#670 ⟨a, b | aabababba=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group
  5. Isomorphic instances
  6. Anti-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 ⇒ ab2c [18]
7. b2a2 ⇒ a2dbcb [23]
8. bab2c ⇒ a(ab)3 [14]
9. b(ab)2d ⇒ adbab2 [11]
10. bab2ac ⇒ a2(ba)3 [16]
11. (ba)3d ⇒ adbab2a [12]
12. (ba)3a ⇒ adb(bc)2 [26]
13. (ba)2b2 ⇒ d [3]
14. (b2c)2 ⇒ a2dba2cb(ab)2 [28]
15. b2cb2ac ⇒ a2dba2c(ba)3 [29]
# ab:aabababba=1 reversed:cda/b aaa=c,bababb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
bcba=abbc
bbaa=aadbcb
babbc=aababab
bababd=adbabb
babbac=aabababa
bababad=adbabba
bababaa=adbbcbc
bababb=d
bbcbbc=aadbaacbabab
bbcbbac=aadbaacbababa

Other submonoids of same group

6 unique, 6 total

Σ#PresentationDescriptionRelated
7207⟨a, b | aaaba=bb⟩Infinite cancellative non-commutative monoid
8504⟨a, b | aaaba=bab⟩Infinite cancellative non-commutative monoid
9850⟨a, b | abababba=b⟩Infinite cancellative non-commutative monoid
91174⟨a, b | aaaba=baab⟩Infinite cancellative non-commutative monoid
114828⟨a, b | abababba=bab⟩Infinite cancellative non-commutative monoid
115942⟨a, b | abbbba=babbb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

6 unique, 6 total

Σ#PresentationDescriptionRelated
7174⟨a, b | aaabba=b⟩Infinite cancellative non-commutative monoid
8362⟨a, b | aaababa=b⟩Infinite cancellative non-commutative monoid
9765⟨a, b | aaabaaba=b⟩Infinite cancellative non-commutative monoid
101612⟨a, b | aaabaaaba=b⟩Infinite cancellative non-commutative monoid
102742⟨a, b | baaab=aaaba⟩Infinite cancellative non-commutative monoid
113430⟨a, b | aaabaaaaba=b⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

8 total

Σ#PresentationMapping
9716⟨a, b | ababbaaab=1⟩φ(a) = a, φ(b) = aadab
113069⟨a, b | aabababbaab=1⟩φ(a) = cbababaada, φ(b) = aadabab
113106⟨a, b | aabbaabaaba=1⟩φ(a) = aad, φ(b) = aaba
113194⟨a, b | abaaabbaaba=1⟩φ(a) = aad, φ(b) = aaba
113202⟨a, b | abaabaaabba=1⟩φ(a) = aad, φ(b) = aaba
113210⟨a, b | abaabababba=1⟩φ(a) = cbababaada, φ(b) = abaadab
113253⟨a, b | ababbaabaab=1⟩φ(a) = cbababaada, φ(b) = aadabab
113291⟨a, b | abbabbabbba=1⟩φ(a) = aaba, φ(b) = aad

Anti-isomorphic instances

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

10 total

Σ#PresentationMapping
9682⟨a, b | aabbababa=1⟩φ(a) = a, φ(b) = aadab
9715⟨a, b | abababbba=1⟩φ(a) = aadab, φ(b) = a
9718⟨a, b | ababbbaab=1⟩φ(a) = aadab, φ(b) = a
113034⟨a, b | aabaabaabba=1⟩φ(a) = aad, φ(b) = aaba
113041⟨a, b | aabaabbaaab=1⟩φ(a) = aad, φ(b) = aaab
113100⟨a, b | aabbaaabaab=1⟩φ(a) = aad, φ(b) = aaab
113120⟨a, b | aabbababaab=1⟩φ(a) = cbababaada, φ(b) = aadabab
113218⟨a, b | abaabbababa=1⟩φ(a) = cbababaada, φ(b) = abaadab
113246⟨a, b | abababbabba=1⟩φ(a) = abaadab, φ(b) = cbababaada
113257⟨a, b | ababbabbaab=1⟩φ(a) = aadabab, φ(b) = cbababaada