Certificate for #6263 ⟨a, b | aaa=a, abbba=b⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #4.

Referenced by [3], [4].

Axiom: abbba=b.

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

Overlap of [1] aaa=a with [2] abbba=b:

Critical pair: aab=abbba.

Reduce RHS:

Defines rule #3.

Referenced by [5], [8].

Overlap of [2] abbba=b with [1] aaa=a:

Critical pair: abbba=baa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [3] aab=b with [2] abbba=b:

Critical pair: ab=bbba.

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] abbba=b with [4] baa=b:

Critical pair: abbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Simplify [5] bbba=ab.

Reduce LHS:

Referenced by [8].

Overlap of [3] aab=b with [7] abbbbbbbbb=ab:

Critical pair: aab=bbbbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.