Certificate for #16202 ⟨a, b | aab=ab, bbba=ab⟩

Completion settings:

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

Axiom: aab=ab.

Referenced by [3].

Axiom: bbba=ab.

Flip LHS and RHS.

Defines rule #2.

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

Simplify [1] aab=ab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aab=bbba with [2] ab=bbba:

Critical pair: abbba=bbba.

Reduce LHS:

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

Overlap of [2] ab=bbba with [4] bbbbbbbbbaa=bbba:

Critical pair: abbba=bbbabbbbbbbbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

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

Overlap of [4] bbbbbbbbbaa=bbba with [2] ab=bbba:

Critical pair: bbbbbbbbbabbba=bbbab.

Reduce LHS:

Reduce RHS:

Referenced by [7].

Overlap of [6] bbbbbbaa=bbbbbba with [2] ab=bbba:

Critical pair: bbbbbbabbba=bbbbbbab.

Reduce LHS:

Reduce RHS:

Referenced by [8], [10].

Overlap of [7] bbbaa=bbbbbbbbba with [2] ab=bbba:

Critical pair: bbbabbba=bbbbbbbbbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [8] bbbbbbbbbbbba=bbbbbba with [2] ab=bbba:

Critical pair: bbbbbbbbbbbbbbba=bbbbbbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [10].

Simplify [7] bbbaa=bbbbbbbbba.

Reduce RHS:

Defines rule #3.