Certificate for #16467 ⟨a, b | aba=bb, babb=ab

Completion settings:

[1] aba=bb

Axiom: aba=bb.

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

[2] babb=ab

Axiom: babb=ab.

Referenced by [4], [7], [9], [10].

[3] abbb=bbba

Overlap of [1] aba=bb with [1] aba=bb:

ab a aba

Critical pair: abbb=bbba.

Referenced by [6].

[4] aab=bbbb

Overlap of [1] aba=bb with [2] babb=ab:

a ba babb

Critical pair: aab=bbbb.

Referenced by [5], [7].

[5] abb=bbbba

Overlap of [4] aab=bbbb with [1] aba=bb:

a ab aba

Critical pair: abb=bbbba.

Referenced by [6], [7], [9].

[6] bbbbab=bbba

Simplify [3] abbb=bbba.

Reduce LHS:

[5](abb)b
bbbbab

Referenced by [7], [8], [9], [10].

[7] bbbbaa=bbbbbbb

Overlap of [2] babb=ab with [6] bbbbab=bbba:

ba bb bbbbab

Critical pair: babbba=abbbab.

Reduce LHS:

[2](babb)ba
[5](abb)a
bbbbaa

Reduce RHS:

[5](abb)bab
[6](bbbbab)ab
[4]bbb(aab)
bbbbbbb

Referenced by [11].

[8] bbbaa=bbbbbb

Overlap of [6] bbbbab=bbba with [1] aba=bb:

bbbb ab aba

Critical pair: bbbbbb=bbbaa.

Flip LHS and RHS.

Referenced by [9], [12].

[9] bab=bbbbbba

Overlap of [5] abb=bbbba with [8] bbbaa=bbbbbb:

a bb bbbaa

Critical pair: abbbbbb=bbbbabaa.

Reduce LHS:

[5](abb)bbbb
[6](bbbbab)bbb
[2]bb(babb)b
[2]b(babb)
bab

Reduce RHS:

[6](bbbbab)aa
[8](bbbaa)a
bbbbbba

Referenced by [10].

[10] ab=bbbbba

Overlap of [2] babb=ab with [9] bab=bbbbbba:

babb bab

Critical pair: bbbbbbab=ab.

Reduce LHS:

[6]bb(bbbbab)
bbbbba

Flip LHS and RHS.

Defines rule #2.

Referenced by [11].

[11] bbbbbbbb=bb

Overlap of [1] aba=bb with [10] ab=bbbbba:

aba ab

Critical pair: bbbbbaa=bb.

Reduce LHS:

[7]b(bbbbaa)
bbbbbbbb

Defines rule #1.

Referenced by [12].

[12] bbaa=bbbbb

Overlap of [11] bbbbbbbb=bb with [8] bbbaa=bbbbbb:

bbbbb bbb bbbaa

Critical pair: bbbbbbbbbbb=bbaa.

Reduce LHS:

[11](bbbbbbbb)bbb
bbbbb

Flip LHS and RHS.

Defines rule #3.