#4215 ⟨a, b | aabbbbbaa=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. ab4 ⇒ c [2]
2. acba2 ⇒ ab [3]
3. acbac ⇒ cb [4]
4. cb2a2 ⇒ acbab [7]
5. cb2ac ⇒ a(cb)2 [8]
6. c2ba2 ⇒ cb [15]
7. abcba2 ⇒ ab2 [5]
8. abcbac ⇒ cb2 [6]
9. cb5 ⇒ c2bac [17]
10. cb3a2 ⇒ abcbab [13]
11. cb3ac ⇒ ab(cb)2 [14]
12. (cb)2a2 ⇒ cb2 [16]
13. c2bacb ⇒ (cb)2ac [18]
14. ab2cba2 ⇒ ab3 [9]
15. ab2cbac ⇒ cb3 [10]
16. cb4a2 ⇒ ab2cbab [24]
17. cb4ac ⇒ ab2(cb)2 [25]
18. cb2cba2 ⇒ cb3 [20]
19. (cb)2acb ⇒ cb2cbac [21]
20. ab3cbab ⇒ c2baca2 [26]
21. ab3cba2 ⇒ c [11]
22. ab3cbac ⇒ cb4 [12]
23. ab3(cb)2 ⇒ c2b(ac)2 [27]
24. cb3cba2 ⇒ cb4 [19]
25. cb2cbacb ⇒ cb3cbac [23]
26. (cb)2aca2 ⇒ c2bab [30]
27. (cb)2(ac)2 ⇒ c(cb)2 [31]
28. cb4cba2 ⇒ c2bac [22]
29. cb3cbacb ⇒ cb4cbac [28]
30. cb2cbaca2 ⇒ (cb)2ab [32]
31. cb2cb(ac)2 ⇒ (cb)3 [33]
32. c2b(ac)2a2 ⇒ ab3cb2 [51]
33. cb4cbacb ⇒ (c2ba)2c [29]
34. cb3cbaca2 ⇒ cb2cbab [34]
35. cb3cb(ac)2 ⇒ cb2(cb)2 [35]
36. c2baca2b3 ⇒ ab3cbc [46]
37. ab(b2c)2bac ⇒ c2b(ac)3b [53]
38. cb4cbaca2 ⇒ cb3cbab [36]
39. cb4cb(ac)2 ⇒ cb3(cb)2 [39]
40. c2b(ac)2b4 ⇒ ab3cbc2bac [52]
41. c2b(ac)3a2 ⇒ ab3c2bab [54]
42. c2b(ac)4 ⇒ ab3c(cb)2 [56]
43. (c2ba)2ca2 ⇒ cb4cbab [37]
44. (c2ba)2cac ⇒ cb4(cb)2 [40]
45. a(b3c)2bac ⇒ c2b(ac)3b2 [58]
46. cb(cbac)2a2 ⇒ (c2ba)2b [38]
47. cb(cbac)2ac ⇒ c2bac(cb)2 [41]
48. a(b3cb)2ac ⇒ c2b(ac)3b3 [59]
49. cb2(cbac)2a2 ⇒ (cb)2ac2bab [42]
50. cb2(cbac)2ac ⇒ (cb)2ac(cb)2 [43]
51. c2baca2b2cbab ⇒ ab3cbc2baca2 [47]
52. c2baca2b2(cb)2 ⇒ ab3cbc2b(ac)2 [50]
53. c2b(ac)3b4 ⇒ ab3(c2ba)2c [60]
54. (c2baca)2a ⇒ ab3cbc2bab [55]
55. c(cb(ac)2)2 ⇒ ab3(cbc)2b [57]
56. cb3(cbac)2a2 ⇒ cb2cbac2bab [44]
57. cb3(cbac)2ac ⇒ cb2cbac(cb)2 [48]
58. cb4(cbac)2a2 ⇒ cb3cbac2bab [45]
59. cb4(cbac)2ac ⇒ cb3cbac(cb)2 [49]
60. c2b(ac)3cbaca2 ⇒ ab3(c2ba)2b [61]
61. c2b(ac)3cb(ac)2 ⇒ ab3c2bac(cb)2 [62]
62. c2baca2(b2c)2bac ⇒ ab3cbc2b(ac)3b [63]
63. c2baca2(b2cb)2ac ⇒ ab3cbc2b(ac)3b2 [64]
64. c2baca2b2cb4cbac ⇒ ab3cbc2b(ac)3b3 [65]
# ab:aabbbbbaa=ab bac abbbb=c morph:5/0
abbbb=c
acbaa=ab
acbac=cb
cbbaa=acbab
cbbac=acbcb
ccbaa=cb
abcbaa=abb
abcbac=cbb
cbbbbb=ccbac
cbbbaa=abcbab
cbbbac=abcbcb
cbcbaa=cbb
ccbacb=cbcbac
abbcbaa=abbb
abbcbac=cbbb
cbbbbaa=abbcbab
cbbbbac=abbcbcb
cbbcbaa=cbbb
cbcbacb=cbbcbac
abbbcbab=ccbacaa
abbbcbaa=c
abbbcbac=cbbbb
abbbcbcb=ccbacac
cbbbcbaa=cbbbb
cbbcbacb=cbbbcbac
cbcbacaa=ccbab
cbcbacac=ccbcb
cbbbbcbaa=ccbac
cbbbcbacb=cbbbbcbac
cbbcbacaa=cbcbab
cbbcbacac=cbcbcb
ccbacacaa=abbbcbb
cbbbbcbacb=ccbaccbac
cbbbcbacaa=cbbcbab
cbbbcbacac=cbbcbcb
ccbacaabbb=abbbcbc
abbbcbbcbac=ccbacacacb
cbbbbcbacaa=cbbbcbab
cbbbbcbacac=cbbbcbcb
ccbacacbbbb=abbbcbccbac
ccbacacacaa=abbbccbab
ccbacacacac=abbbccbcb
ccbaccbacaa=cbbbbcbab
ccbaccbacac=cbbbbcbcb
abbbcbbbcbac=ccbacacacbb
cbcbaccbacaa=ccbaccbab
cbcbaccbacac=ccbaccbcb
abbbcbbbbcbac=ccbacacacbbb
cbbcbaccbacaa=cbcbaccbab
cbbcbaccbacac=cbcbaccbcb
ccbacaabbcbab=abbbcbccbacaa
ccbacaabbcbcb=abbbcbccbacac
ccbacacacbbbb=abbbccbaccbac
ccbacaccbacaa=abbbcbccbab
ccbacaccbacac=abbbcbccbcb
cbbbcbaccbacaa=cbbcbaccbab
cbbbcbaccbacac=cbbcbaccbcb
cbbbbcbaccbacaa=cbbbcbaccbab
cbbbbcbaccbacac=cbbbcbaccbcb
ccbacacaccbacaa=abbbccbaccbab
ccbacacaccbacac=abbbccbaccbcb
ccbacaabbcbbcbac=abbbcbccbacacacb
ccbacaabbcbbbcbac=abbbcbccbacacacbb
ccbacaabbcbbbbcbac=abbbcbccbacacacbbb