#2932 ⟨a, b | aaababaabba=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 [11]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [10]
5. a4 ⇒ c [2]
6. ba2b2c ⇒ a3baba2b [15]
7. baba2bd ⇒ adba2b2 [12]
8. b2cba ⇒ a(ab)2a2b [26]
9. bc(ba)2 ⇒ a2b2cb [29]
10. ba2b2ac ⇒ a3b(aba)2 [17]
11. b(aba)2d ⇒ adba2b2a [13]
12. ba2b2a2 ⇒ a3dbcbab [34]
13. ba(ba2)2 ⇒ dbcbabc [20]
14. baba2b2 ⇒ d [3]
15. bcbab3c ⇒ ab(a2ba)2ba2b [41]
16. bcbabcb2c ⇒ (c(ba)2)2ab [22]
17. b(aba)2b2c ⇒ a2db2a3cbaba2b [49]
18. b2cb2a2bd ⇒ a2dbcba2dba2b2 [30]
19. bcbab3ac ⇒ aba2ba3b(aba)2 [42]
20. bcbabcb2ac ⇒ (c(ba)2)2aba [39]
21. b(aba)2b2ac ⇒ a2db2a3cb(aba)2 [51]
22. b2cb2a2bad ⇒ a2dbcba2dba2b2a [43]
23. bcbab3a2 ⇒ aba2ba3dbcbab [52]
24. bcbabcb2a2 ⇒ cb(ab)2cbab [38]
25. b(aba)2b2a2 ⇒ a2db2a3bcbab [47]
26. b2cb(ba2)2 ⇒ a2(dbcba)2bc [50]
27. b2cb2a2b2 ⇒ a2dbcbad [25]
28. b2cb2a2bab2c ⇒ a2dbcba3db2a3cbaba2b [55]
29. b2cb2a2bab2ac ⇒ a2dbcba3db2a3cb(aba)2 [56]
30. b2cb2a2bab2a2 ⇒ a2dbcba3db2a3bcbab [54]
# ab:aaababaabba=1 reversed:cda/b aaaa=c,babaabb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaa=c
baabbc=aaababaab
babaabd=adbaabb
bbcba=aababaab
bcbaba=aabbcb
baabbac=aaababaaba
babaabad=adbaabba
baabbaa=aaadbcbab
babaabaa=dbcbabc
babaabb=d
bcbabbbc=abaabaaababaab
bcbabcbbc=cbabacbabaab
babaababbc=aadbbaaacbabaab
bbcbbaabd=aadbcbaadbaabb
bcbabbbac=abaabaaababaaba
bcbabcbbac=cbabacbabaaba
babaababbac=aadbbaaacbabaaba
bbcbbaabad=aadbcbaadbaabba
bcbabbbaa=abaabaaadbcbab
bcbabcbbaa=cbababcbab
babaababbaa=aadbbaaabcbab
bbcbbaabaa=aadbcbadbcbabc
bbcbbaabb=aadbcbad
bbcbbaababbc=aadbcbaaadbbaaacbabaab
bbcbbaababbac=aadbcbaaadbbaaacbabaaba
bbcbbaababbaa=aadbcbaaadbbaaabcbab

Other submonoids of same group

3 unique, 3 total

Σ#PresentationProperties
9981⟨a, b | abaabba=bb⟩Can Inf
113816⟨a, b | abbababbba=b⟩Can Inf
115856⟨a, b | abaaba=baabb⟩Can Inf

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationProperties
9845⟨a, b | abaabbba=b⟩Can Inf
114712⟨a, b | aabbabba=bab⟩Can Inf

Isomorphic instances

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

2 total

Σ#PresentationMapping
113060⟨a, b | aababaabbaa=1⟩φ(a) = a, φ(b) = aaadab
113214⟨a, b | abaabbaaaab=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.

4 total

Σ#PresentationMapping
112962⟨a, b | aaabbaababa=1⟩φ(a) = a, φ(b) = abaaad
113181⟨a, b | abaaaabbaab=1⟩φ(a) = a, φ(b) = abaaad
113229⟨a, b | ababaaaabba=1⟩φ(a) = a, φ(b) = abaaad
113289⟨a, b | abbababbbba=1⟩φ(a) = abaaad, φ(b) = a