Certificate for #16330 ⟨a, b | aab=bb, bbba=ab⟩

Completion settings:

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

Axiom: aab=bb.

Referenced by [3].

Axiom: bbba=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4], [6], [8].

Overlap of [1] aab=bb with [2] ab=bbba:

Critical pair: abbba=bb.

Reduce LHS:

Referenced by [4], [5], [6], [9].

Overlap of [3] bbbbbbbbbaa=bb with [2] ab=bbba:

Critical pair: bbbbbbbbbabbba=bbb.

Reduce LHS:

Referenced by [5], [6], [7].

Overlap of [4] bbbbbbbbbbb=bbb with [3] bbbbbbbbbaa=bb:

Critical pair: bbbb=bbbaa.

Flip LHS and RHS.

Referenced by [6], [7], [8], [9].

Overlap of [2] ab=bbba with [5] bbbaa=bbbb:

Critical pair: abbbb=bbbabbaa.

Reduce LHS:

Reduce RHS:

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

Overlap of [4] bbbbbbbbbbb=bbb with [5] bbbaa=bbbb:

Critical pair: bbbbbbbbbbbbb=bbbbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [8], [10].

Overlap of [7] bbaa=bbbbb with [2] ab=bbba:

Critical pair: bbabbba=bbbbbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [3] bbbbbbbbbaa=bb with [8] bbbbbb=bbbb:

Critical pair: bbbbbbbaa=bb.

Reduce LHS:

Defines rule #1.

Referenced by [10].

Simplify [7] bbaa=bbbbb.

Reduce RHS:

Defines rule #3.