Certificate for #12449 ⟨a, b | aabb=aa, bbab=b⟩

Back:⟨a, b | aabb=aa, bbab=b⟩

Completion settings:

[1] aabb=aa

Axiom: aabb=aa.

Defines rule #2.

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

[2] bbab=b

Axiom: bbab=b.

Defines rule #3.

Referenced by [3], [4].

[3] aaab=aab

Overlap of [1] aabb=aa with [2] bbab=b:

aa bb bbab

Critical pair: aab=aaab.

Flip LHS and RHS.

Referenced by [5].

[4] aabab=aa

Overlap of [1] aabb=aa with [2] bbab=b:

aab b bbab

Critical pair: aabb=aabab.

Reduce LHS:

[1](aabb)
⇒ aa

Flip LHS and RHS.

Defines rule #4.

[5] aaa=aa

Overlap of [3] aaab=aab with [1] aabb=aa:

a aab aabb

Critical pair: aaa=aabb.

Reduce RHS:

[1](aabb)
⇒ aa

Defines rule #1.