Morphocompletion for #4107 ⟨a, b | bab=aaa, bbbb=1⟩

Back:⟨a, b | bab=aaa, bbbb=1⟩

Solved by morph:3/0,10/0. (See Morphocompletion.)

Step 1

Checking up to 80 rules for overlaps.

Rewriting system is not complete: roundsLimit

#Rule
1. aaaab ⇒ baaaa
2. bab ⇒ aaa
3. abaab ⇒ bbaaaaaaa
4. aaabbaaa ⇒ baab
5. bbbaaa ⇒ ab
6. aaabbb ⇒ ba
7. aaabbaabaaaa ⇒ baabaaab
8. bbbb ⇒ 1
9. bbbaabaaaa ⇒ abaaab
10. aaabbaabbaaaa ⇒ baabaaabb
11. aaabbaabaaabaaaa ⇒ baabaaabaaab
12. bbbaabbaaaa ⇒ abaaabb
13. bbbaabaaabaaaa ⇒ abaaabaaab
14. aaabbaabbaaba ⇒ baabaaabaaabb
15. aaabbaabbaaabaaaa ⇒ baabbaabb
16. aaabbaabaaabaaabaaaa ⇒ baabaaabaaabaaab
17. bbbaabbaaba ⇒ abaaabaaabb
18. bbbaabbaaabaaaa ⇒ abbaabb
19. bbbaabaaabaaabaaaa ⇒ abaaabaaabaaab
20. abaaabbaabbb ⇒ bbbaabbaaaba
21. aaabbaabbbaaba ⇒ baabbaabbb
22. aaabbaabbaabbaaaa ⇒ baabaaabbaabb
23. aaabbaabbaaabaaabaaaa ⇒ baabbaabbaaab
24. aaabbaabaaabbaaba ⇒ baabaaabaaabaaabb
25. aaabbaabaaabaaabaaabaaaa ⇒ baabaaabaaabaaabaaab
26. bbbaabbbaaba ⇒ abbaabbb
27. bbbaabbaabbaaaa ⇒ abaaabbaabb
28. bbbaabbaaabaaabaaaa ⇒ abbaabbaaab
29. bbbaabaaabbaaba ⇒ abaaabaaabaaabb
30. bbbaabaaabaaabaaabaaaa ⇒ abaaabaaabaaabaaab
31. abbaabbaabbb ⇒ bbbaabbaaabaaaba
32. aaabbaabbaabbaab ⇒ baabaaabaaabbaabbaaa
33. aaabbaabbaabbaaabaaaa ⇒ baabaaabbaabbaaab
34. aaabbaabbaaabbaaba ⇒ baabbaabbaaabb
35. aaabbaabbaaabaaabaaabaaaa ⇒ baabbaabbaaabaaab
36. aaabbaabaaabaaabbaaba ⇒ baabaaabaaabaaabaaabb
37. bbbaabbaabbaab ⇒ abaaabaaabbaabbaaa
38. bbbaabbaabbaaabaaaa ⇒ abaaabbaabbaaab
39. bbbaabbaaabbaaba ⇒ abbaabbaaabb
40. bbbaabbaaabaaabaaabaaaa ⇒ abbaabbaaabaaab
41. bbbaabaaabaaabbaaba ⇒ abaaabaaabaaabaaabb
42. bbbaabaaabaaabaaabaaabaaaa ⇒ abaaabaaabaaabaaabaaab
43. abbaabbbaabbb ⇒ bbbaabbbaabba
44. abaaabaaabbaabbaaabb ⇒ bbaaabbaabbaaabaaaba
