Certificate for #652 ⟨a, b | bb=aa, aaa=a⟩

Back:⟨a, b | bb=aa, aaa=a⟩

Completion settings:

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Defines rule #1.

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

[2] bba=a

Axiom: aaa=a.

Reduce LHS:

[1](aa)a
⇒ bba

Defines rule #2.

Referenced by [3], [4].

[3] abb=a

Overlap of [1] aa=bb with [1] aa=bb:

a a aa

Critical pair: abb=bba.

Reduce RHS:

[2](bba)
⇒ a

Defines rule #3.

[4] bbbb=bb

Overlap of [2] bba=a with [1] aa=bb:

bb a aa

Critical pair: bbbb=aa.

Reduce RHS:

[1](aa)
⇒ bb

Defines rule #4.