Certificate for #5322 ⟨a, b, c | ab=a, acba=b⟩

Completion settings:

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

Axiom: ab=a.

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

Axiom: acba=b.

Referenced by [3], [4], [5], [6], [7], [9], [10].

Overlap of [2] acba=b with [1] ab=a:

Critical pair: acba=bb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4], [6].

Overlap of [2] acba=b with [2] acba=b:

Critical pair: acbb=bcba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5], [6].

Overlap of [1] ab=a with [4] bcba=acb:

Critical pair: aacb=acba.

Reduce RHS:

Referenced by [7], [8].

Overlap of [4] bcba=acb with [2] acba=b:

Critical pair: bcbb=acbcba.

Reduce LHS:

Reduce RHS:

Referenced by [9].

Overlap of [5] aacb=b with [2] acba=b:

Critical pair: ab=ba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8], [9], [11], [12].

Overlap of [5] aacb=b with [7] ba=a:

Critical pair: aaca=ba.

Reduce RHS:

Defines rule #1.

Overlap of [6] bcb=acacb with [7] ba=a:

Critical pair: bca=acacba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [2] acba=b with [9] acb=bca:

Critical pair: bcaa=b.

Referenced by [11].

Overlap of [9] acb=bca with [7] ba=a:

Critical pair: aca=bcaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [12].

Overlap of [7] ba=a with [11] b=aca:

Critical pair: acaa=a.

Defines rule #2.