Certificate for #19802 ⟨a, b | aaa=a, aabb=baa⟩

Back:⟨a, b | aaa=a, aabb=baa⟩

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #1.

Referenced by [3], [4], [5], [6].

[2] aabb=baa

Axiom: aabb=baa.

Referenced by [3], [4], [6].

[3] abb=abaa

Overlap of [1] aaa=a with [2] aabb=baa:

a aa aabb

Critical pair: abaa=abb.

Flip LHS and RHS.

Defines rule #4.

[4] aabaa=baa

Overlap of [1] aaa=a with [2] aabb=baa:

aa a aabb

Critical pair: aabaa=aabb.

Reduce RHS:

[2](aabb)
⇒ baa

Referenced by [5], [6].

[5] aaba=ba

Overlap of [4] aabaa=baa with [1] aaa=a:

aab aa aaa

Critical pair: aaba=baaa.

Reduce RHS:

[1]b(aaa)
⇒ ba

Defines rule #2.

Referenced by [6].

[6] bba=ba

Overlap of [4] aabaa=baa with [5] aaba=ba:

aab aa aaba

Critical pair: aabba=baaba.

Reduce LHS:

[2](aabb)a
[1]⇒ b(aaa)
⇒ ba

Reduce RHS:

[5]b(aaba)
⇒ bba

Flip LHS and RHS.

Defines rule #3.