Certificate for #12444 ⟨a, b | aabb=aa, babb=a⟩

Back:⟨a, b | aabb=aa, babb=a⟩

Completion settings:

[1] aabb=aa

Axiom: aabb=aa.

Defines rule #3.

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

[2] babb=a

Axiom: babb=a.

Defines rule #5.

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

[3] baba=aa

Overlap of [2] babb=a with [2] babb=a:

bab b babb

Critical pair: baba=aabb.

Reduce RHS:

[1](aabb)
⇒ aa

Defines rule #4.

Referenced by [5].

[4] aaba=aaa

Overlap of [1] aabb=aa with [2] babb=a:

aab b babb

Critical pair: aaba=aaabb.

Reduce RHS:

[1]a(aabb)
⇒ aaa

Defines rule #2.

[5] baa=aa

Overlap of [3] baba=aa with [2] babb=a:

ba ba babb

Critical pair: baa=aabb.

Reduce RHS:

[1](aabb)
⇒ aa

Defines rule #1.