Certificate for #656 ⟨a, b | bb=aa, aba=a⟩

Completion settings:

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

Axiom: bb=aa.

Defines rule #5.

Referenced by [3], [4].

Axiom: aba=a.

Defines rule #3.

Referenced by [4], [5].

Overlap of [1] bb=aa with [1] bb=aa:

Critical pair: baa=aab.

Flip LHS and RHS.

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

Overlap of [2] aba=a with [3] aab=baa:

Critical pair: abbaa=aab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [6].

Overlap of [3] aab=baa with [2] aba=a:

Critical pair: aa=baaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Simplify [3] aab=baa.

Reduce RHS:

Defines rule #4.