#2853 ⟨a, b | aaaabaabbba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Isomorphic instances
  5. 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 [13]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [12]
5. a5 ⇒ c [2]
6. bcba2 ⇒ cba2b [22]
7. ba2ba3 ⇒ d(bc)2 [24]
8. b3c ⇒ a3ba2b2 [17]
9. ba2b2d ⇒ a2db3 [14]
10. b3ac ⇒ a3ba2b2a [19]
11. ba2b2ad ⇒ a2db3a [15]
12. b3a2c ⇒ a3ba2b2a2 [26]
13. ba2b2a2d ⇒ a2db3a2 [27]
14. b3a3 ⇒ a3db2cb [30]
15. ba2b2a3 ⇒ db(bc)2 [28]
16. ba2b3 ⇒ d [3]
# ab:aaaabaabbba=1 reversed:cda/b aaaaa=c,baabbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaa=c
bcbaa=cbaab
baabaaa=dbcbc
bbbc=aaabaabb
baabbd=aadbbb
bbbac=aaabaabba
baabbad=aadbbba
bbbaac=aaabaabbaa
baabbaad=aadbbbaa
bbbaaa=aaadbbcb
baabbaaa=dbbcbc
baabbb=d

Other submonoids of same group

1 unique, 1 total

Σ#PresentationProperties
114714⟨a, b | aabbabba=bbb⟩Can Inf

Isomorphic instances

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

3 total

Σ#PresentationMapping
112924⟨a, b | aaabaabbbaa=1⟩φ(a) = a, φ(b) = b
113134⟨a, b | aabbbaaaaab=1⟩φ(a) = a, φ(b) = b
113163⟨a, b | aabbbbbabba=1⟩φ(a) = b, 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
112886⟨a, b | aaaabbbaaba=1⟩φ(a) = a, φ(b) = b
112983⟨a, b | aaabbbaabaa=1⟩φ(a) = a, φ(b) = b
113133⟨a, b | aabbabbbbba=1⟩φ(a) = b, φ(b) = a
113176⟨a, b | abaaaaabbba=1⟩φ(a) = a, φ(b) = b