#123 ⟨a, b | bab=aba⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same 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. ca ⇒ bc [4]
2. cb ⇒ ac [5]
3. aba ⇒ c [2]
4. bab ⇒ c [3]
# ab:bab=aba abc aba=c magic:0
ca=bc
cb=ac
aba=c
bab=c

Other submonoids of same group

12 unique, 57 total

Σ#PresentationPropertiesφ
530⟨a, b | aabba=1⟩Grp Inf40
543⟨a, b | abba=b⟩Can Inf
546⟨a, b | aaa=bb⟩Can Inf
553⟨a, b | aba=bb⟩Can Inf
691⟨a, b | ababa=b⟩Can Inf5
7267⟨a, b | abba=bab⟩Can Inf
8555⟨a, b | abbba=bab⟩Can Inf
91137⟨a, b | abbbba=bab⟩Can Inf
91262⟨a, b | ababa=baab⟩Can Inf
102361⟨a, b | abbbbba=bab⟩Can Inf
114887⟨a, b | abbbbbba=bab⟩Can Inf
115855⟨a, b | abaaba=baaab⟩Can Inf