#1356 ⟨a, b | aaabababba=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group
  5. Isomorphic instances
  6. Anti-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. dc ⇒ 1 [12]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [11]
5. a4 ⇒ c [2]
6. bcba ⇒ ab2c [20]
7. b2a3 ⇒ a3dbcb [25]
8. bab2c ⇒ a2(ab)3 [16]
9. b(ab)2d ⇒ adbab2 [13]
10. bab2ac ⇒ a3(ba)3 [18]
11. (ba)3d ⇒ adbab2a [14]
12. bab2a2c ⇒ a3(ba)3a [27]
13. (ba)3ad ⇒ adbab2a2 [26]
14. (ba)3a2 ⇒ adb(bc)2 [29]
15. (ba)2b2 ⇒ d [3]
16. (b2c)2 ⇒ a3dba3cb(ab)2 [31]
17. b2cb2ac ⇒ a3dba3c(ba)3 [32]
18. b2cb2a2c ⇒ a3dba3c(ba)3a [33]
# ab:aaabababba=1 reversed:cda/b aaaa=c,bababb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaa=c
bcba=abbc
bbaaa=aaadbcb
babbc=aaababab
bababd=adbabb
babbac=aaabababa
bababad=adbabba
babbaac=aaabababaa
bababaad=adbabbaa
bababaaa=adbbcbc
bababb=d
bbcbbc=aaadbaaacbabab
bbcbbac=aaadbaaacbababa
bbcbbaac=aaadbaaacbababaa

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
8506⟨a, b | aaaba=bbb⟩Infinite cancellative non-commutative monoid
102059⟨a, b | abababba=bb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationDescriptionRelated
8370⟨a, b | aaabbba=b⟩Infinite cancellative non-commutative monoid
101628⟨a, b | aaabababa=b⟩Infinite cancellative non-commutative monoid
102765⟨a, b | babab=aaaba⟩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
101423⟨a, b | aabababbaa=1⟩φ(a) = a, φ(b) = aaadab
101517⟨a, b | ababbaaaab=1⟩φ(a) = a, φ(b) = aaadab

Anti-isomorphic instances

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

3 total

Σ#PresentationMapping
101373⟨a, b | aaabbababa=1⟩φ(a) = a, φ(b) = aaadab
101516⟨a, b | abababbbba=1⟩φ(a) = aaadab, φ(b) = a
101524⟨a, b | ababbbbaab=1⟩φ(a) = aaadab, φ(b) = a