#3516 ⟨a, b | aa=1, abbab=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. b6 ⇒ b3
  2. bab2 ⇒ ab4
  3. b2ab ⇒ ab2
  4. a2 ⇒ 1 
# ab:aa=1,abbab=bb b/a
bbbbbb=bbb
babb=abbbb
bbab=abb
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.

10 total

Σ#PresentationMapping
1127021⟨a, b | aa=1, aaabbab=bb⟩φ(a) = a, φ(b) = b
1127098⟨a, b | aa=1, abaabab=bb⟩φ(a) = a, φ(b) = b
1127133⟨a, b | aa=1, abbaaab=bb⟩φ(a) = a, φ(b) = b
1127591⟨a, b | aa=1, aabbab=abb⟩φ(a) = a, φ(b) = b
1127713⟨a, b | aa=1, baabab=abb⟩φ(a) = a, φ(b) = b
1128079⟨a, b | aa=1, aaabb=bbab⟩φ(a) = a, φ(b) = b
1128153⟨a, b | aa=1, abaab=bbab⟩φ(a) = a, φ(b) = b
1128185⟨a, b | aa=1, abbab=aabb⟩φ(a) = a, φ(b) = b
1128191⟨a, b | aa=1, abbab=baab⟩φ(a) = a, φ(b) = b
1128194⟨a, b | aa=1, abbab=bbaa⟩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.

7 total

Σ#PresentationMapping
93672⟨a, b | aa=1, babb=bba⟩φ(a) = a, φ(b) = b
1127052⟨a, b | aa=1, aababba=bb⟩φ(a) = a, φ(b) = b
1127580⟨a, b | aa=1, aababb=bba⟩φ(a) = a, φ(b) = b
1127645⟨a, b | aa=1, ababba=abb⟩φ(a) = a, φ(b) = b
1127708⟨a, b | aa=1, baaabb=bba⟩φ(a) = a, φ(b) = b
1128119⟨a, b | aa=1, aabba=babb⟩φ(a) = a, φ(b) = b
1128172⟨a, b | aa=1, ababb=abba⟩φ(a) = a, φ(b) = b