Certificate for #5855 ⟨a, b | abaaba=baaab⟩

Completion settings:

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

Axiom: abaaba=baaab.

Referenced by [4].

Axiom: baab=c.

Defines rule #19.

Referenced by [4], [5], [6], [8], [10], [12], [18], [20], [22].

Axiom: caaab=d.

Defines rule #10.

Referenced by [6], [7], [8], [9], [10], [13].

Overlap of [1] abaaba=baaab with [2] baab=c:

Critical pair: aca=baaab.

Flip LHS and RHS.

Defines rule #20.

Referenced by [7], [8], [9], [10], [11], [14], [17], [18], [20], [22].

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

Critical pair: baac=caab.

Defines rule #16.

Referenced by [7], [17].

Overlap of [3] caaab=d with [2] baab=c:

Critical pair: caaac=daab.

Defines rule #8.

Referenced by [7], [12], [17].

Overlap of [5] baac=caab with [3] caaab=d:

Critical pair: baad=caabaaab.

Reduce RHS:

Defines rule #13.

Referenced by [17], [18], [19], [20], [22].

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

Critical pair: baaaca=caaab.

Reduce RHS:

Referenced by [15].

Overlap of [3] caaab=d with [4] baaab=aca:

Critical pair: caaaaca=daaab.

Defines rule #9.

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

Critical pair: baaac=acaaab.

Reduce RHS:

Defines rule #17.

Referenced by [12], [13], [14], [15], [17].

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

Critical pair: baaaaca=acaaaab.

Defines rule #18.

Overlap of [2] baab=c with [10] baaac=ad:

Critical pair: baaad=caaac.

Reduce RHS:

Defines rule #14.

Overlap of [3] caaab=d with [10] baaac=ad:

Critical pair: caaaad=daaac.

Defines rule #7.

Overlap of [4] baaab=aca with [10] baaac=ad:

Critical pair: baaaad=acaaaac.

Defines rule #15.

Simplify [8] baaaca=d.

Reduce LHS:

Defines rule #1.

Referenced by [16], [19], [21].

Overlap of [15] ada=d with [15] ada=d:

Critical pair: add=dda.

Defines rule #2.

Overlap of [5] baac=caab with [6] caaac=daab:

Critical pair: baadaab=caabaaac.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [2] baab=c with [7] baad=daaba:

Critical pair: baadaaba=caad.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [7] baad=daaba with [15] ada=d:

Critical pair: bad=daabaa.

Defines rule #12.

Referenced by [20], [21].

Overlap of [2] baab=c with [19] bad=daabaa:

Critical pair: baadaabaa=cad.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [19] bad=daabaa with [15] ada=d:

Critical pair: bd=daabaaa.

Defines rule #11.

Referenced by [22].

Overlap of [2] baab=c with [21] bd=daabaaa:

Critical pair: baadaabaaa=cd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.