Certificate for #3488 ⟨a, b, c | bb=aa, aca=c⟩

Completion settings:

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

Axiom: bb=aa.

Defines rule #10.

Referenced by [5], [9], [11].

Axiom: aca=c.

Defines rule #12.

Referenced by [6], [7], [8], [13], [15], [18], [19].

Axiom: aba=d.

Defines rule #3.

Referenced by [4], [7], [9], [10], [12], [14], [17].

Overlap of [3] aba=d with [3] aba=d:

Critical pair: abd=dba.

Defines rule #9.

Overlap of [1] bb=aa with [1] bb=aa:

Critical pair: baa=aab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8], [9], [10], [14], [16].

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

Critical pair: acc=cca.

Defines rule #19.

Overlap of [2] aca=c with [3] aba=d:

Critical pair: acd=cba.

Defines rule #13.

Overlap of [2] aca=c with [5] aab=baa:

Critical pair: acbaa=cab.

Defines rule #14.

Overlap of [3] aba=d with [5] aab=baa:

Critical pair: abbaa=dab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [17].

Overlap of [5] aab=baa with [3] aba=d:

Critical pair: ad=baaa.

Flip LHS and RHS.

Defines rule #2.

Referenced by [11], [12], [13], [14].

Overlap of [1] bb=aa with [10] baaa=ad:

Critical pair: bad=aaaaa.

Defines rule #8.

Overlap of [3] aba=d with [10] baaa=ad:

Critical pair: aad=daa.

Defines rule #1.

Overlap of [10] baaa=ad with [2] aca=c:

Critical pair: baac=adca.

Defines rule #17.

Referenced by [18].

Overlap of [10] baaa=ad with [5] aab=baa:

Critical pair: babaa=adb.

Reduce LHS:

Defines rule #7.

Referenced by [15], [16].

Overlap of [14] bda=adb with [2] aca=c:

Critical pair: bdc=adbca.

Referenced by [20].

Overlap of [14] bda=adb with [5] aab=baa:

Critical pair: bdbaa=adbab.

Defines rule #11.

Overlap of [9] dab=aaaaa with [3] aba=d:

Critical pair: dd=aaaaaa.

Defines rule #5.

Overlap of [13] baac=adca with [2] aca=c:

Critical pair: bac=adcaa.

Defines rule #16.

Referenced by [19].

Overlap of [18] bac=adcaa with [2] aca=c:

Critical pair: bc=adcaaa.

Defines rule #15.

Referenced by [20].

Simplify [15] bdc=adbca.

Reduce RHS:

Defines rule #18.