Morphocompletion for #10660 ⟨a, b | aaaa=bab, bbbb=1⟩

Back:⟨a, b | aaaa=bab, bbbb=1⟩

Solved by morph:3/0,13/0. (See Morphocompletion.)

Step 1

Checking up to 80 rules for overlaps.

Rewriting system is not complete: roundsLimit

#Rule
1. aaaaab ⇒ baaaaa
2. bab ⇒ aaaa
3. abaab ⇒ bbaaaaaaaaa
4. aaaabbaaaa ⇒ baab
5. bbbaaaa ⇒ ab
6. aaaabbb ⇒ ba
7. aaaabbaabaaaaa ⇒ baabaaab
8. aaaabbaaabaaaaa ⇒ baabaaaab
9. bbbb ⇒ 1
10. bbbaabaaaaa ⇒ abaaab
11. bbbaaabaaaaa ⇒ abaaaab
12. abaaabbb ⇒ bbbaaaba
13. aaaabbaabbaaaaa ⇒ baabaaabb
14. aaaabbaabaaabaaaaa ⇒ baabaaabaaab
15. aaaabbaabaaaabaaaaa ⇒ baabaaabaaaab
16. aaaabbaaabbaaaaa ⇒ baabaaaabb
17. aaaabbaaabaaabaaaaa ⇒ baabaaaabaaab
18. aaaabbaaabaaaabaaaaa ⇒ baabaaaabaaaab
19. bbbaabbaaaaa ⇒ abaaabb
20. bbbaabaaabaaaaa ⇒ abaaabaaab
21. bbbaabaaaabaaaaa ⇒ abaaabaaaab
22. bbbaaabbaaaaa ⇒ abaaaabb
23. bbbaaabaaabaaaaa ⇒ abaaaabaaab
24. bbbaaabaaaabaaaaa ⇒ abaaaabaaaab
25. aaaabbaabbaaba ⇒ baabaaabaaaabb
26. aaaabbaabbaaabaaaaa ⇒ baabaaabbaaab
27. aaaabbaabbaaaabaaaaa ⇒ baabaaabbaaaab
28. aaaabbaabaaabbaaaaa ⇒ baabaaabaaabb
29. aaaabbaaabbaaba ⇒ baabaaaabaaaabb
30. aaaabbaaabbaaabaaaaa ⇒ baabaaaabbaaab
31. aaaabbaaabbaaaabaaaaa ⇒ baabbaabb
32. aaaabbaaabaaabbaaaaa ⇒ baabaaaabaaabb
33. bbbaabbaaba ⇒ abaaabaaaabb
34. bbbaabbaaabaaaaa ⇒ abaaabbaaab
35. bbbaabbaaaabaaaaa ⇒ abaaabbaaaab
36. bbbaabaaabbaaaaa ⇒ abaaabaaabb
37. bbbaabaaabaaabaaaaa ⇒ abaaabaaabaaab
38. bbbaabaaabaaaabaaaaa ⇒ abaaabaaabaaaab
39. bbbaaabbaaba ⇒ abaaaabaaaabb
40. bbbaaabbaaabaaaaa ⇒ abaaaabbaaab
