Certificate for #20158 ⟨a, b | aab=b, bbab=bba

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #1.

Referenced by [3].

[2] bbab=bba

Axiom: bbab=bba.

Defines rule #4.

Referenced by [3], [4].

[3] bbb=bbaa

Overlap of [2] bbab=bba with [2] bbab=bba:

bba b bbab

Critical pair: bbabba=bbabab.

Reduce LHS:

[2](bbab)ba
[2](bbab)a
bbaa

Reduce RHS:

[2](bbab)ab
[1]bb(aab)
bbb

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] bbaaa=bba

Overlap of [2] bbab=bba with [3] bbb=bbaa:

bba b bbb

Critical pair: bbabbaa=bbabb.

Reduce LHS:

[2](bbab)baa
[2](bbab)aa
bbaaa

Reduce RHS:

[2](bbab)b
[2](bbab)
bba

Defines rule #2.