Certificate for #4155 ⟨a, b | abb=aaa, bba=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 [3], [4], [5].

Axiom: bba=b.

Referenced by [3], [4], [6], [7], [8], [9].

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

Critical pair: aabb=abba.

Reduce RHS:

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

Overlap of [2] bba=b with [1] aaa=abb:

Critical pair: bbabb=baa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [1] aaa=abb with [3] aabb=ab:

Critical pair: aab=abbbb.

Defines rule #3.

Referenced by [7].

Overlap of [2] bba=b with [3] aabb=ab:

Critical pair: bbab=babb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [3] aabb=ab with [2] bba=b:

Critical pair: aabb=abba.

Reduce LHS:

Reduce RHS:

Referenced by [9].

Overlap of [2] bba=b with [4] baa=bbb:

Critical pair: bbbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Overlap of [6] babb=bb with [8] ba=bbbb:

Critical pair: babbbbb=bba.

Reduce LHS:

Reduce RHS:

Defines rule #1.