Certificate for #16366 ⟨a, b | aba=aa, babb=aa⟩

Back:⟨a, b | aba=aa, babb=aa⟩

Completion settings:

[1] aba=aa

Axiom: aba=aa.

Defines rule #1.

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

[2] babb=aa

Axiom: babb=aa.

Defines rule #4.

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

[3] aabb=aaa

Overlap of [1] aba=aa with [2] babb=aa:

a ba babb

Critical pair: aaa=aabb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] baaa=aaaa

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

bab b babb

Critical pair: babaa=aaabb.

Reduce LHS:

[1]b(aba)a
⇒ baaa

Reduce RHS:

[3]a(aabb)
⇒ aaaa

Defines rule #3.

[5] aaaaa=aaaa

Overlap of [3] aabb=aaa with [2] babb=aa:

aab b babb

Critical pair: aabaa=aaaabb.

Reduce LHS:

[1]a(aba)a
⇒ aaaa

Reduce RHS:

[3]aa(aabb)
⇒ aaaaa

Flip LHS and RHS.

Defines rule #5.