Certificate for #1262 ⟨a, b | ababa=baab⟩

Completion settings:

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

Axiom: ababa=baab.

Referenced by [4].

Axiom: bab=c.

Defines rule #17.

Referenced by [4], [5], [6], [9], [10], [12], [14], [20].

Axiom: caab=d.

Defines rule #9.

Referenced by [6], [7], [8], [10], [11], [12], [15].

Overlap of [1] ababa=baab with [2] bab=c:

Critical pair: aca=baab.

Flip LHS and RHS.

Defines rule #18.

Referenced by [7], [8], [9], [10], [11], [12], [13], [16], [20].

Overlap of [2] bab=c with [2] bab=c:

Critical pair: bac=cab.

Defines rule #14.

Referenced by [7].

Overlap of [3] caab=d with [2] bab=c:

Critical pair: caac=dab.

Defines rule #7.

Referenced by [7], [8], [14].

Overlap of [5] bac=cab with [3] caab=d:

Critical pair: bad=cabaab.

Reduce RHS:

Defines rule #11.

Referenced by [9], [18], [20].

Overlap of [6] caac=dab with [3] caab=d:

Critical pair: caad=dabaab.

Reduce RHS:

Defines rule #5.

Overlap of [2] bab=c with [7] bad=daba:

Critical pair: badaba=cad.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [2] bab=c with [4] baab=aca:

Critical pair: baaca=caab.

Reduce RHS:

Referenced by [17].

Overlap of [3] caab=d with [4] baab=aca:

Critical pair: caaaca=daab.

Defines rule #8.

Overlap of [4] baab=aca with [2] bab=c:

Critical pair: baac=acaab.

Reduce RHS:

Defines rule #15.

Referenced by [14], [15], [16], [17].

Overlap of [4] baab=aca with [4] baab=aca:

Critical pair: baaaca=acaaab.

Defines rule #16.

Overlap of [2] bab=c with [12] baac=ad:

Critical pair: baad=caac.

Reduce RHS:

Defines rule #12.

Overlap of [3] caab=d with [12] baac=ad:

Critical pair: caaad=daac.

Defines rule #6.

Overlap of [4] baab=aca with [12] baac=ad:

Critical pair: baaad=acaaac.

Defines rule #13.

Simplify [10] baaca=d.

Reduce LHS:

Defines rule #1.

Referenced by [18], [19].

Overlap of [7] bad=daba with [17] ada=d:

Critical pair: bd=dabaa.

Defines rule #10.

Referenced by [20].

Overlap of [17] ada=d with [17] ada=d:

Critical pair: add=dda.

Defines rule #2.

Overlap of [2] bab=c with [18] bd=dabaa:

Critical pair: badabaa=cd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.