Certificate for #20051 ⟨a, b | aab=b, aaaa=abb⟩

Completion settings:

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

Axiom: aab=b.

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

Axiom: aaaa=abb.

Referenced by [3], [4], [9].

Overlap of [2] aaaa=abb with [1] aab=b:

Critical pair: aab=abbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5], [6].

Overlap of [2] aaaa=abb with [2] aaaa=abb:

Critical pair: aabb=abba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] aab=b with [3] abbb=b:

Critical pair: ab=bbb.

Defines rule #2.

Referenced by [6], [7], [9].

Overlap of [3] abbb=b with [5] ab=bbb:

Critical pair: bbbbb=b.

Defines rule #1.

Referenced by [8].

Simplify [4] abba=bb.

Reduce LHS:

Referenced by [8].

Overlap of [6] bbbbb=b with [7] bbbba=bb:

Critical pair: bbb=ba.

Flip LHS and RHS.

Defines rule #3.

Simplify [2] aaaa=abb.

Reduce RHS:

Defines rule #4.