Certificate for #19766 ⟨a, b | aba=b, babbb=aa⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [3], [5], [7], [8], [9].

Axiom: babbb=aa.

Referenced by [4].

Overlap of [1] aba=b with [1] aba=b:

Critical pair: abb=bba.

Referenced by [4].

Simplify [2] babbb=aa.

Reduce LHS:

Referenced by [5], [10].

Overlap of [4] bbbab=aa with [1] aba=b:

Critical pair: bbbb=aaa.

Defines rule #4.

Referenced by [6], [10].

Overlap of [5] bbbb=aaa with [5] bbbb=aaa:

Critical pair: baaa=aaab.

Flip LHS and RHS.

Referenced by [7].

Overlap of [6] aaab=baaa with [1] aba=b:

Critical pair: aab=baaaa.

Referenced by [8].

Overlap of [7] aab=baaaa with [1] aba=b:

Critical pair: ab=baaaaa.

Defines rule #3.

Referenced by [9], [10].

Overlap of [1] aba=b with [8] ab=baaaaa:

Critical pair: baaaaaa=b.

Defines rule #2.

Overlap of [4] bbbab=aa with [8] ab=baaaaa:

Critical pair: bbbbaaaaa=aa.

Reduce LHS:

Defines rule #1.