1128075⟨a, b | aa=1, aaabb=baab⟩φ(a) = a, φ(b) = b
1128078⟨a, b | aa=1, aaabb=bbaa⟩φ(a) = a, φ(b) = b
1128097⟨a, b | aa=1, aabab=abab⟩φ(a) = a, φ(b) = ab
1128114⟨a, b | aa=1, aabba=abba⟩φ(a) = a, φ(b) = b
1128143⟨a, b | aa=1, abaab=aabb⟩φ(a) = a, φ(b) = b
1128149⟨a, b | aa=1, abaab=baab⟩φ(a) = a, φ(b) = b
1128152⟨a, b | aa=1, abaab=bbaa⟩φ(a) = a, φ(b) = b
1128228⟨a, b | aa=1, baaab=abab⟩φ(a) = a, φ(b) = ab

Other anti-isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

17 total

Σ#PresentationMapping
93497⟨a, b | aa=1, aabba=bb⟩φ(a) = a, φ(b) = b
93636⟨a, b | aa=1, aabb=bba⟩φ(a) = a, φ(b) = b
93649⟨a, b | aa=1, abba=abb⟩φ(a) = a, φ(b) = b
1126994⟨a, b | aa=1, aaaabba=bb⟩φ(a) = a, φ(b) = b
1127037⟨a, b | aa=1, aabaaba=bb⟩φ(a) = a, φ(b) = b
1127524⟨a, b | aa=1, aaaabb=bba⟩φ(a) = a, φ(b) = b
1127545⟨a, b | aa=1, aaabba=abb⟩φ(a) = a, φ(b) = b
1127564⟨a, b | aa=1, aabaab=bba⟩φ(a) = a, φ(b) = b
1127571⟨a, b | aa=1, aababa=bab⟩φ(a) = a, φ(b) = ba
1127623⟨a, b | aa=1, abaaba=abb⟩φ(a) = a, φ(b) = b
1128072⟨a, b | aa=1, aaabb=abba⟩φ(a) = a, φ(b) = b
1128102⟨a, b | aa=1, aabab=baba⟩φ(a) = a, φ(b) = ba
1128111⟨a, b | aa=1, aabba=aabb⟩φ(a) = a, φ(b) = b
1128117⟨a, b | aa=1, aabba=baab⟩φ(a) = a, φ(b) = b
1128120⟨a, b | aa=1, aabba=bbaa⟩φ(a) = a, φ(b) = b
1128146⟨a, b | aa=1, abaab=abba⟩φ(a) = a, φ(b) = b
1128160⟨a, b | aa=1, ababa=abab⟩φ(a) = a, φ(b) = ba