Certificate for #2623 ⟨a, b, c | aba=b, caac=1⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [9], [11], [13].

Axiom: caac=1.

Referenced by [5], [6], [7], [8], [10].

Axiom: cc=d.

Defines rule #1.

Referenced by [4], [6], [7].

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

Critical pair: cd=dc.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Overlap of [2] caac=1 with [2] caac=1:

Critical pair: caa=aac.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

Overlap of [2] caac=1 with [3] cc=d:

Critical pair: caad=c.

Referenced by [8].

Overlap of [3] cc=d with [2] caac=1:

Critical pair: c=daac.

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [2] caac=1 with [6] caad=c:

Critical pair: caac=aad.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [9], [12].

Overlap of [1] aba=b with [8] aad=1:

Critical pair: ab=bad.

Defines rule #6.

Referenced by [11], [14].

Overlap of [2] caac=1 with [7] cdaa=c:

Critical pair: caac=daa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11], [12].

Overlap of [10] daa=1 with [1] aba=b:

Critical pair: dab=ba.

Reduce LHS:

Referenced by [14].

Overlap of [10] daa=1 with [8] aad=1:

Critical pair: da=ad.

Defines rule #3.

Referenced by [13], [14].

Overlap of [12] da=ad with [1] aba=b:

Critical pair: db=adba.

Flip LHS and RHS.

Referenced by [15].

Overlap of [12] da=ad with [9] ab=bad:

Critical pair: dbad=adb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [13] adba=db with [14] adb=ba:

Critical pair: baa=db.

Flip LHS and RHS.

Defines rule #7.