#1046 ⟨a, b | aa=1, abbabb=1⟩

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  1. Properties
  2. Rewriting system
  3. 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. a2 ⇒ 1 [1]
2. c2 ⇒ 1 [10]
3. cb ⇒ abca [8]
4. cab ⇒ bac [5]
5. bab ⇒ c [3]
# ab:aa=1,abbabb=1 ac/b bab=c morph:3/0
aa=1
cc=1
cb=abca
cab=bac
bab=c

Isomorphic instances

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

24 total

Σ#PresentationMapping
81055⟨a, b | aa=1, babbab=1⟩φ(a) = a, φ(b) = b
81132⟨a, b | aa=1, bbabb=a⟩φ(a) = a, φ(b) = b
105988⟨a, b | aaa=a, abbabb=1⟩φ(a) = a, φ(b) = b
105997⟨a, b | aaa=a, babbab=1⟩φ(a) = a, φ(b) = b
106129⟨a, b | aab=b, abbabb=1⟩φ(a) = a, φ(b) = b
106147⟨a, b | aab=b, babbab=1⟩φ(a) = a, φ(b) = b
106156⟨a, b | aab=b, bbabba=1⟩φ(a) = a, φ(b) = b
109410⟨a, b | aa=1, aaabbabb=1⟩φ(a) = a, φ(b) = b
109426⟨a, b | aa=1, aababbab=1⟩φ(a) = a, φ(b) = b
109433⟨a, b | aa=1, aabbabba=1⟩φ(a) = a, φ(b) = b
109450⟨a, b | aa=1, abaababb=1⟩φ(a) = a, φ(b) = b
109460⟨a, b | aa=1, ababbaba=1⟩φ(a) = a, φ(b) = b
109466⟨a, b | aa=1, abbaaabb=1⟩φ(a) = a, φ(b) = b
109470⟨a, b | aa=1, abbabaab=1⟩φ(a) = a, φ(b) = b
109490⟨a, b | aa=1, baaabbab=1⟩φ(a) = a, φ(b) = b
109500⟨a, b | aa=1, babaabab=1⟩φ(a) = a, φ(b) = b
109706⟨a, b | aa=1, aabbabb=a⟩φ(a) = a, φ(b) = b
109734⟨a, b | aa=1, ababbab=a⟩φ(a) = a, φ(b) = b
109746⟨a, b | aa=1, abbabba=a⟩φ(a) = a, φ(b) = b
109770⟨a, b | aa=1, baababb=a⟩φ(a) = a, φ(b) = b
109788⟨a, b | aa=1, bbaaabb=a⟩φ(a) = a, φ(b) = b
1010013⟨a, b | aa=1, abbabb=aa⟩φ(a) = a, φ(b) = b
1010047⟨a, b | aa=1, babbab=aa⟩φ(a) = a, φ(b) = b
1010332⟨a, b | aa=1, bbabb=aaa⟩φ(a) = a, φ(b) = b