Certificate for #19614 ⟨a, b | aab=b, bbabb=ba⟩

Completion settings:

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

Axiom: aab=b.

Defines rule #5.

Referenced by [3], [4], [5], [6].

Axiom: bbabb=ba.

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

Overlap of [2] bbabb=ba with [2] bbabb=ba:

Critical pair: bbaba=baabb.

Reduce RHS:

Referenced by [4], [5], [7].

Overlap of [2] bbabb=ba with [3] bbaba=bbb:

Critical pair: bbabbb=baaba.

Reduce LHS:

Reduce RHS:

Defines rule #3.

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

Overlap of [3] bbaba=bbb with [1] aab=b:

Critical pair: bbabb=bbbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [2] bbabb=ba with [4] bab=bba:

Critical pair: bbabbba=baab.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [3] bbaba=bbb with [4] bab=bba:

Critical pair: bbabba=bbbb.

Reduce LHS:

Defines rule #4.

Referenced by [8].

Simplify [6] bbaa=bb.

Reduce LHS:

Defines rule #1.