Certificate for #1804 ⟨a, b | abbaabaab=b⟩

Completion settings:

• Auxiliary generators:
  1. c = ab
  2. d = bbac
• Reduction order:
  • Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(d) = deg(b) = 1, d < b

Axiom: abbaabaab=b.

Referenced by [4].

Axiom: ab=c.

Referenced by [4], [5], [9].

Axiom: bbac=d.

Referenced by [5], [10].

Overlap of [1] abbaabaab=b with [2] ab=c:

Critical pair: cbaabaab=b.

Reduce LHS:

Referenced by [7].

Overlap of [2] ab=c with [3] bbac=d:

Critical pair: ad=cbac.

Flip LHS and RHS.

Referenced by [6], [7], [10], [11].

Overlap of [5] cbac=ad with [5] cbac=ad:

Critical pair: cbaad=adbac.

Referenced by [8].

Simplify [4] cbacac=b.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [8], [9], [10], [11].

Simplify [6] cbaad=adbac.

Reduce LHS:

Reduce RHS:

Referenced by [12], [15], [20].

Overlap of [2] ab=c with [7] b=adac:

Critical pair: aadac=c.

Defines rule #3.

Referenced by [12], [13], [15], [18], [20].

Overlap of [3] bbac=d with [7] b=adac:

Critical pair: adacbac=d.

Reduce LHS:

Defines rule #9.

Referenced by [13], [14], [16], [17].

Overlap of [5] cbac=ad with [7] b=adac:

Critical pair: cadacac=ad.

Defines rule #5.

Referenced by [17], [19].

Overlap of [8] cadacaad=adadacac with [9] aadac=c:

Critical pair: cadacc=adadacacac.

Flip LHS and RHS.

Referenced by [18].

Overlap of [10] adaad=d with [9] aadac=c:

Critical pair: adc=dac.

Defines rule #1.

Referenced by [15].

Overlap of [10] adaad=d with [10] adaad=d:

Critical pair: adad=daad.

Defines rule #8.

Referenced by [15], [16], [18], [20].

Overlap of [8] cadacaad=adadacac with [13] adc=dac:

Critical pair: cadacadac=adadacacc.

Reduce RHS:

Referenced by [17].

Overlap of [14] adad=daad with [10] adaad=d:

Critical pair: add=daadaad.

Reduce RHS:

Defines rule #7.

Overlap of [15] cadacadac=dcacc with [11] cadacac=ad:

Critical pair: cadaad=dcaccac.

Reduce LHS:

Defines rule #2.

Simplify [12] adadacacac=cadacc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [19].

Overlap of [18] cadacc=dcacac with [11] cadacac=ad:

Critical pair: cadacad=dcacacadacac.

Reduce RHS:

Defines rule #10.

Simplify [8] cadacaad=adadacac.

Reduce RHS:

Defines rule #11.