#2815 ⟨a, b | aaaaabaabba=1⟩

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Contents

  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:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 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 ⇒ a4ba2b [18]
7. ba2bd ⇒ a2db2 [16]
8. b2ac ⇒ a3(aba)2 [20]
9. ba2bad ⇒ a2db2a [14]
10. bcba2 ⇒ cba2b [21]
11. b2a2c ⇒ a4(ba2)2 [24]
12. (ba2)2d ⇒ a2db2a2 [23]
13. b2a3c ⇒ a4ba2ba3 [27]
14. ba2ba3d ⇒ a2db2a3 [26]
15. b2a4 ⇒ a4dbcb [29]
16. ba2ba4 ⇒ d(bc)2 [25]
17. ba2b2 ⇒ d [3]
# ab:aaaaabaabba=1 reversed:cda/b aaaaaa=c,baabb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaaa=c
bbc=aaaabaab
baabd=aadbb
bbac=aaaabaaba
baabad=aadbba
bcbaa=cbaab
bbaac=aaaabaabaa
baabaad=aadbbaa
bbaaac=aaaabaabaaa
baabaaad=aadbbaaa
bbaaaa=aaaadbcb
baabaaaa=dbcbc
baabb=d

Other submonoids of same group

3 unique, 3 total

Σ#PresentationProperties
91238⟨a, b | aabba=bbbb⟩Can Inf
102342⟨a, b | ababbba=bbb⟩Can Inf
114350⟨a, b | abbabbbba=bb⟩Can Inf

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationProperties
9966⟨a, b | aabbbba=bb⟩Can Inf
101798⟨a, b | ababbbbba=b⟩Can Inf

Isomorphic instances

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

3 total

Σ#PresentationMapping
112851⟨a, b | aaaabaabbaa=1⟩φ(a) = a, φ(b) = aaaaadaaaaadaab
112920⟨a, b | aaabaabbaaa=1⟩φ(a) = a, φ(b) = aaaaadaaaaadaab
113095⟨a, b | aabbaaaaaab=1⟩φ(a) = a, φ(b) = aaaaadaaaaadaab

Anti-isomorphic instances

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

4 total

Σ#PresentationMapping
112827⟨a, b | aaaaabbaaba=1⟩φ(a) = a, φ(b) = aabaaaaadaaaaad
112873⟨a, b | aaaabbaabaa=1⟩φ(a) = a, φ(b) = aabaaaaadaaaaad
113172⟨a, b | abaaaaaabba=1⟩φ(a) = a, φ(b) = aabaaaaadaaaaad
113294⟨a, b | abbabbbbbba=1⟩φ(a) = aabaaaaadaaaaad, φ(b) = a