#8060 ⟨a, b | aaa=1, abab=bba⟩

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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. a3 ⇒ 1
  2. b2a ⇒ (ab)2
  3. baba2 ⇒ a2b2
  4. ba2(ba)2 ⇒ (a2b)2b
  5. (ba)4 ⇒ (a2b)3b
  6. b(a2b)3ab ⇒ (a2b)4b
  7. (ba2)4b2 ⇒ a(ba2)3b3 
# ab:aaa=1,abab=bba reversed:a/b
aaa=1
bba=abab
babaa=aabb
baababa=aabaabb
babababa=aabaabaabb
baabaabaabab=aabaabaabaabb
baabaabaabaabb=abaabaabaabbb

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.

1 total

Σ#PresentationMapping
1122769⟨a, b | aaa=1, aabba=bab⟩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.

1 total

Σ#PresentationMapping
1122230⟨a, b | aaa=1, aababa=bb⟩φ(a) = a, φ(b) = b