#7546 ⟨a, b | aaa=1, bbaabb=a⟩

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Quick links

  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. c3 ⇒ 1 [10]
2. b2cb2 ⇒ c2 [8]
3. cb2cb ⇒ bcb2c [12]
4. c2bcb2 ⇒ b2cbc2 [11]
5. a ⇒ c2 [13]
# ab:aaa=1,bbaabb=a bc/a aa=c morph:2/0
ccc=1
bbcbb=cc
cbbcb=bcbbc
ccbcbb=bbcbcc
a=cc

Isomorphic instances

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

3 total

Σ#PresentationMapping
1121167⟨a, b | aaa=1, aabbaabb=1⟩φ(a) = cc, φ(b) = b
1121204⟨a, b | aaa=1, abbaabba=1⟩φ(a) = cc, φ(b) = b
1121231⟨a, b | aaa=1, baabbaab=1⟩φ(a) = cc, φ(b) = b