Certificate for #1607 ⟨a, b | aaa=bb, bab=b⟩

Completion settings:

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

Axiom: aaa=bb.

Defines rule #5.

Referenced by [3], [6].

Axiom: bab=b.

Defines rule #3.

Referenced by [4], [5], [8].

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

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [4], [5], [9].

Overlap of [2] bab=b with [3] bba=abb:

Critical pair: baabb=bba.

Reduce RHS:

Referenced by [7].

Overlap of [3] bba=abb with [2] bab=b:

Critical pair: bb=abbb.

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] aaa=bb with [5] abbb=bb:

Critical pair: aabb=bbbbb.

Referenced by [7].

Simplify [4] baabb=abb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [9].

Overlap of [2] bab=b with [7] abb=bbbbbb:

Critical pair: bbbbbbb=bb.

Defines rule #1.

Simplify [3] bba=abb.

Reduce RHS:

Defines rule #4.