#310 ⟨a, b | aababbba=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Isomorphic instances

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. dc ⇒ 1 [10]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [9]
5. a3 ⇒ c [2]
6. bcba ⇒ cbab [19]
7. baba2 ⇒ d(bc)2 [21]
8. b3c ⇒ a2bab2 [14]
9. bab2d ⇒ adb3 [11]
10. b3ac ⇒ a2bab2a [16]
11. bab2ad ⇒ adb3a [12]
12. b3a2 ⇒ a2db2cb [26]
13. bab2a2 ⇒ db(bc)2 [24]
14. bab3 ⇒ d [3]
# ab:aababbba=1 reversed:cda/b aaa=c,babbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
bcba=cbab
babaa=dbcbc
bbbc=aababb
babbd=adbbb
bbbac=aababba
babbad=adbbba
bbbaa=aadbbcb
babbaa=dbbcbc
babbb=d

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
8450⟨a, b | aababa=bb⟩Infinite cancellative non-commutative monoid
101792⟨a, b | ababbabba=b⟩Infinite cancellative non-commutative monoid
102220⟨a, b | aabaaba=bab⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

2 total

Σ#PresentationMapping
8317⟨a, b | aabbbaba=1⟩φ(a) = b, φ(b) = a
8339⟨a, b | abbbaaab=1⟩φ(a) = a, φ(b) = b