#4140 ⟨a, b | aababbbaa=ab⟩

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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. a2bca ⇒ ab [3]
2. cbca2 ⇒ a2bc2 [23]
3. cabca ⇒ cb [5]
4. (ab)2ca ⇒ ab2 [7]
5. (a2b)2c2 ⇒ ab2caca2 [24]
6. a2bcb ⇒ ab2ca [8]
7. cbabca ⇒ cb2 [9]
8. cba2bc2 ⇒ a2bc2b(ca)3a [33]
9. (cb)2 ⇒ a2bc2b(ca)2 [22]
10. cbcab ⇒ a2bc2bca [17]
11. caba2bc2 ⇒ cb2caca2 [25]
12. cabcb ⇒ cb2ca [10]
13. ab3a ⇒ c [2]
14. ab2abca ⇒ ab3 [11]
15. (ab)2a2bc2 ⇒ ab3caca2 [27]
16. (ab)2cb ⇒ ab3ca [13]
17. a(ab)3c2 ⇒ ab2(ca)2ba [35]
18. cb3a ⇒ ab3c [4]
19. cb2abca ⇒ cb3 [12]
20. cb(ab)2c2 ⇒ a2bc2b(ca)3ba [42]
21. cbaba2bc2 ⇒ cb3caca2 [29]
22. cbabcb ⇒ cb3ca [15]
23. c(ab)3c2 ⇒ cb2(ca)2ba [36]
24. ab4 ⇒ cbca [14]
25. ab2aba2bc2 ⇒ cb(ca)3a [31]
26. ab2abcb ⇒ cb(ca)2 [18]
27. (ab)4c2 ⇒ ab3(ca)2ba [38]
28. a2bab3c ⇒ ab2cab2a [20]
29. a2(bab)2c2 ⇒ ab2(ca)2b2a [43]
30. cb4 ⇒ ab3cbca [16]
31. cb2aba2bc2 ⇒ ab3cb(ca)3a [34]
32. cb2abcb ⇒ ab3cb(ca)2 [19]
33. cbab3c ⇒ a2bc2b(ca)2b2a [32]
34. c(bab)2c2 ⇒ a2bc2b(ca)3b2a [49]
35. cb(ab)3c2 ⇒ cb3(ca)2ba [39]
36. cabab3c ⇒ cb2cab2a [21]
37. ca(bab)2c2 ⇒ cb2(ca)2b2a [44]
38. ab2(ab)3c2 ⇒ cb(ca)3ba [40]
39. (ab)3b2c ⇒ ab3cab2a [26]
40. (ab)3babc2 ⇒ ab3(ca)2b2a [45]
41. cb2(ab)3c2 ⇒ ab3cb(ca)3ba [41]
42. c(ba)2b3c ⇒ cb3cab2a [28]
43. cba(bab)2c2 ⇒ cb3(ca)2b2a [46]
44. ab(ba)2b3c ⇒ cb(ca)2b2a [30]
45. (ab2ab)2c2 ⇒ cb(ca)3b2a [47]
46. cb(ba)2b3c ⇒ ab3cb(ca)2b2a [37]
47. cb2a(bab)2c2 ⇒ ab3cb(ca)3b2a [48]
# ab:aababbbaa=ab a/c/b abbba=c morph:5/0
aabca=ab
cbcaa=aabcc
cabca=cb
ababca=abb
aabaabcc=abbcacaa
aabcb=abbca
cbabca=cbb
cbaabcc=aabccbcacacaa
cbcb=aabccbcaca
cbcab=aabccbca
cabaabcc=cbbcacaa
cabcb=cbbca
abbba=c
abbabca=abbb
ababaabcc=abbbcacaa
ababcb=abbbca
aabababcc=abbcacaba
cbbba=abbbc
cbbabca=cbbb
cbababcc=aabccbcacacaba
cbabaabcc=cbbbcacaa
cbabcb=cbbbca
cabababcc=cbbcacaba
abbbb=cbca
abbabaabcc=cbcacacaa
abbabcb=cbcaca
ababababcc=abbbcacaba
aababbbc=abbcabba
aababbabcc=abbcacabba
cbbbb=abbbcbca
cbbabaabcc=abbbcbcacacaa
cbbabcb=abbbcbcaca
cbabbbc=aabccbcacabba
cbabbabcc=aabccbcacacabba
cbabababcc=cbbbcacaba
cababbbc=cbbcabba
cababbabcc=cbbcacabba
abbabababcc=cbcacacaba
abababbbc=abbbcabba
abababbabcc=abbbcacabba
cbbabababcc=abbbcbcacacaba
cbababbbc=cbbbcabba
cbababbabcc=cbbbcacabba
abbababbbc=cbcacabba
abbababbabcc=cbcacacabba
cbbababbbc=abbbcbcacabba
cbbababbabcc=abbbcbcacacabba