Certificate for #15957 ⟨a, b | aaa=aa, aabb=ab⟩

Back:⟨a, b | aaa=aa, aabb=ab⟩

Completion settings:

[1] aaa=aa

Axiom: aaa=aa.

Defines rule #1.

Referenced by [3], [4].

[2] aabb=ab

Axiom: aabb=ab.

Referenced by [3], [4].

[3] aab=ab

Overlap of [1] aaa=aa with [2] aabb=ab:

a aa aabb

Critical pair: aab=aabb.

Reduce RHS:

[2](aabb)
⇒ ab

Defines rule #2.

Referenced by [4].

[4] abb=ab

Overlap of [1] aaa=aa with [2] aabb=ab:

aa a aabb

Critical pair: aaab=aaabb.

Reduce LHS:

[1](aaa)b
[3]⇒ (aab)
⇒ ab

Reduce RHS:

[1](aaa)bb
[3]⇒ (aab)b
⇒ abb

Flip LHS and RHS.

Defines rule #3.