Certificate for #19041 ⟨a, b | aab=b, babaaa=b⟩

Completion settings:

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

Axiom: aab=b.

Defines rule #2.

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

Axiom: babaaa=b.

Referenced by [3], [4], [5], [7], [8].

Overlap of [2] babaaa=b with [1] aab=b:

Critical pair: babab=bb.

Referenced by [5], [6].

Overlap of [2] babaaa=b with [1] aab=b:

Critical pair: babaab=bab.

Reduce LHS:

Referenced by [5], [9].

Overlap of [4] babb=bab with [2] babaaa=b:

Critical pair: babb=bababaaa.

Reduce LHS:

Reduce RHS:

Referenced by [6], [7], [8], [9], [10].

Simplify [3] babab=bb.

Reduce LHS:

Referenced by [7].

Overlap of [6] bbb=bb with [2] babaaa=b:

Critical pair: bbb=bbabaaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [2] babaaa=b with [5] bab=bbaaa:

Critical pair: bbaaaaaa=b.

Reduce LHS:

Defines rule #3.

Referenced by [9], [10].

Overlap of [4] babb=bab with [5] bab=bbaaa:

Critical pair: babbbaaa=babab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Simplify [5] bab=bbaaa.

Reduce RHS:

Defines rule #4.