#2209 ⟨a, b | aabaaab=aba⟩

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Contents

  1. Properties
  2. Rewriting system

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. c9b ⇒ cbc [25]
2. ca ⇒ ac2 [6]
3. c6bc8b ⇒ c6b2c [44]
4. c5ba ⇒ cbac [24]
5. abc ⇒ c2ba [8]
6. ac2bc ⇒ c3ba [12]
7. ac4bc ⇒ c4ba [16]
8. ac6b ⇒ cba [20]
9. ac8b ⇒ c2ba [22]
10. c6bc4ba ⇒ c6b2ac [53]
11. cbacbc ⇒ c5bc2ba [29]
12. cbac3bc ⇒ c5bc3ba [30]
13. cbac5bc ⇒ c(c4b)2a [41]
14. cbac7b ⇒ c5bcba [34]
15. c2bac5b ⇒ c6b2a [39]
16. c3ba2 ⇒ cba2c [14]
17. abac2 ⇒ c2ba2 [13]
18. ac2bac ⇒ cba2 [7]
19. ac4ba ⇒ abac [9]
20. a2c4b ⇒ aba [10]
21. c6b2acbc ⇒ c6bc4bc2ba [58]
22. c6b2ac3bc ⇒ c5(cbc3)2ba [59]
23. c6b2ac5bc ⇒ c2(c4b)3a [61]
24. c6b2ac7b ⇒ c6bc4bcba [62]
25. c6bc2ba2 ⇒ c6b2a2c [52]
26. (cba)2c2 ⇒ c5bc2ba2 [31]
27. cbac3bac ⇒ c5bcba2 [28]
28. c2(bac)2 ⇒ c6b2a2 [45]
29. cba2cbc ⇒ c(c2ba)2 [19]
30. cba2c3bc ⇒ (c3ba)2 [35]
31. cba2c5b ⇒ c3(ba)2 [33]
32. cba2c7b ⇒ c2(cba)2 [36]
33. cba3 ⇒ c5 [18]
34. abacbc ⇒ c3(cba)2 [37]
35. aba2 ⇒ c2 [5]
36. ac2ba2 ⇒ c3 [11]
37. a2ba ⇒ c [2]
38. c6b(bac)2c ⇒ c6bc4bc2ba2 [60]
39. c6b2ac3bac ⇒ c6bc4bcba2 [57]
40. c6b2a2cbc ⇒ c6b(c2ba)2 [48]
41. c6b2a2c3bc ⇒ c6bc2bac3ba [49]
42. c6b2a2c5b ⇒ c6bc2(ba)2 [50]
43. c6b2a2c7b ⇒ c6bc(cba)2 [51]
44. c6b2a3 ⇒ c6bc4 [46]
45. (cba)2a ⇒ c5bc2 [27]
46. cba2cba ⇒ c3bc [15]
47. cba2c2ba ⇒ c5bc [17]
48. cba2c3ba ⇒ c7bc [26]
49. a(ba)2 ⇒ c6b [21]
50. abacba ⇒ c8b [32]
51. ac2(ba)2 ⇒ c7b [23]
52. c6b2acba2 ⇒ c6bc4bc2 [56]
53. c6b2a2cba ⇒ c5(cbc)2 [55]
54. c6b2a2c2ba ⇒ c6bc4bc [54]
55. c6b2a2c3ba ⇒ (c6b)2c [47]
56. (cba)2ba ⇒ c5bc6b [40]
57. (cba)3 ⇒ c5bc8b [42]
58. cbac3(ba)2 ⇒ c5bc7b [43]
59. c6b2ac(ba)2 ⇒ c6bc4bc6b [63]
60. c6b2a(cba)2 ⇒ c6bc4bc8b [65]
61. c6b2ac3(ba)2 ⇒ c6bc4bc7b [64]
# ab:aabaaab=aba c/ba aaba=c morph:4/0
cccccccccb=cbc
ca=acc
ccccccbccccccccb=ccccccbbc
cccccba=cbac
abc=ccba
accbc=cccba
accccbc=ccccba
accccccb=cba
accccccccb=ccba
ccccccbccccba=ccccccbbac
cbacbc=cccccbccba
cbacccbc=cccccbcccba
cbacccccbc=cccccbccccba
cbacccccccb=cccccbcba
ccbacccccb=ccccccbba
cccbaa=cbaac
abacc=ccbaa
accbac=cbaa
accccba=abac
aaccccb=aba
ccccccbbacbc=ccccccbccccbccba
ccccccbbacccbc=ccccccbccccbcccba
ccccccbbacccccbc=ccccccbccccbccccba
ccccccbbacccccccb=ccccccbccccbcba
ccccccbccbaa=ccccccbbaac
cbacbacc=cccccbccbaa
cbacccbac=cccccbcbaa
ccbacbac=ccccccbbaa
cbaacbc=cccbaccba
cbaacccbc=cccbacccba
cbaacccccb=cccbaba
cbaacccccccb=cccbacba
cbaaa=ccccc
abacbc=ccccbacba
abaa=cc
accbaa=ccc
aaba=c
ccccccbbacbacc=ccccccbccccbccbaa
ccccccbbacccbac=ccccccbccccbcbaa
ccccccbbaacbc=ccccccbccbaccba
ccccccbbaacccbc=ccccccbccbacccba
ccccccbbaacccccb=ccccccbccbaba
ccccccbbaacccccccb=ccccccbccbacba
ccccccbbaaa=ccccccbcccc
cbacbaa=cccccbcc
cbaacba=cccbc
cbaaccba=cccccbc
cbaacccba=cccccccbc
ababa=ccccccb
abacba=ccccccccb
accbaba=cccccccb
ccccccbbacbaa=ccccccbccccbcc
ccccccbbaacba=ccccccbccbc
ccccccbbaaccba=ccccccbccccbc
ccccccbbaacccba=ccccccbccccccbc
cbacbaba=cccccbccccccb
cbacbacba=cccccbccccccccb
cbacccbaba=cccccbcccccccb
ccccccbbacbaba=ccccccbccccbccccccb
ccccccbbacbacba=ccccccbccccbccccccccb
ccccccbbacccbaba=ccccccbccccbcccccccb