#3040 ⟨a, b | aabaababbba=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. cd ⇒ 1 [25]
2. dc ⇒ 1 [11]
3. bc ⇒ cb [5]
4. bd ⇒ db [24]
5. b3 ⇒ c [2]
6. ca3 ⇒ abacadb2 [31]
7. dabaca ⇒ a3b [8]
8. cba3 ⇒ (ba)2cadb2 [32]
9. d(ba)2ca ⇒ ba3b [27]
10. cb2a3 ⇒ b(ba)2cadb2 [35]
11. db(ba)2ca ⇒ b2a3b [34]
12. ba2baca ⇒ (aba)2c [29]
13. b2(aba)2 ⇒ ca2bacad [37]
14. d(a2b)2a ⇒ a3ba2db [33]
15. db(a2b)2a ⇒ ba3ba2db [26]
16. b2a3ba2 ⇒ a2baca2db2 [42]
17. b2(a2b)2a ⇒ ca2baca2d [40]
18. a(a2b)2a ⇒ d [3]
# ab:aabaababbba=1 cdb/a bbb=c,aaabaaba=d magic:1
cd=1
dc=1
bc=cb
bd=db
bbb=c
caaa=abacadbb
dabaca=aaab
cbaaa=babacadbb
dbabaca=baaab
cbbaaa=bbabacadbb
dbbabaca=bbaaab
baabaca=abaabac
bbabaaba=caabacad
daabaaba=aaabaadb
dbaabaaba=baaabaadb
bbaaabaa=aabacaadbb
bbaabaaba=caabacaad
aaabaaba=d

Other submonoids of same group

2 unique, 2 total

Σ#PresentationProperties
113612⟨a, b | aababbabba=b⟩Can Inf
115146⟨a, b | aabaaba=bbab⟩Can Inf

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationProperties
114091⟨a, b | aabaababa=bb⟩Can Inf

Isomorphic instances

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

2 total

Σ#PresentationMapping
113084⟨a, b | aababbbaaab=1⟩φ(a) = a, φ(b) = aabaabacab
113148⟨a, b | aabbbabbaba=1⟩φ(a) = aabaabacab, φ(b) = a

Anti-isomorphic instances

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

4 total

Σ#PresentationMapping
113083⟨a, b | aababbabbba=1⟩φ(a) = abaabaabac, φ(b) = a
113144⟨a, b | aabbbabaaba=1⟩φ(a) = a, φ(b) = abaabaabac
113198⟨a, b | abaaabbbaba=1⟩φ(a) = a, φ(b) = abaabaabac
113292⟨a, b | abbabbbaaab=1⟩φ(a) = abaabaabac, φ(b) = a