#672 ⟨a, b | aababbaba=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. ca ⇒ ac [5]
2. cd ⇒ 1 [8]
3. da ⇒ ad [9]
4. dc ⇒ 1 [10]
5. a3 ⇒ c [2]
6. cbab ⇒ babc [14]
7. dbab ⇒ babd [11]
8. ab2ab ⇒ babcbad [15]
9. a2bab2 ⇒ b2aba2 [22]
10. a(ab)2cb ⇒ cb2aba2 [23]
11. a(ab)2db ⇒ db2aba2 [24]
12. acb2ab ⇒ babc2bad [16]
13. adb2ab ⇒ bab2ad [12]
14. c2b2ab ⇒ a(ab)2c2bad [26]
15. d2b2ab ⇒ a(ab)2d2bad [28]
16. b2abcb ⇒ a2d [21]
# ab:aababbaba=1 acd/b aaa=c,babbab=d magic:0
ca=ac
cd=1
da=ad
dc=1
aaa=c
cbab=babc
dbab=babd
abbab=babcbad
aababb=bbabaa
aababcb=cbbabaa
aababdb=dbbabaa
acbbab=babccbad
adbbab=babbad
ccbbab=aababccbad
ddbbab=aababddbad
bbabcb=aad

Other submonoids of same group

11 unique, 13 total

Σ#PresentationDescriptionRelated
7182⟨a, b | aabbaa=b⟩Infinite cancellative non-commutative monoid1 iso
7214⟨a, b | aabaa=bb⟩Infinite cancellative non-commutative monoid
8378⟨a, b | aababaa=b⟩Infinite cancellative non-commutative monoid
8519⟨a, b | aabaa=bab⟩Infinite cancellative non-commutative monoid
9796⟨a, b | aabaabaa=b⟩Infinite cancellative non-commutative monoid
9854⟨a, b | ababbaba=b⟩Infinite cancellative non-commutative monoid1 iso
91204⟨a, b | aabaa=baab⟩Infinite cancellative non-commutative monoid
101670⟨a, b | aabaaabaa=b⟩Infinite cancellative non-commutative monoid
102743⟨a, b | baaab=aabaa⟩Infinite cancellative non-commutative monoid
114843⟨a, b | ababbaba=bab⟩Infinite cancellative non-commutative monoid
115943⟨a, b | abbbba=bbabb⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

10 total

Σ#PresentationMapping
9719⟨a, b | ababbbaba=1⟩φ(a) = aadab, φ(b) = a
9725⟨a, b | abbabaaab=1⟩φ(a) = a, φ(b) = aadab
113042⟨a, b | aabaabbaaba=1⟩φ(a) = aad, φ(b) = aaba
113079⟨a, b | aababbabaab=1⟩φ(a) = babcbaaada, φ(b) = aadabab
113105⟨a, b | aabbaabaaab=1⟩φ(a) = aad, φ(b) = aaab
113188⟨a, b | abaaabaabba=1⟩φ(a) = aad, φ(b) = aaba
113212⟨a, b | abaababbaba=1⟩φ(a) = babcbaaada, φ(b) = abaadab
113258⟨a, b | ababbabbaba=1⟩φ(a) = abaadab, φ(b) = babcbaaada
113285⟨a, b | abbabaabaab=1⟩φ(a) = babcbaaada, φ(b) = aadabab
113293⟨a, b | abbabbbabba=1⟩φ(a) = aaba, φ(b) = aad