45. aabbbaabbaaabaaabaaaba ⇒ baabaaabbaabbaaabb
46. aaabbaabbbaabbaab ⇒ baabbaabbbaabbaaa
47. aaabbaabbbaabbaaaba ⇒ baabbaaabbaabbb
48. aaabbaabbaabbaaabaaabaaaa ⇒ baabaaabbaabbaaabaaab
49. aaabbaabbaaabaaabbaaba ⇒ baabbaabbaaabaaabb
50. aaabbaabaaabbaabbaab ⇒ baabaaabaaabaaabbaabbaaa
51. bbbaabbbaabbaab ⇒ abbaabbbaabbaaa
52. bbbaabbbaabbaaaba ⇒ abbaaabbaabbb
53. bbbaabbaabbbaaba ⇒ abaaabbaabbaaabb
54. bbbaabbaabbaaabaaabaaaa ⇒ abaaabbaabbaaabaaab
55. bbbaabbaaabaaabbaaba ⇒ abbaabbaaabaaabb
56. bbbaabbaaabaaabaaabaaabaaaa ⇒ abbaabbaaabaaabaaab
57. bbbaabaaabbaabbaab ⇒ abaaabaaabaaabbaabbaaa
58. bbbaabaaabaaabaaabbaaba ⇒ abaaabaaabaaabaaabaaabb
59. abbaabbaaabbaabbb ⇒ bbbaabbaaabbaabba
60. abbaabaaabbaabbaaabb ⇒ bbbaabbaabbaaabaaaba
61. abaaabbaabbaabbaaabb ⇒ bbaaabbaabbaaabaaabaaaba
62. aaabbaabbaabbaaabbaaba ⇒ baabaaabbaabbaaabaaabb
63. aaabbaabbaaabbaabbaab ⇒ baabbaabbaaabbaabbaaa
64. bbbaabbaabbaaabbaaba ⇒ abaaabbaabbaaabaaabb
65. bbbaabbaaabbaabbaab ⇒ abbaabbaaabbaabbaaa
66. bbbaabbaaabaaabaaabbaaba ⇒ abbaabbaaabaaabaaabb
67. abbaabbbaabbaabbb ⇒ bbbaabbaaabbaabbaaaba
68. abbaabbaabbaabbaaabb ⇒ bbbaabbaabbaaabaaabaaaba
69. aabbbaabbbaabbbaab ⇒ baabbbaabbbaabbbaa
70. aabbbaabbbaabbaaabba ⇒ baabbbaabbbaabbb
71. aabbbaabbaaabbaabbaaaba ⇒ baabbaabbbaabbaaabb
72. aaabbaabbbaabbaaabbaab ⇒ baabbaaabbaabbbaabbaaa
73. bbbaabbbaabbbaabba ⇒ abbbaabbbaabbb
74. bbbaabbbaabbaaabbaab ⇒ abbaaabbaabbbaabbaaa
75. bbbaabbaabbbaabbaab ⇒ abaaabbaabbaaabbaabbaaa
76. bbbaabbaaabbaabbaaabaaaba ⇒ abbaaabaaabbaabbaaabb
77. bbbaabbaaabaaabbaabbaab ⇒ abbaabbaaabaaabbaabbaaa
78. bbbaabbaabbbaabbaaabaaaba ⇒ abbaabbaaabbaabbaaabb
79. abbbaabbbaabbbaabbb ⇒ bbbaabbbaabbbaabbba
80. abbaabbbaabbaaabbaabbb ⇒ bbbaabbaaabbaabbbaabba
...

