Certificate for #12421 ⟨a, b | aaba=bb, babb=b⟩

Completion settings:

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

Axiom: aaba=bb.

Referenced by [3], [4].

Axiom: babb=b.

Referenced by [3], [5], [6], [9], [10], [12].

Overlap of [1] aaba=bb with [2] babb=b:

Critical pair: aab=bbbb.

Defines rule #3.

Referenced by [4], [7].

Overlap of [1] aaba=bb with [3] aab=bbbb:

Critical pair: bbbba=bb.

Referenced by [5].

Overlap of [2] babb=b with [4] bbbba=bb:

Critical pair: babb=bbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [2] babb=b with [5] bbba=b:

Critical pair: bab=bba.

Flip LHS and RHS.

Referenced by [8].

Overlap of [5] bbba=b with [3] aab=bbbb:

Critical pair: bbbbbbb=bab.

Flip LHS and RHS.

Referenced by [8], [9].

Simplify [6] bba=bab.

Reduce RHS:

Referenced by [9], [10].

Overlap of [2] babb=b with [8] bba=bbbbbbb:

Critical pair: babbbbbbb=ba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [8] bba=bbbbbbb with [2] babb=b:

Critical pair: bb=bbbbbbbbb.

Flip LHS and RHS.

Referenced by [11].

Simplify [9] ba=bbbbbbbbbbbbb.

Reduce RHS:

Defines rule #2.

Referenced by [12].

Overlap of [2] babb=b with [11] ba=bbbbbb:

Critical pair: bbbbbbbb=b.

Defines rule #1.