#5827 ⟨a, b | abaaab=baaba⟩

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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. ea ⇒ ac [9]
2. da ⇒ e [4]
3. ab ⇒ d [3]
4. ba2 ⇒ c [2]
5. c2a ⇒ (ac)2 [16]
6. ace ⇒ c2 [13]
7. acd ⇒ bae [10]
8. cb ⇒ bad [8]
9. eb ⇒ d2 [7]
10. c2e ⇒ bac2 [14]
11. ece ⇒ dc2 [15]
12. c2d ⇒ be2 [11]
13. ecd ⇒ dbae [12]
# ab:abaaab=baaba reversed:a/cedb baa=c,ab=d,da=e morph:3/2,2/2,2/0
ea=ac
da=e
ab=d
baa=c
cca=acac
ace=cc
acd=bae
cb=bad
eb=dd
cce=bacc
ece=dcc
ccd=bee
ecd=dbae

Other submonoids of same group

17 unique, 17 total

Σ#PresentationProperties
6107⟨a, b | aabb=ba⟩Can Inf
6121⟨a, b | baa=abb⟩Can Inf
7217⟨a, b | aabab=ba⟩Can Inf
7262⟨a, b | abab=baa⟩Can Inf
8445⟨a, b | aabaab=ba⟩Can Inf
8541⟨a, b | abaab=baa⟩Can Inf
9927⟨a, b | aabaaab=ba⟩Can Inf
9976⟨a, b | abaabab=ba⟩Can Inf
91107⟨a, b | abaaab=baa⟩Can Inf
91249⟨a, b | abaab=baba⟩Can Inf
101937⟨a, b | aabaaaab=ba⟩Can Inf
102295⟨a, b | abaaaab=baa⟩Can Inf
114063⟨a, b | aabaaaaab=ba⟩Can Inf
114242⟨a, b | abaaabaab=ba⟩Can Inf
114289⟨a, b | ababaabab=ba⟩Can Inf
114757⟨a, b | abaaaaab=baa⟩Can Inf
115349⟨a, b | ababaab=baba⟩Can Inf