#3068 ⟨a, b | aababababba=1⟩

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Contents

  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:
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 [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. (ba)2b2c ⇒ a(ab)4 [14]
9. b(ab)3d ⇒ ad(ba)2b2 [11]
10. (ba)2b2ac ⇒ a2(ba)4 [16]
11. (ba)4d ⇒ ad(ba)2b2a [12]
12. (ba)4a ⇒ adbab(bc)2 [26]
13. (ba)3b2 ⇒ d [3]
14. ba(b2c)2 ⇒ a2dba2cb(ab)3 [28]
15. bab2cb2ac ⇒ a2dba2c(ba)4 [30]
16. (b2c)3 ⇒ a2d(ba2)2cb(ab)3 [32]
17. b2(cb2)2ac ⇒ a2d(ba2)2c(ba)4 [33]
# ab:aababababba=1 reversed:cda/b aaa=c,babababb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
bcba=abbc
bbaa=aadbcb
bababbc=aabababab
babababd=adbababb
bababbac=aababababa
babababad=adbababba
babababaa=adbabbcbc
babababb=d
babbcbbc=aadbaacbababab
babbcbbac=aadbaacbabababa
bbcbbcbbc=aadbaabaacbababab
bbcbbcbbac=aadbaabaacbabababa

Other submonoids of same group

5 unique, 5 total

Σ#PresentationProperties
8423⟨a, b | aaaaba=bb⟩Can Inf
91022⟨a, b | aaaaba=bab⟩Can Inf
102398⟨a, b | aaaaba=baab⟩Can Inf
113771⟨a, b | ababababba=b⟩Can Inf
115486⟨a, b | aaaaba=baaab⟩Can Inf

Other submonoids of anti-isomorphic group

4 unique, 4 total

Σ#PresentationProperties
8354⟨a, b | aaaabba=b⟩Can Inf
9752⟨a, b | aaaababa=b⟩Can Inf
101584⟨a, b | aaaabaaba=b⟩Can Inf
113371⟨a, b | aaaabaaaba=b⟩Can Inf

Isomorphic instances

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

2 total

Σ#PresentationMapping
113245⟨a, b | abababbaaab=1⟩φ(a) = a, φ(b) = aadab
113251⟨a, b | ababbaaabab=1⟩φ(a) = a, φ(b) = aadab

Anti-isomorphic instances

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

3 total

Σ#PresentationMapping
113121⟨a, b | aabbabababa=1⟩φ(a) = a, φ(b) = abaad
113244⟨a, b | ababababbba=1⟩φ(a) = abaad, φ(b) = a
113247⟨a, b | abababbbaab=1⟩φ(a) = abaad, φ(b) = a