Certificate for #12413 ⟨a, b | aaba=bb, abbb=b⟩

Completion settings:

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

Axiom: aaba=bb.

Referenced by [3], [6].

Axiom: abbb=b.

Referenced by [3], [4], [5], [7], [9], [10].

Overlap of [1] aaba=bb with [1] aaba=bb:

Critical pair: aabbb=bbaba.

Reduce LHS:

Flip LHS and RHS.

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

Overlap of [3] bbaba=ab with [2] abbb=b:

Critical pair: bbabb=abbbb.

Reduce RHS:

Referenced by [5].

Overlap of [2] abbb=b with [4] bbabb=bb:

Critical pair: abbb=babb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [1] aaba=bb with [5] babb=b:

Critical pair: aab=bbbb.

Referenced by [9].

Overlap of [3] bbaba=ab with [5] babb=b:

Critical pair: bbab=abbb.

Reduce RHS:

Referenced by [8].

Overlap of [3] bbaba=ab with [7] bbab=b:

Critical pair: ba=ab.

Referenced by [11].

Overlap of [6] aab=bbbb with [2] abbb=b:

Critical pair: ab=bbbbbb.

Defines rule #2.

Referenced by [10], [11].

Overlap of [2] abbb=b with [9] ab=bbbbbb:

Critical pair: bbbbbbbb=b.

Defines rule #1.

Simplify [8] ba=ab.

Reduce RHS:

Defines rule #3.