#2975 ⟨a, b | aaabbabbaba=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. 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 [26]
2. cd ⇒ 1 [27]
3. cb ⇒ bc [5]
4. db ⇒ bd [29]
5. b2 ⇒ c [2]
6. a(ca)2b ⇒ (ca)2ba [32]
7. ac(ab)2 ⇒ d(ac)3 [33]
8. a4c ⇒ baba3 [42]
9. aba3d ⇒ bda4 [37]
10. acaba2b ⇒ da(ac)3 [34]
11. a4bc ⇒ baba3b [45]
12. aba3bd ⇒ bda4b [41]
13. aba4b ⇒ da3(ca)2 [38]
14. acaba3b ⇒ da2(ac)3 [35]
15. acaba4 ⇒ d [3]
16. (ac)3a3d ⇒ caca5 [48]
17. a3caca2b ⇒ ba3d(ac)3 [51]
18. (ac)3a3bd ⇒ caca5b [50]
19. (ac)3a4b ⇒ (ca)2bda3(ca)2 [54]
20. a3caca3b ⇒ ba3da(ac)3 [55]
21. a3caca4d ⇒ (ba4)2 [52]
22. a3caca4b ⇒ ba3da2(ac)3 [56]
23. a3da2(ac)3c ⇒ bda3(cab)2a3b [59]
24. a3caca5 ⇒ ba3d [49]
# ab:aaabbabbaba=1 reversed:cdb/a bb=c,abbabaaaa=d magic:1
dc=1
cd=1
cb=bc
db=bd
bb=c
acacab=cacaba
acabab=dacacac
aaaac=babaaa
abaaad=bdaaaa
acabaab=daacacac
aaaabc=babaaab
abaaabd=bdaaaab
abaaaab=daaacaca
acabaaab=daaacacac
acabaaaa=d
acacacaaad=cacaaaaa
aaacacaab=baaadacacac
acacacaaabd=cacaaaaab
acacacaaaab=cacabdaaacaca
aaacacaaab=baaadaacacac
aaacacaaaad=baaaabaaaa
aaacacaaaab=baaadaaacacac
aaadaaacacacc=bdaaacabcabaaab
aaacacaaaaa=baaad

Isomorphic instances

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

2 total

Σ#PresentationMapping
113090⟨a, b | aababbbbaab=1⟩φ(a) = b, φ(b) = a
113213⟨a, b | abaababbbba=1⟩φ(a) = b, φ(b) = a