Certificate for #5155 ⟨a, b | aab=ab, bbba=b

Completion settings:

[1] aab=ab

Axiom: aab=ab.

Defines rule #2.

Referenced by [3].

[2] bbba=b

Axiom: bbba=b.

Referenced by [3], [4], [5], [6], [7].

[3] bab=bb

Overlap of [2] bbba=b with [1] aab=ab:

bbb a aab

Critical pair: bbbab=bab.

Reduce LHS:

[2](bbba)b
bb

Flip LHS and RHS.

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

[4] bbbb=bb

Overlap of [2] bbba=b with [3] bab=bb:

bb ba bab

Critical pair: bbbb=bb.

Referenced by [5].

[5] bba=bb

Overlap of [3] bab=bb with [2] bbba=b:

ba b bbba

Critical pair: bab=bbbba.

Reduce LHS:

[3](bab)
bb

Reduce RHS:

[4](bbbb)a
bba

Flip LHS and RHS.

Referenced by [6].

[6] bbb=b

Overlap of [3] bab=bb with [5] bba=bb:

ba b bba

Critical pair: babb=bbba.

Reduce LHS:

[3](bab)b
bbb

Reduce RHS:

[2](bbba)
b

Defines rule #3.

Referenced by [7].

[7] ba=b

Overlap of [2] bbba=b with [6] bbb=b:

bbba bbb

Critical pair: ba=b.

Defines rule #1.