#3646 ⟨a, b | aabbabaaba=b⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. ba ⇒ c [2]
2. a2bc2ac ⇒ b [3]
3. cabc(ca)2 ⇒ bc [5]
4. b2 ⇒ cabc2ac [4]
5. a2(bc)2 ⇒ cbc(ca)4 [9]
6. a2bc2abc ⇒ cbc(ca)2 [7]
7. ca(bc)2 ⇒ (bc)2(ca)4 [10]
8. (cabc)2 ⇒ (bc)2(ca)2 [8]
9. cabc2acb ⇒ bcabc2ac [6]
# ab:aabbabaaba=b ac/b ba=c morph:2/0
ba=c
aabccac=b
cabccaca=bc
bb=cabccac
aabcbc=cbccacacaca
aabccabc=cbccaca
cabcbc=bcbccacacaca
cabccabc=bcbccaca
cabccacb=bcabccac

Other submonoids of same group

2 unique, 2 total

Σ#PresentationProperties
113572⟨a, b | aabaabbaba=b⟩Can Inf
115236⟨a, b | aabbaba=bbab⟩Can Inf

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationProperties
115202⟨a, b | aababba=babb⟩Can Inf