Certificate for #13189 ⟨a, b | abb=aaa, bba=bb⟩

Back:⟨a, b | abb=aaa, bba=bb⟩

Completion settings:

[1] aaa=abb

Axiom: abb=aaa.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[2] bba=bb

Axiom: bba=bb.

Defines rule #1.

Referenced by [3], [4].

[3] aabb=abb

Overlap of [1] aaa=abb with [1] aaa=abb:

a aa aaa

Critical pair: aabb=abba.

Reduce RHS:

[2]a(bba)
⇒ abb

Defines rule #4.

[4] bbbb=bb

Overlap of [2] bba=bb with [1] aaa=abb:

bb a aaa

Critical pair: bbabb=bbaa.

Reduce LHS:

[2](bba)bb
⇒ bbbb

Reduce RHS:

[2](bba)a
[2]⇒ (bba)
⇒ bb

Defines rule #3.