Certificate for #12207 ⟨a, b | aaaa=bb, abbb=b⟩

Completion settings:

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

Axiom: aaaa=bb.

Defines rule #4.

Referenced by [3], [4].

Axiom: abbb=b.

Referenced by [4], [5], [6], [7], [8], [9], [10], [11].

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

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [5], [7], [8], [9], [10].

Overlap of [1] aaaa=bb with [2] abbb=b:

Critical pair: aaab=bbbbb.

Referenced by [9].

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

Critical pair: ababb=ba.

Referenced by [6].

Overlap of [5] ababb=ba with [2] abbb=b:

Critical pair: abb=bab.

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [6] bab=abb with [3] bba=abb:

Critical pair: baabb=abbba.

Reduce RHS:

Referenced by [8].

Overlap of [6] bab=abb with [6] bab=abb:

Critical pair: baabb=abbab.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [3] bba=abb with [4] aaab=bbbbb:

Critical pair: bbbbbbb=abbaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] bba=abb with [9] aab=bbbbbbb:

Critical pair: bbbbbbbbb=abbab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [11], [12].

Overlap of [2] abbb=b with [10] ab=bbbbbbbbb:

Critical pair: bbbbbbbbbbb=b.

Defines rule #1.

Simplify [8] ba=ab.

Reduce RHS:

Defines rule #3.