#1297 ⟨a, b | aaaaababba=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 [15]
2. cd ⇒ 1 [9]
3. ca ⇒ ac [6]
4. da ⇒ ad [13]
5. a6 ⇒ c [2]
6. b2c ⇒ a5bab [18]
7. babd ⇒ adb2 [16]
8. bcba ⇒ cbab [24]
9. b2ac ⇒ a5(ba)2 [20]
10. (ba)2d ⇒ adb2a [14]
11. b2a2c ⇒ a5baba2 [26]
12. baba2d ⇒ adb2a2 [22]
13. b2a3c ⇒ a5baba3 [30]
14. baba3d ⇒ adb2a3 [28]
15. b2a4c ⇒ a5baba4 [33]
16. baba4d ⇒ adb2a4 [32]
17. b2a5 ⇒ a5dbcb [36]
18. baba5 ⇒ d(bc)2 [29]
19. bab2 ⇒ d [3]
# ab:aaaaababba=1 reversed:cda/b aaaaaa=c,babb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaaa=c
bbc=aaaaabab
babd=adbb
bcba=cbab
bbac=aaaaababa
babad=adbba
bbaac=aaaaababaa
babaad=adbbaa
bbaaac=aaaaababaaa
babaaad=adbbaaa
bbaaaac=aaaaababaaaa
babaaaad=adbbaaaa
bbaaaaa=aaaaadbcb
babaaaaa=dbcbc
babb=d

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
91147⟨a, b | aaaaa=babb⟩Infinite cancellative non-commutative monoid
102614⟨a, b | ababba=bbbb⟩Infinite cancellative non-commutative monoid
114878⟨a, b | abbabbba=bbb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
9830⟨a, b | aabbbbba=b⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

3 total

Σ#PresentationMapping
101318⟨a, b | aaaababbaa=1⟩φ(a) = a, φ(b) = aaaaadab
101358⟨a, b | aaababbaaa=1⟩φ(a) = a, φ(b) = aaaaadab
101527⟨a, b | abbaaaaaab=1⟩φ(a) = a, φ(b) = aaaaadab

Anti-isomorphic instances

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

3 total

Σ#PresentationMapping
101301⟨a, b | aaaaabbaba=1⟩φ(a) = a, φ(b) = aaaaadab
101326⟨a, b | aaaabbabaa=1⟩φ(a) = a, φ(b) = aaaaadab
101526⟨a, b | ababbbbbba=1⟩φ(a) = aaaaadab, φ(b) = a