#995 ⟨a, b | abbaaab=ba⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

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. dc2bd ⇒ cb [9]
2. dc3b ⇒ c [15]
3. (dc2)2bc ⇒ c4b [18]
4. d2c2dcbd2 ⇒ cdb [22]
5. cb2 ⇒ bd [8]
6. cbc3b ⇒ dc2bc [16]
7. cdbc3b ⇒ d2c2dcbdc [25]
8. c3bdb ⇒ dc2dcbd2 [14]
9. dc(cb)2 ⇒ cbc2bd [10]
10. dc2bcdb ⇒ cbdc2dcbd2 [23]
11. dc2bc4b ⇒ cbc2dc2bc [19]
12. c4bc2b ⇒ dc(cd)2c2bc [21]
13. d2c2dcbcdb ⇒ cdbc2dcbd2 [27]
14. d2c2(dcb)2 ⇒ cdbc2bd [24]
15. d2c2dcbdcdb ⇒ cdbdc2dcbd2 [28]
16. d2c2dcbdc4b ⇒ cdbc2dc2bc [26]
17. cbc2bdb ⇒ dcbd2 [13]
18. cdbc2bdb ⇒ d2c2dc(bd)2 [29]
19. c4bcbdb ⇒ dc2(dc)2bd2 [20]
20. ab ⇒ d [3]
21. ca ⇒ dc4b [17]
22. da ⇒ acb [7]
23. ba ⇒ cb [6]
# ab:abbaaab=ba cd/b/a abbaaa=c,ab=d morph:6/0,2/4
dccbd=cb
dcccb=c
dccdccbc=ccccb
ddccdcbdd=cdb
cbb=bd
cbcccb=dccbc
cdbcccb=ddccdcbdc
cccbdb=dccdcbdd
dccbcb=cbccbd
dccbcdb=cbdccdcbdd
dccbccccb=cbccdccbc
ccccbccb=dccdcdccbc
ddccdcbcdb=cdbccdcbdd
ddccdcbdcb=cdbccbd
ddccdcbdcdb=cdbdccdcbdd
ddccdcbdccccb=cdbccdccbc
cbccbdb=dcbdd
cdbccbdb=ddccdcbdbd
ccccbcbdb=dccdcdcbdd
ab=d
ca=dccccb
da=acb
ba=cb

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
114285⟨a, b | ababaaaab=ba⟩Infinite cancellative non-commutative monoid
114334⟨a, b | abbaabaab=ba⟩Infinite cancellative non-commutative monoid