Certificate for #4156 ⟨a, b | abb=aaa, bbb=a⟩

Back:⟨a, b | abb=aaa, bbb=a⟩

Completion settings:

[1] aaa=abb

Axiom: abb=aaa.

Flip LHS and RHS.

Referenced by [3].

[2] a=bbb

Axiom: bbb=a.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] aaa=bbbbb

Simplify [1] aaa=abb.

Reduce RHS:

[2](a)bb
⇒ bbbbb

Referenced by [4].

[4] bbbbbbbbb=bbbbb

Overlap of [3] aaa=bbbbb with [2] a=bbb:

aaa a

Critical pair: bbbaa=bbbbb.

Reduce LHS:

[2]bbb(a)a
[2]⇒ bbbbbb(a)
⇒ bbbbbbbbb

Defines rule #1.