Certificate for #1604 ⟨a, b | aaa=bb, abb=a⟩

Back:⟨a, b | aaa=bb, abb=a⟩

Completion settings:

[1] aaa=bb

Axiom: aaa=bb.

Defines rule #1.

Referenced by [3], [4].

[2] abb=a

Axiom: abb=a.

Defines rule #2.

Referenced by [3], [4].

[3] bba=a

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

a aa aaa

Critical pair: abb=bba.

Reduce LHS:

[2](abb)
⇒ a

Flip LHS and RHS.

Defines rule #3.

[4] bbbb=bb

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

aa a abb

Critical pair: aaa=bbbb.

Reduce LHS:

[1](aaa)
⇒ bb

Flip LHS and RHS.

Defines rule #4.