41. bbbaaabbaaaabaaaaa ⇒ abbaabb
42. bbbaaabaaabbaaaaa ⇒ abaaaabaaabb
43. abaaabbaabbb ⇒ bbbaabbaaaba
44. abaaabbaaabbb ⇒ bbbaabbaaaaba
45. abaaabaaabbaaaabb ⇒ bbaaaabbaaabaaaba
46. abaaaabbaabbb ⇒ bbbaaabbaaaba
47. abaaaabbaaabbb ⇒ bbbaaabbaaaaba
48. aaaabbaabbbaaba ⇒ baabaaabbaaaabb
49. aaaabbaabbaabbaaaaa ⇒ baabaaabbaabb
50. aaaabbaabbaaabbaaaaa ⇒ baabaaabbaaabb
51. aaaabbaaabbbaaba ⇒ baabbaabbb
52. aaaabbaaabbbaaaba ⇒ baabbaaabbb
53. aaaabbaaabbaabbaaaaa ⇒ baabaaaabbaabb
54. bbbaabbbaaba ⇒ abaaabbaaaabb
55. bbbaabbaabbaaaaa ⇒ abaaabbaabb
56. bbbaabbaaabbaaaaa ⇒ abaaabbaaabb
57. bbbaabaaabbaaba ⇒ abaaabaaabaaaabb
58. bbbaabaaaabbaaba ⇒ abaaabaaaabaaaabb
59. bbbaaabbbaaba ⇒ abbaabbb
60. bbbaaabbbaaaba ⇒ abbaaabbb
61. bbbaaabbaabbaaaaa ⇒ abaaaabbaabb
62. bbbaaabbaaabbaaaaa ⇒ abaaaabbaaabb
63. bbbaaabbaaaabaaabaaaaa ⇒ abbaabbaaab
64. bbbaaabaaabbaaba ⇒ abaaaabaaabaaaabb
65. abbaabbaabbb ⇒ bbbaaabbaaaabaaaba
66. abbaabbaaabbb ⇒ bbbaaabbaaaabaaaaba
67. abbaabaaabbaaaabb ⇒ bbbaaabbaaabaaaba
68. bbbaabbaaabbaaba ⇒ abaaabbaaabaaaabb
69. bbbaaabbaaaabbaaba ⇒ abbaabbaaaabb
70. abbaabbbaabbb ⇒ bbbaaabbaaaabbaaaba
71. abbaabbbaaabbb ⇒ bbbaaabbbaabba
72. abbaaabbbaaabbb ⇒ bbbaaabbbaaabba
73. abaaabbaaabbaabbb ⇒ bbbaabbaaabbaaaba
74. abaaabbaaaabbaaabbb ⇒ bbbaabbbaabba
75. bbbaabbaabbbaaba ⇒ abaaabbaabbaaaabb
76. bbbaaabbbaabbaab ⇒ abbaabbbaaabbaaaa
77. bbbaaabbbaabbaaaba ⇒ abbaaabbaabbb
78. bbbaaabbbaabbaaaaba ⇒ abbaaabbaaabbb
79. bbbaaabbbaaabbaaaba ⇒ abbaaaabbaabbb
80. bbbaaabbbaabbbaaaba ⇒ abbaaabbbaabbb
...