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] aaaa, [4/1] aaab
Length 5:[5/0] aaabb, [5/1] baaba
Length 6:[6/0] abbaab, [6/1] bbbaab

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

Step 2

Checking up to 80 rules for overlaps.

Rewriting system is not complete: wordLimit

#Rule
1. aaaac ⇒ caaaa
2. caaac ⇒ a
3. acc ⇒ caacaaa
4. aaacaac ⇒ cca
5. ccca ⇒ aaac
6. caacaacaaa ⇒ ac
7. aaacacaacaaa ⇒ ccac
8. cccc ⇒ 1
9. caacacaacaaaaaaa ⇒ acac
10. caacaacacaaaa ⇒ acaac
11. acacaacaac ⇒ caacaacaca
12. acaacaacaac ⇒ caacaacaaca
13. aaacacacaacaaaaaaa ⇒ ccacac
14. aaacacaacacaaaa ⇒ ccacaac
15. caacacacaacaaaaaaaaaaa ⇒ acacac
16. caacacaacacaaaaaaaa ⇒ acacaac
17. caacaacacacaaaa ⇒ acaacac
18. caacaacacaacaaaa ⇒ acaacaac
19. caacaacaacaca ⇒ aacaacaac
20. acacaacacaacaaa ⇒ caacaacacac
21. acaacaacacaacaaa ⇒ caacaacaacac
22. aacaacaacacaca ⇒ ccacaacaac
23. aacaacaacacaaca ⇒ ccaacaacaac
24. aaacacacacaacaaaaaaaaaaa ⇒ ccacacac
25. aaacacacaacacaaaaaaaa ⇒ ccacacaac
26. aaacacaacacacaaaa ⇒ ccacaacac
27. caacacacacaacaaaaaaaaaaaaaaa ⇒ acacacac
28. caacacacaacacaaaaaaaaaaaa ⇒ acacacaac
29. caacacaacacacaaaaaaaa ⇒ acacaacac
30. caacaacacacacaaaa ⇒ acaacacac
31. caacaacacacaacaaaa ⇒ acaacacaac
32. caacaacacaacacaaaa ⇒ acaacaacac
33. acacacaacacaac ⇒ caacacaacacaca
34. acacaacacacaacaaaaaaa ⇒ caacaacacacac
35. acacaacacaacacaaaa ⇒ caacaacacacaac
36. aaacacacacaacacaaaaaaaaaaaa ⇒ ccacacacaac
37. aaacacacaacacacaaaaaaaa ⇒ ccacacaacac
38. aaacacaacacacacaaaa ⇒ ccacaacacac
39. aaacacaacacacaacaaaa ⇒ ccacaacacaac
40. cacaacaacacacaca ⇒ acacaacacaac
41. cacaacaacacaacaca ⇒ acaacaacacaac
42. caacacacaacacacaaaaaaaaaaaa ⇒ acacacaacac
43. caacacaacacacacaaaaaaaa ⇒ acacaacacac
44. caacaacacacacacaaaa ⇒ acaacacacac
45. caacaacacacacaacaaaa ⇒ acaacacacaac
46. caacaacacacaacacaaaa ⇒ acaacacaacac
47. caacaacacaacacaca ⇒ aacacaacacaac
48. acacacaacacacaacaaa ⇒ caacacaacacacac
49. acacaacacaacacacaaaa ⇒ caacaacacacaacac
50. acacaacacaacacaac ⇒ caacacaacacaacaca
51. acaacaacacaacacaaca ⇒ ccacaacaacacaac
52. aacaacacaacacacacaaaaa ⇒ ccacacaacacaac
53. aaacacacaacacacacaaaaaaaa ⇒ ccacacaacacac
54. aaacacaacacacacacaaaa ⇒ ccacaacacacac
55. aaacacaacacacacaacaaaa ⇒ ccacaacacacaac
56. aaacacaacacacaacacaaaa ⇒ ccacaacacaacac
57. aaacacaacacaacacaca ⇒ ccaacacaacacaac
58. cacaacaacacacaacaca ⇒ acaacacaacacaac
59. caacaacacacacacacaaaa ⇒ acaacacacacac
60. caacaacacacacacaacaaaa ⇒ acaacacacacaac
61. caacaacacacacaacacaaaa ⇒ acaacacacaacac
62. caacaacacacaacacacaaaa ⇒ acaacacaacacac
63. caacaacacaacacaacaca ⇒ aacaacacaacacaac
64. aacaacacaacacacacaca ⇒ ccacacaacacacaac
65. b ⇒ ccc
...

Collecting factors up to length 14, frequency 1:

Length 2:[2/0] ac
Length 3:[3/0] aca
Length 4:[4/0] caac
Length 5:[5/0] acaca
Length 6:[6/0] cacaac
Length 7:[7/0] caacaac
Length 8:[8/0] acaacaca
Length 9:[9/0] caacacaac
Length 10:[10/0] caacaacaac
Length 11:[11/0] caacaacacac
Length 12:[12/0] acacaacacaac
Length 13:[13/0] acaacaacacaac

Considering [length 10 / frequency 0] caacaacaac=d.

Step 3

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