Certificate for #9739 ⟨a, b | aa=1, ababbbb=b⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #3.

Referenced by [3].

Axiom: ababbbb=b.

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

Overlap of [1] aa=1 with [2] ababbbb=b:

Critical pair: ab=babbbb.

Flip LHS and RHS.

Referenced by [4], [5].

Overlap of [3] babbbb=ab with [3] babbbb=ab:

Critical pair: babbbab=ababbbb.

Reduce RHS:

Referenced by [5], [6], [8].

Overlap of [4] babbbab=b with [3] babbbb=ab:

Critical pair: babbab=bbbb.

Referenced by [7].

Overlap of [4] babbbab=b with [4] babbbab=b:

Critical pair: babbb=bbbab.

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [2] ababbbb=b with [6] bbbab=babbb:

Critical pair: ababbabbb=bab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

Overlap of [4] babbbab=b with [7] bab=abbbbbb:

Critical pair: abbbbbbbbab=b.

Reduce LHS:

Defines rule #1.