#1433 ⟨a, b | aababbbaba=1⟩

Up:Monoids with two generators and one relation
Prev:#1431 ⟨a, b | aababbabba=1⟩
Next:#1435 ⟨a, b | aababbbbab=1⟩

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. cbab2 ⇒ b2abc [15]
7. db2ab ⇒ bab2d [12]
8. abcbab ⇒ babcba [23]
9. cabab2 ⇒ ab2abc [16]
10. dab2ab ⇒ abab2d [14]
11. a(ab)2cb ⇒ (cb)2abda2 [32]
12. ca2bab2 ⇒ a2b2abc [20]
13. da2b2ab ⇒ a2bab2d [21]
14. ab3ab ⇒ b2abcbda [19]
15. a2b2abcb ⇒ cb3aba2 [31]
16. a2bab3 ⇒ b3aba2 [27]
17. b3abcb ⇒ da2 [26]
18. abcb2abcb ⇒ ba(bc)2(ab)2da2 [34]
# ab:aababbbaba=1 cda/b aaa=c,babbbab=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
cbabb=bbabc
dbbab=babbd
abcbab=babcba
cababb=abbabc
dabbab=ababbd
aababcb=cbcbabdaa
caababb=aabbabc
daabbab=aababbd
abbbab=bbabcbda
aabbabcb=cbbbabaa
aababbb=bbbabaa
bbbabcb=daa
abcbbabcb=babcbcababdaa

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
9939⟨a, b | aababaa=bb⟩Infinite cancellative non-commutative monoid
114617⟨a, b | aabaabaa=bab⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

1 total

Σ#PresentationMapping
101543⟨a, b | abbbabaaab=1⟩φ(a) = bbabcbaba, φ(b) = b