Certificate for #18415 ⟨a, b | aab=a, bbbbbbb=1⟩

Completion settings:

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

Axiom: aab=a.

Referenced by [3], [4], [5], [6], [7], [8], [9].

Axiom: bbbbbbb=1.

Defines rule #3.

Referenced by [3].

Overlap of [1] aab=a with [2] bbbbbbb=1:

Critical pair: aa=abbbbbb.

Flip LHS and RHS.

Referenced by [4].

Overlap of [1] aab=a with [3] abbbbbb=aa:

Critical pair: aaa=abbbbb.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aab=a with [4] abbbbb=aaa:

Critical pair: aaaa=abbbb.

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] aab=a with [5] abbbb=aaaa:

Critical pair: aaaaa=abbb.

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] aab=a with [6] abbb=aaaaa:

Critical pair: aaaaaa=abb.

Flip LHS and RHS.

Referenced by [8].

Overlap of [1] aab=a with [7] abb=aaaaaa:

Critical pair: aaaaaaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Overlap of [1] aab=a with [8] ab=aaaaaaa:

Critical pair: aaaaaaaa=a.

Defines rule #1.