#8060 ⟨a, b | aaa=1, abab=bba⟩

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  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-isomorphic instances

Properties

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
#RuleProof
1. a3 ⇒ 1 [1]
2. b2a ⇒ (ab)2 [2]
3. baba2 ⇒ a2b2 [4]
4. ba2(ba)2 ⇒ (a2b)2b [6]
5. (ba)4 ⇒ (a2b)3b [8]
6. b(a2b)3ab ⇒ (a2b)4b [10]
7. (ba2)4b2 ⇒ a(ba2)3b3 [11]
# ab:aaa=1,abab=bba reversed:a/b
aaa=1
bba=abab
babaa=aabb
baababa=aabaabb
babababa=aabaabaabb
baabaabaabab=aabaabaabaabb
baabaabaabaabb=abaabaabaabbb

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

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