Collecting factors up to length 7, frequency 2:

Length 2:[2/0] bb, [2/1] ba
Length 3:[3/0] bbb, [3/1] aba
Length 4:[4/0] abba, [4/1] aaaa
Length 5:[5/0] aaaaa, [5/1] aaaab
Length 6:[6/0] aaaabb, [6/1] abbaab

Considering [length 3 / frequency 0] bbb=c.

Step 2

Checking up to 80 rules for overlaps.

Rewriting system is not complete: arenaTotalLimit

#Rule
1. aaaaab ⇒ baaaaa
2. caaaa ⇒ ab
3. aaaac ⇒ ba
4. bab ⇒ aaaa
5. abaab ⇒ bbaaaaaaaaa
6. aaaabbaaaa ⇒ baab
7. bc ⇒ 1
8. bac ⇒ aaaabb
9. cb ⇒ 1
10. cab ⇒ bbaaaa
11. caaba ⇒ abaac
12. caaaba ⇒ abaaac
13. cc ⇒ bb
14. bbb ⇒ c
15. aaaabbaabaaaaa ⇒ baabaaab
16. aaaabbaaabaaaaa ⇒ baabaaaab
17. baabaac ⇒ aaaabbaaba
18. baabaaac ⇒ aaaabbaaaba
19. caabba ⇒ abaacaaac
20. caaabba ⇒ abaaacaaac
21. bbaaaabb ⇒ cac
22. aaaabbaabbaaaaa ⇒ baabaaabb
23. aaaabbaabaaabaaaaa ⇒ baabaaabaaab
24. aaaabbaaabbaaaaa ⇒ baabaaaabb
25. baabaaabaac ⇒ aaaabbaabaaaba
26. baabaaabaaac ⇒ aaaabbaabaaaaba
27. baabaaaabaac ⇒ aaaabbaaabaaaba
28. baabaaaabaaac ⇒ aaaabbaaabaaaaba
29. abaacaaacaaac ⇒ caaca
30. abaaacaaacaaac ⇒ caaaca
31. aaacaaacaaacaab ⇒ baacaaacaaacaaa
32. acacaaacaaac ⇒ caaacaaacaca
33. acaacaaacaaac ⇒ caaacaaacaaca
34. acaaacaaacaaac ⇒ caaacaaacaaaca
35. aaacaaacaaacaca ⇒ baacaaacaaac
36. aaacaaacaaacaaca ⇒ baaacaaacaaac
37. bbaaaabaaaabb ⇒ cacac
38. aaaabbaabbaaba ⇒ baabaaabaaaabb
39. aaaabbaaabbaaba ⇒ baabaaaabaaaabb
40. aaaabbaaabbaaaabaaaaa ⇒ baabbaabb
41. baabaaabbaac ⇒ aaaabbaabbaaaba
42. baabaaabbaaac ⇒ aaaabbaabbaaaaba
43. baabaaaabbaac ⇒ aaaabbaaabbaaaba
44. baabaaaabbaaac ⇒ aaaabbaaabbaaaaba
45. abaaabbaaacaaac ⇒ caacaca
46. abaaaabbaaacaaac ⇒ caaacaca
47. abbaacaaacaaac ⇒ caaacaaca
48. abbaaacaaacaaac ⇒ caaacaaaca
49. abaacaaacaaabb ⇒ caacac
50. abaaacaaacaaabb ⇒ caaacac
51. caaacaaacacac ⇒ acacaaacaaabb
52. caaacaaacaacac ⇒ acaacaaacaaabb
53. caaacaaacaaacac ⇒ acaaacaaacaaabb
54. bbaaaabaaaabaaaabb ⇒ cacacac
55. abbaabbaaacaaac ⇒ caaacacaca
56. abbaaabbaaacaaac ⇒ caaacaacaca
57. abaaabbaaaabaaacaaac ⇒ caacacaca
58. abaaabbaaacaaabb ⇒ caacacac
59. abaaaabbaaacaaabb ⇒ caaacacac
60. abbaacaaacaaabb ⇒ caaacaacac
61. abbaaacaaacaaabb ⇒ caaacaaacac
62. abaaabaacaaacaacaaac ⇒ cacaacaca
63. abaaabaaacaaacaacaaac ⇒ cacaaacaca
64. abaaaabaacaaacaacaaac ⇒ caacaacaca
65. abaaacacaaacaaabb ⇒ caacaacac
66. abaaacaacaaacaaabb ⇒ caacaaacac
67. cacacaaacaaabb ⇒ bbaaacaaacacac
68. cacaacaaacaaabb ⇒ bbaaacaaacaacac
69. abbaabbaaacaaabb ⇒ caaacacacac
70. abbaaabbaaacaaabb ⇒ caaacaacacac
71. abaacaacacaaacaaabb ⇒ cacaacaacac
...

Collecting factors up to length 14, frequency 1:

Length 2:[2/0] ba
Length 3:[3/0] aca
Length 4:[4/0] aaac
Length 5:[5/0] aaaaa
Length 6:[6/0] aaaabb
Length 7:[7/0] aaacaaa
Length 8:[8/0] aaacaaac
Length 9:[9/0] caaacaaac
Length 10:[10/0] caaacaaabb
Length 11:[11/0] aaacaaacaaa
Length 12:[12/0] aaacaaacaaac
Length 13:[13/0] caaacaaacaaac

Considering [length 13 / frequency 0] caaacaaacaaac=d.

Step 3

Rewriting system is complete. See ⟨a, b | aaaa=bab, bbbb=1⟩.