Certificate for #12289 ⟨a, b | aaab=ba, babb=b⟩

Completion settings:

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

Axiom: aaab=ba.

Referenced by [3], [4], [7].

Axiom: babb=b.

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

Overlap of [1] aaab=ba with [2] babb=b:

Critical pair: aaab=baabb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4], [5].

Overlap of [1] aaab=ba with [3] baabb=ba:

Critical pair: aaaba=baaabb.

Reduce LHS:

Reduce RHS:

Referenced by [5].

Overlap of [2] babb=b with [3] baabb=ba:

Critical pair: babba=baabb.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Referenced by [6], [7].

Overlap of [2] babb=b with [5] ba=bbb:

Critical pair: bbbbb=b.

Defines rule #1.

Simplify [1] aaab=ba.

Reduce RHS:

Defines rule #3.