Certificate for #12981 ⟨a, b | abb=aaa, baaa=b⟩

Completion settings:

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

Axiom: abb=aaa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [5], [6].

Axiom: baaa=b.

Reduce LHS:

Referenced by [4], [6], [8].

Overlap of [1] aaa=abb with [1] aaa=abb:

Critical pair: aabb=abba.

Flip LHS and RHS.

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

Overlap of [2] babb=b with [3] abba=aabb:

Critical pair: baabb=ba.

Referenced by [5], [6], [7].

Overlap of [3] abba=aabb with [4] baabb=ba:

Critical pair: abba=aabbabb.

Reduce LHS:

Reduce RHS:

Referenced by [9].

Overlap of [4] baabb=ba with [3] abba=aabb:

Critical pair: baaabb=baa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [4] baabb=ba with [6] baa=bbb:

Critical pair: bbbbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

Overlap of [2] babb=b with [7] ba=bbbbb:

Critical pair: bbbbbbb=b.

Defines rule #1.

Referenced by [9].

Overlap of [5] aabb=abbbbbb with [8] bbbbbbb=b:

Critical pair: aab=abbbbbbbbbbb.

Reduce RHS:

Defines rule #3.