Certificate for #24719 ⟨a, b | aa=a, bbabbb=ba

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #3.

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

[2] bbabbb=ba

Axiom: bbabbb=ba.

Referenced by [3], [4], [5], [8], [11].

[3] bbabba=babbb

Overlap of [2] bbabbb=ba with [2] bbabbb=ba:

bbab bb bbabbb

Critical pair: bbabba=baabbb.

Reduce RHS:

[1]b(aa)bbb
babbb

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

[4] bababbb=ba

Overlap of [2] bbabbb=ba with [2] bbabbb=ba:

bbabb b bbabbb

Critical pair: bbabbba=bababbb.

Reduce LHS:

[2](bbabbb)a
[1]b(aa)
ba

Flip LHS and RHS.

Referenced by [7].

[5] babba=babbbbbb

Overlap of [2] bbabbb=ba with [3] bbabba=babbb:

bbab bb bbabba

Critical pair: bbabbabbb=baabba.

Reduce LHS:

[3](bbabba)bbb
babbbbbb

Reduce RHS:

[1]b(aa)bba
babba

Flip LHS and RHS.

Referenced by [9].

[6] babbba=babbb

Overlap of [3] bbabba=babbb with [1] aa=a:

bbabb a aa

Critical pair: bbabba=babbba.

Reduce LHS:

[3](bbabba)
babbb

Flip LHS and RHS.

Referenced by [8], [10].

[7] babbbbba=bba

Overlap of [3] bbabba=babbb with [3] bbabba=babbb:

bba bba bbabba

Critical pair: bbababbb=babbbbba.

Reduce LHS:

[4]b(bababbb)
bba

Flip LHS and RHS.

Referenced by [8], [10].

[8] baba=bba

Overlap of [6] babbba=babbb with [3] bbabba=babbb:

bab bba bbabba

Critical pair: babbabbb=babbbbba.

Reduce LHS:

[2]ba(bbabbb)
baba

Reduce RHS:

[7](babbbbba)
bba

Referenced by [9], [12].

[9] bbba=babbbbbb

Overlap of [8] baba=bba with [8] baba=bba:

ba ba baba

Critical pair: babba=bbaba.

Reduce LHS:

[5](babba)
babbbbbb

Reduce RHS:

[8]b(baba)
bbba

Flip LHS and RHS.

Referenced by [10].

[10] bba=babbbbbbbbb

Simplify [7] babbbbba=bba.

Reduce LHS:

[9]babb(bbba)
[6](babbba)bbbbbb
babbbbbbbbb

Flip LHS and RHS.

Defines rule #2.

Referenced by [11], [12].

[11] babbbbbbbbbbbb=ba

Overlap of [2] bbabbb=ba with [10] bba=babbbbbbbbb:

bbabbb bba

Critical pair: babbbbbbbbbbbb=ba.

Defines rule #1.

[12] baba=babbbbbbbbb

Simplify [8] baba=bba.

Reduce RHS:

[10](bba)
babbbbbbbbb

Defines rule #4.