#2861 ⟨a, b | aaaabababba=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 [13]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [12]
5. a5 ⇒ c [2]
6. bcba ⇒ ab2c [21]
7. b2a4 ⇒ a4dbcb [26]
8. bab2c ⇒ a3(ab)3 [17]
9. b(ab)2d ⇒ adbab2 [14]
10. bab2ac ⇒ a4(ba)3 [19]
11. (ba)3d ⇒ adbab2a [15]
12. bab2a2c ⇒ a4(ba)3a [28]
13. (ba)3ad ⇒ adbab2a2 [27]
14. bab2a3c ⇒ a3(ab)3a3 [30]
15. (ba)3a2d ⇒ adbab2a3 [29]
16. (ba)3a3 ⇒ adb(bc)2 [32]
17. (ba)2b2 ⇒ d [3]
18. (b2c)2 ⇒ a4dba4cb(ab)2 [34]
19. b2cb2ac ⇒ a4dba4c(ba)3 [35]
20. b2cb2a2c ⇒ a4dba4c(ba)3a [36]
21. b2cb2a3c ⇒ a4dba4c(ba)3a2 [37]
# ab:aaaabababba=1 reversed:cda/b aaaaa=c,bababb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaa=c
bcba=abbc
bbaaaa=aaaadbcb
babbc=aaaababab
bababd=adbabb
babbac=aaaabababa
bababad=adbabba
babbaac=aaaabababaa
bababaad=adbabbaa
babbaaac=aaaabababaaa
bababaaad=adbabbaaa
bababaaaa=adbbcbc
bababb=d
bbcbbc=aaaadbaaaacbabab
bbcbbac=aaaadbaaaacbababa
bbcbbaac=aaaadbaaaacbababaa
bbcbbaaac=aaaadbaaaacbababaaa

Other submonoids of same group

2 unique, 2 total

Σ#PresentationProperties
91180⟨a, b | aaaba=bbbb⟩Can Inf
114830⟨a, b | abababba=bbb⟩Can Inf

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationProperties
9788⟨a, b | aaabbbba=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
112938⟨a, b | aaabababbaa=1⟩φ(a) = a, φ(b) = aaaadab
113250⟨a, b | ababbaaaaab=1⟩φ(a) = a, φ(b) = aaaadab

Anti-isomorphic instances

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

4 total

Σ#PresentationMapping
112879⟨a, b | aaaabbababa=1⟩φ(a) = a, φ(b) = abaaaad
112970⟨a, b | aaabbababaa=1⟩φ(a) = a, φ(b) = abaaaad
113249⟨a, b | abababbbbba=1⟩φ(a) = abaaaad, φ(b) = a
113266⟨a, b | ababbbbbaab=1⟩φ(a) = abaaaad, φ(b) = a