Certificate for #19494 ⟨a, b | aab=a, bbbab=ba⟩

Completion settings:

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

Axiom: aab=a.

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

Axiom: bbbab=ba.

Referenced by [3], [6].

Overlap of [1] aab=a with [2] bbbab=ba:

Critical pair: aaba=abbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4], [7].

Overlap of [3] abbab=aa with [3] abbab=aa:

Critical pair: abbaa=aabab.

Reduce RHS:

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

Overlap of [1] aab=a with [4] abbaa=a:

Critical pair: aa=abaa.

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] bbbab=ba with [4] abbaa=a:

Critical pair: bbba=babaa.

Reduce RHS:

Defines rule #3.

Overlap of [3] abbab=aa with [4] abbaa=a:

Critical pair: abba=aabaa.

Reduce RHS:

Referenced by [8].

Overlap of [4] abbaa=a with [1] aab=a:

Critical pair: abba=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Overlap of [4] abbaa=a with [1] aab=a:

Critical pair: abbaa=aab.

Reduce LHS:

Reduce RHS:

Defines rule #1.