Certificate for #23325 ⟨a, b | aaa=1, bbbb=abab

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #10.

Referenced by [3].

[2] abab=bbbb

Axiom: bbbb=abab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [3], [4], [5], [6], [12].

[3] aabbbb=bab

Overlap of [1] aaa=1 with [2] abab=bbbb:

aa a abab

Critical pair: aabbbb=bab.

Defines rule #5.

Referenced by [5], [6], [7], [8], [9], [12], [13].

[4] bbbbab=abbbbb

Overlap of [2] abab=bbbb with [2] abab=bbbb:

ab ab abab

Critical pair: abbbbb=bbbbab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [5], [6], [7], [8], [9], [12].

[5] abbabb=bbbabbbbb

Overlap of [2] abab=bbbb with [4] bbbbab=abbbbb:

aba b bbbbab

Critical pair: abaabbbbb=bbbbbbbab.

Reduce LHS:

[3]ab(aabbbb)b
abbabb

Reduce RHS:

[4]bbb(bbbbab)
bbbabbbbb

Defines rule #7.

Referenced by [7], [9].

[6] babbab=abbbbbbbb

Overlap of [3] aabbbb=bab with [4] bbbbab=abbbbb:

aab bbb bbbbab

Critical pair: aababbbbb=babbab.

Reduce LHS:

[2]a(abab)bbbb
abbbbbbbb

Flip LHS and RHS.

Defines rule #8.

Referenced by [9].

[7] babbbab=abbbabbbbbbbb

Overlap of [3] aabbbb=bab with [4] bbbbab=abbbbb:

aabb bb bbbbab

Critical pair: aabbabbbbb=babbbab.

Reduce LHS:

[5]a(abbabb)bbb
abbbabbbbbbbb

Flip LHS and RHS.

Defines rule #9.

Referenced by [9].

[8] aabbbabbbbb=bbabb

Overlap of [3] aabbbb=bab with [4] bbbbab=abbbbb:

aabbb b bbbbab

Critical pair: aabbbabbbbb=babbbbab.

Reduce RHS:

[4]ba(bbbbab)
[3]b(aabbbb)b
bbabb

Referenced by [9], [10], [11].

[9] bbbabbbbbbbbbbbbbbbbbbbbbbbbbb=bbbabb

Overlap of [8] aabbbabbbbb=bbabb with [4] bbbbab=abbbbb:

aabbbabbb bb bbbbab

Critical pair: aabbbabbbabbbbb=bbabbbbab.

Reduce LHS:

[7]aabb(babbbab)bbbb
[5]a(abbabb)babbbbbbbbbbbb
[4]abbbabb(bbbbab)bbbbbbbbbbb
[6]abb(babbab)bbbbbbbbbbbbbbb
[5](abbabb)bbbbbbbbbbbbbbbbbbbbb
bbbabbbbbbbbbbbbbbbbbbbbbbbbbb

Reduce RHS:

[4]bba(bbbbab)
[3]bb(aabbbb)b
bbbabb

Referenced by [10].

[10] aabbbabb=bbabbbbbbbbbbbbbbbbbbbbbbb

Overlap of [8] aabbbabbbbb=bbabb with [9] bbbabbbbbbbbbbbbbbbbbbbbbbbbbb=bbbabb:

aa bbbabbbbb bbbabbbbbbbbbbbbbbbbbbbbbbbbbb

Critical pair: aabbbabb=bbabbbbbbbbbbbbbbbbbbbbbbb.

Defines rule #11.

Referenced by [11], [12].

[11] bbabbbbbbbbbbbbbbbbbbbbbbbbbb=bbabb

Overlap of [8] aabbbabbbbb=bbabb with [10] aabbbabb=bbabbbbbbbbbbbbbbbbbbbbbbb:

aabbbabbbbb aabbbabb

Critical pair: bbabbbbbbbbbbbbbbbbbbbbbbbbbb=bbabb.

Defines rule #3.

[12] bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bbbbbb

Overlap of [10] aabbbabb=bbabbbbbbbbbbbbbbbbbbbbbbb with [4] bbbbab=abbbbb:

aabbba bb bbbbab

Critical pair: aabbbaabbbbb=bbabbbbbbbbbbbbbbbbbbbbbbbbbab.

Reduce LHS:

[3]aabbb(aabbbb)b
[3](aabbbb)abb
[2]b(abab)b
bbbbbb

Reduce RHS:

[4]bbabbbbbbbbbbbbbbbbbbbbb(bbbbab)
[4]bbabbbbbbbbbbbbbbbbb(bbbbab)bbbb
[4]bbabbbbbbbbbbbbb(bbbbab)bbbbbbbb
[4]bbabbbbbbbbb(bbbbab)bbbbbbbbbbbb
[4]bbabbbbb(bbbbab)bbbbbbbbbbbbbbbb
[4]bbab(bbbbab)bbbbbbbbbbbbbbbbbbbb
[2]bb(abab)bbbbbbbbbbbbbbbbbbbbbbbb
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.

Referenced by [13].

[13] babbbbbbbbbbbbbbbbbbbbbbbbbbb=babbb

Overlap of [3] aabbbb=bab with [12] bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bbbbbb:

aa bbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Critical pair: aabbbbbb=babbbbbbbbbbbbbbbbbbbbbbbbbbb.

Reduce LHS:

[3](aabbbb)bb
babbb

Flip LHS and RHS.

Defines rule #2.