#2949 ⟨a, b | aaababbbaba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. 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 [16]
2. dc ⇒ 1 [19]
3. ac ⇒ ca [5]
4. ad ⇒ da [20]
5. a4 ⇒ c [2]
6. cbab2 ⇒ b2abc [24]
7. db2ab ⇒ bab2d [21]
8. abcbab ⇒ babcba [37]
9. cabab2 ⇒ ab2abc [25]
10. dab2ab ⇒ abab2d [23]
11. ca2bab2 ⇒ a2b2abc [29]
12. da2b2ab ⇒ a2bab2d [30]
13. a3babcb ⇒ (cb)2abda3 [43]
14. ca3bab2 ⇒ a3b2abc [34]
15. da3b2ab ⇒ a3bab2d [35]
16. ab3ab ⇒ b2abcbda [28]
17. a3b2abcb ⇒ cb3aba3 [42]
18. a3bab3 ⇒ b3aba3 [41]
19. b3abcb ⇒ da3 [32]
20. abcb2abcb ⇒ ba(bc)2(ab)2da3 [45]
# ab:aaababbbaba=1 cda/b aaaa=c,babbbab=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaaa=c
cbabb=bbabc
dbbab=babbd
abcbab=babcba
cababb=abbabc
dabbab=ababbd
caababb=aabbabc
daabbab=aababbd
aaababcb=cbcbabdaaa
caaababb=aaabbabc
daaabbab=aaababbd
abbbab=bbabcbda
aaabbabcb=cbbbabaaa
aaababbb=bbbabaaa
bbbabcb=daaa
abcbbabcb=babcbcababdaaa

Other submonoids of same group

2 unique, 2 total

Σ#PresentationProperties
102236⟨a, b | aababaa=bbb⟩Can Inf
114122⟨a, b | aabababaa=bb⟩Can Inf

Isomorphic instances

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

3 total

Σ#PresentationMapping
113087⟨a, b | aababbbabaa=1⟩φ(a) = a, φ(b) = daaaab
113091⟨a, b | aababbbbaba=1⟩φ(a) = daaaab, φ(b) = a
113299⟨a, b | abbbabaaaab=1⟩φ(a) = a, φ(b) = daaaab