Certificate for #16385 ⟨a, b | aba=ab, aabb=aa⟩

Back:⟨a, b | aba=ab, aabb=aa⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #2.

Referenced by [3], [4].

[2] aabb=aa

Axiom: aabb=aa.

Defines rule #3.

Referenced by [4], [5].

[3] abba=abb

Overlap of [1] aba=ab with [1] aba=ab:

ab a aba

Critical pair: abab=abba.

Reduce LHS:

[1](aba)b
⇒ abb

Flip LHS and RHS.

Defines rule #4.

Referenced by [5].

[4] abbb=ab

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

ab a aabb

Critical pair: abaa=ababb.

Reduce LHS:

[1](aba)a
[1]⇒ (aba)
⇒ ab

Reduce RHS:

[1](aba)bb
⇒ abbb

Flip LHS and RHS.

Defines rule #5.

[5] aaa=aa

Overlap of [2] aabb=aa with [3] abba=abb:

a abb abba

Critical pair: aabb=aaa.

Reduce LHS:

[2](aabb)
⇒ aa

Flip LHS and RHS.

Defines rule #1.