Certificate for #16550 ⟨a, b | aba=bb, bab=aba⟩

Back:⟨a, b | aba=bb, bab=aba⟩

Completion settings:

[1] aba=bb

Axiom: aba=bb.

Defines rule #1.

Referenced by [2], [3], [4].

[2] bab=bb

Axiom: bab=aba.

Reduce RHS:

[1](aba)
⇒ bb

Defines rule #2.

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

[3] bbb=abb

Overlap of [1] aba=bb with [2] bab=bb:

a ba bab

Critical pair: abb=bbb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

[4] bba=abb

Overlap of [2] bab=bb with [1] aba=bb:

b ab aba

Critical pair: bbb=bba.

Reduce LHS:

[3](bbb)
⇒ abb

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] aabb=abb

Overlap of [4] bba=abb with [2] bab=bb:

b ba bab

Critical pair: bbb=abbb.

Reduce LHS:

[3](bbb)
⇒ abb

Reduce RHS:

[3]a(bbb)
⇒ aabb

Flip LHS and RHS.

Defines rule #5.