Certificate for #12439 ⟨a, b | aabb=aa, baaa=b⟩

Back:⟨a, b | aabb=aa, baaa=b⟩

Completion settings:

[1] aabb=aa

Axiom: aabb=aa.

Defines rule #2.

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

[2] baaa=b

Axiom: baaa=b.

Defines rule #3.

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

[3] aaaaa=aa

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

aab b baaa

Critical pair: aabb=aaaaa.

Reduce LHS:

[1](aabb)
⇒ aa

Flip LHS and RHS.

Defines rule #5.

[4] bbb=b

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

ba aa aabb

Critical pair: baaa=bbb.

Reduce LHS:

[2](baaa)
⇒ b

Flip LHS and RHS.

Defines rule #1.

[5] babb=ba

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

baa a aabb

Critical pair: baaaa=babb.

Reduce LHS:

[2](baaa)a
⇒ ba

Flip LHS and RHS.

Defines rule #4.