Certificate for #12910 ⟨a, b | aab=aaa, bbbb=a⟩

Completion settings:

Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1

[1] aaa=aab

Axiom: aab=aaa.

Flip LHS and RHS.

Referenced by [3].

[2] a=bbbb

Axiom: bbbb=a.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] aaa=bbbbbbbbb

Simplify [1] aaa=aab.

Reduce RHS:

[2]	(a)ab
[2]	⇒ bbbb(a)b
	⇒ bbbbbbbbb

Referenced by [4].

[4] bbbbbbbbbbbb=bbbbbbbbb

Overlap of [3] aaa=bbbbbbbbb with [2] a=bbbb:

aaa a

Critical pair: bbbbaa=bbbbbbbbb.

Reduce LHS:

[2]	bbbb(a)a
[2]	⇒ bbbbbbbb(a)
	⇒ bbbbbbbbbbbb

Defines rule #1.