Certificate for #2585 ⟨a, b | aaa=1, abbb=bb⟩

Back:⟨a, b | aaa=1, abbb=bb⟩

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #3.

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

[2] abbb=bb

Axiom: abbb=bb.

Referenced by [3].

[3] aabb=bbb

Overlap of [1] aaa=1 with [2] abbb=bb:

aa a abbb

Critical pair: aabb=bbb.

Referenced by [4], [5].

[4] abb=bbbb

Overlap of [1] aaa=1 with [3] aabb=bbb:

aa a aabb

Critical pair: aabbb=abb.

Reduce LHS:

[3](aabb)b
⇒ bbbb

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] bbbbb=bb

Overlap of [1] aaa=1 with [4] abb=bbbb:

aa a abb

Critical pair: aabbbb=bb.

Reduce LHS:

[3](aabb)bb
⇒ bbbbb

Defines rule #1.