#3519 ⟨a, b | aa=1, abbba=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. b7 ⇒ b2
  2. bab2 ⇒ ab6
  3. b2a ⇒ ab3
  4. a2 ⇒ 1 
# ab:aa=1,abbba=bb b/a
bbbbbbb=bb
babb=abbbbbb
bba=abbb
aa=1

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.

17 total

Σ#PresentationMapping
93651⟨a, b | aa=1, abba=bbb⟩φ(a) = a, φ(b) = b
93658⟨a, b | aa=1, abbb=bba⟩φ(a) = a, φ(b) = b
1127025⟨a, b | aa=1, aaabbba=bb⟩φ(a) = a, φ(b) = b
1127102⟨a, b | aa=1, abaabba=bb⟩φ(a) = a, φ(b) = b
1127549⟨a, b | aa=1, aaabba=bbb⟩φ(a) = a, φ(b) = b
1127556⟨a, b | aa=1, aaabbb=bba⟩φ(a) = a, φ(b) = b
1127599⟨a, b | aa=1, aabbba=abb⟩φ(a) = a, φ(b) = b
1127625⟨a, b | aa=1, abaaba=bbb⟩φ(a) = a, φ(b) = b
1127632⟨a, b | aa=1, abaabb=bba⟩φ(a) = a, φ(b) = b
1127664⟨a, b | aa=1, abbaab=bba⟩φ(a) = a, φ(b) = b
1128080⟨a, b | aa=1, aaabb=bbba⟩φ(a) = a, φ(b) = b
1128115⟨a, b | aa=1, aabba=abbb⟩φ(a) = a, φ(b) = b
1128130⟨a, b | aa=1, aabbb=abba⟩φ(a) = a, φ(b) = b
1128154⟨a, b | aa=1, abaab=bbba⟩φ(a) = a, φ(b) = b
1128201⟨a, b | aa=1, abbba=aabb⟩φ(a) = a, φ(b) = b
1128205⟨a, b | aa=1, abbba=baab⟩φ(a) = a, φ(b) = b
1128240⟨a, b | aa=1, baabb=abba⟩φ(a) = a, φ(b) = b