#1360 ⟨a, b | aaababbaba=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. ca ⇒ ac [5]
2. cd ⇒ 1 [8]
3. da ⇒ ad [12]
4. dc ⇒ 1 [13]
5. a4 ⇒ c [2]
6. cbab ⇒ babc [16]
7. dbab ⇒ babd [9]
8. ab2ab ⇒ babcbad [17]
9. acb2ab ⇒ babc2bad [19]
10. adb2ab ⇒ bab2ad [15]
11. a3bab2 ⇒ b2aba3 [25]
12. a3babcb ⇒ cb2aba3 [27]
13. a3babdb ⇒ db2aba3 [28]
14. a3babc2b ⇒ c2b2aba3 [30]
15. a3babd2b ⇒ d2b2aba3 [31]
16. ac2b2ab ⇒ babc3bad [26]
17. ad2b2ab ⇒ babdbad [18]
18. c3b2ab ⇒ a3babc3bad [32]
19. d3b2ab ⇒ a3babd3bad [34]
20. b2abcb ⇒ a3d [24]
# ab:aaababbaba=1 acd/b aaaa=c,babbab=d magic:0
ca=ac
cd=1
da=ad
dc=1
aaaa=c
cbab=babc
dbab=babd
abbab=babcbad
acbbab=babccbad
adbbab=babbad
aaababb=bbabaaa
aaababcb=cbbabaaa
aaababdb=dbbabaaa
aaababccb=ccbbabaaa
aaababddb=ddbbabaaa
accbbab=babcccbad
addbbab=babdbad
cccbbab=aaababcccbad
dddbbab=aaababdddbad
bbabcb=aaad

Other submonoids of same group

5 unique, 5 total

Σ#PresentationProperties
8388⟨a, b | aabbbaa=b⟩Can Inf
8520⟨a, b | aabaa=bbb⟩Can Inf
101694⟨a, b | aabababaa=b⟩Can Inf
102066⟨a, b | ababbaba=bb⟩Can Inf
102766⟨a, b | babab=aabaa⟩Can Inf

Isomorphic instances

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

3 total

Σ#PresentationMapping
101429⟨a, b | aababbabaa=1⟩φ(a) = a, φ(b) = aaadab
101525⟨a, b | ababbbbaba=1⟩φ(a) = aaadab, φ(b) = a
101535⟨a, b | abbabaaaab=1⟩φ(a) = a, φ(b) = aaadab