#1425 ⟨a, b | aabababbba=1⟩

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Quick links

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

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. cd ⇒ 1 [9]
2. dc ⇒ 1 [11]
3. ac ⇒ ca [5]
4. ad ⇒ da [10]
5. a3 ⇒ c [2]
6. cb(ab)2 ⇒ bc(ba)2 [34]
7. dbcbab ⇒ b(ab)2da2 [38]
8. ab3 ⇒ b2cbda [28]
9. c(ab)3 ⇒ abc(ba)2 [35]
10. dabcbab ⇒ (ab)3da2 [39]
11. a2b2cb ⇒ cb3a2 [24]
12. ca(ab)3 ⇒ a2bc(ba)2 [41]
13. da2bcbab ⇒ a(ab)3da2 [30]
14. db2cbab ⇒ (ba)2b2da2 [26]
15. dab2cbab ⇒ (ab)3bda2 [42]
16. a(ab)3b ⇒ b3cba [29]
17. b3cbab ⇒ da2 [25]
18. dbcb3cb ⇒ b(ab)2da2b2a2 [45]
19. dabcb3cb ⇒ (ab)3da2b2a2 [46]
20. da2bcb3cb ⇒ a(ab)3da2b2a2 [47]
21. d(b2cb)2 ⇒ (ba)2b2da2b2a2 [48]
22. da(b2cb)2 ⇒ (ab)3bda2b2a2 [49]
23. (b3c)2b ⇒ da2b2a2 [44]
# ab:aabababbba=1 cda/b aaa=c,bababbb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
cbabab=bcbaba
dbcbab=bababdaa
abbb=bbcbda
cababab=abcbaba
dabcbab=abababdaa
aabbcb=cbbbaa
caababab=aabcbaba
daabcbab=aabababdaa
dbbcbab=bababbdaa
dabbcbab=abababbdaa
aabababb=bbbcba
bbbcbab=daa
dbcbbbcb=bababdaabbaa
dabcbbbcb=abababdaabbaa
daabcbbbcb=aabababdaabbaa
dbbcbbbcb=bababbdaabbaa
dabbcbbbcb=abababbdaabbaa
bbbcbbbcb=daabbaa

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
9908⟨a, b | aaababa=bb⟩Infinite cancellative non-commutative monoid
114496⟨a, b | aaabaaba=bab⟩Infinite cancellative non-commutative monoid

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

2 total

Σ#PresentationMapping
101463⟨a, b | aabbbababa=1⟩φ(a) = daaab, φ(b) = a
101522⟨a, b | ababbbaaab=1⟩φ(a) = a, φ(b) = daaab