Certificate for #6755 ⟨a, b | aba=a, babb=aa⟩

Back:⟨a, b | aba=a, babb=aa⟩

Completion settings:

[1] aba=a

Axiom: aba=a.

Defines rule #3.

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

[2] babb=aa

Axiom: babb=aa.

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

[3] abb=aaa

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

a ba babb

Critical pair: aaa=abb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

[4] baa=aaaaa

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

bab b babb

Critical pair: babaa=aaabb.

Reduce LHS:

[1]b(aba)a
⇒ baa

Reduce RHS:

[3]aa(abb)
⇒ aaaaa

Defines rule #2.

[5] aaaaaa=aa

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

ab b babb

Critical pair: abaa=aaaabb.

Reduce LHS:

[1](aba)a
⇒ aa

Reduce RHS:

[3]aaa(abb)
⇒ aaaaaa

Flip LHS and RHS.

Defines rule #1.