Certificate for #3490 ⟨a, b, c | bb=aa, acb=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], [6], [8], [10], [20], [22], [24], [25], [27].

Axiom: acb=c.

Defines rule #15.

Referenced by [6], [7], [11], [13], [15], [17], [20], [22], [23], [26].

Axiom: aba=d.

Defines rule #3.

Referenced by [4], [7], [8], [9], [12], [14], [18], [19], [21].

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], [14], [16], [18], [21], [24], [25], [26], [27].

Overlap of [2] acb=c with [1] bb=aa:

Critical pair: acaa=cb.

Defines rule #12.

Referenced by [17], [18], [23].

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

Critical pair: abc=dcb.

Referenced by [20].

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

Critical pair: abbaa=dab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [19].

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

Critical pair: ad=baaa.

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [11], [12], [13], [14], [26].

Overlap of [1] bb=aa with [9] baaa=ad:

Critical pair: bad=aaaaa.

Defines rule #8.

Overlap of [2] acb=c with [9] baaa=ad:

Critical pair: acad=caaa.

Defines rule #14.

Overlap of [3] aba=d with [9] baaa=ad:

Critical pair: aad=daa.

Defines rule #1.

Overlap of [9] baaa=ad with [2] acb=c:

Critical pair: baac=adcb.

Defines rule #19.

Referenced by [22], [23].

Overlap of [9] 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] acb=c:

Critical pair: bdc=adbcb.

Referenced by [20], [24].

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

Critical pair: bdbaa=adbab.

Defines rule #11.

Overlap of [6] acaa=cb with [2] acb=c:

Critical pair: acac=cbcb.

Referenced by [25].

Overlap of [6] acaa=cb with [5] aab=baa:

Critical pair: acabaa=cbab.

Reduce LHS:

Defines rule #13.

Referenced by [20], [21].

Overlap of [8] dab=aaaaa with [3] aba=d:

Critical pair: dd=aaaaaa.

Defines rule #5.

Overlap of [18] acda=cbab with [2] acb=c:

Critical pair: acdc=cbabcb.

Reduce RHS:

Referenced by [27].

Overlap of [18] acda=cbab with [5] aab=baa:

Critical pair: acdbaa=cbabab.

Reduce RHS:

Defines rule #16.

Overlap of [13] baac=adcb with [2] acb=c:

Critical pair: bac=adcbb.

Reduce RHS:

Defines rule #18.

Overlap of [13] baac=adcb with [6] acaa=cb:

Critical pair: bacb=adcbaa.

Reduce LHS:

Defines rule #17.

Referenced by [24], [25], [27].

Simplify [15] bdc=adbcb.

Reduce RHS:

Defines rule #20.

Simplify [17] acac=cbcb.

Reduce RHS:

Defines rule #22.

Referenced by [26].

Overlap of [25] acac=cadcaaaa with [2] acb=c:

Critical pair: acc=cadcaaaab.

Reduce RHS:

Defines rule #21.

Simplify [20] acdc=cadbcbaa.

Reduce RHS:

Defines rule #23.