#4771 ⟨a, b | abaaabab=baa⟩

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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. ba2 ⇒ c [2]
2. c2(ab)2 ⇒ bac [5]
3. ac(ab)2 ⇒ c [4]
4. acabac ⇒ ca2 [6]
5. baca2 ⇒ c2abac [7]
6. ca4 ⇒ acac2abac [11]
7. ca3bab ⇒ acabc [8]
8. ca3bac ⇒ acabca2 [9]
9. (c2aba)2c ⇒ b(ac)2a2 [10]
# ab:abaaabab=baa bc/a baa=c magic:0
baa=c
ccabab=bac
acabab=c
acabac=caa
bacaa=ccabac
caaaa=acaccabac
caaabab=acabc
caaabac=acabcaa
ccabaccabac=bacacaa

Other submonoids of same group

3 unique, 3 total

Σ#PresentationProperties
9935⟨a, b | aabaabb=ba⟩Can Inf
91093⟨a, b | aabbab=bba⟩Can Inf
114078⟨a, b | aabaaabab=ba⟩Can Inf

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationProperties
102311⟨a, b | abaabab=bba⟩Can Inf
102751⟨a, b | baaba=ababb⟩Can Inf