Certificate for #3063 ⟨a, b | aabababaaab=1⟩

Completion settings:

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

Axiom: aabababaaab=1.

Referenced by [4].

Axiom: ab=c.

Referenced by [4], [5], [11].

Axiom: aaca=d.

Defines rule #8.

Referenced by [5], [6], [7], [9], [24].

Overlap of [1] aabababaaab=1 with [2] ab=c:

Critical pair: acababaaab=1.

Reduce LHS:

Referenced by [7], [8], [10], [12], [14], [16].

Overlap of [3] aaca=d with [2] ab=c:

Critical pair: aacc=db.

Flip LHS and RHS.

Referenced by [11], [19].

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

Critical pair: aacd=daca.

Flip LHS and RHS.

Referenced by [20].

Overlap of [4] acccaac=1 with [3] aaca=d:

Critical pair: acccd=a.

Referenced by [9], [10], [11].

Overlap of [4] acccaac=1 with [4] acccaac=1:

Critical pair: accca=ccaac.

Flip LHS and RHS.

Referenced by [22].

Overlap of [3] aaca=d with [7] acccd=a:

Critical pair: aaca=dcccd.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [4] acccaac=1 with [7] acccd=a:

Critical pair: acccaa=ccd.

Referenced by [11], [12], [14], [16], [23].

Overlap of [7] acccd=a with [5] db=aacc:

Critical pair: acccaacc=ab.

Reduce LHS:

Reduce RHS:

Referenced by [12], [13].

Overlap of [4] acccaac=1 with [11] ccdcc=c:

Critical pair: acccaac=cdcc.

Reduce LHS:

Referenced by [13], [14], [15], [16], [17].

Overlap of [11] ccdcc=c with [12] ccdc=cdcc:

Critical pair: cdccc=c.

Referenced by [14].

Overlap of [4] acccaac=1 with [13] cdccc=c:

Critical pair: acccaac=dccc.

Reduce LHS:

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

Overlap of [14] cdcc=dccc with [12] ccdc=cdcc:

Critical pair: cdcdcc=dcccdc.

Reduce LHS:

Reduce RHS:

Referenced by [18].

Overlap of [4] acccaac=1 with [10] acccaa=ccd:

Critical pair: ccdc=1.

Reduce LHS:

Defines rule #2.

Referenced by [17], [18], [25], [27], [30].

Simplify [12] ccdc=cdcc.

Reduce RHS:

Referenced by [22], [26].

Overlap of [15] cddccc=dc with [16] dccc=1:

Critical pair: cd=dc.

Defines rule #1.

Referenced by [19], [20], [21], [23], [30].

Overlap of [18] cd=dc with [5] db=aacc:

Critical pair: caacc=dcb.

Flip LHS and RHS.

Referenced by [22].

Simplify [6] daca=aacd.

Reduce RHS:

Defines rule #3.

Referenced by [21].

Overlap of [18] cd=dc with [20] daca=aadc:

Critical pair: caadc=dcaca.

Flip LHS and RHS.

Defines rule #5.

Referenced by [26].

Overlap of [17] ccdc=1 with [19] dcb=caacc:

Critical pair: cccaacc=b.

Reduce LHS:

Flip LHS and RHS.

Referenced by [29].

Simplify [10] acccaa=ccd.

Reduce RHS:

Referenced by [24], [25].

Overlap of [23] acccaa=dcc with [3] aaca=d:

Critical pair: acccad=dccaca.

Flip LHS and RHS.

Defines rule #7.

Overlap of [23] acccaa=dcc with [23] acccaa=dcc:

Critical pair: acccadcc=dcccccaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [26].

Overlap of [17] ccdc=1 with [21] dcaca=caadc:

Critical pair: cccaadc=aca.

Reduce LHS:

Referenced by [27].

Overlap of [26] cacccad=aca with [16] dccc=1:

Critical pair: caccca=acaccc.

Defines rule #4.

Referenced by [28], [29].

Overlap of [27] caccca=acaccc with [27] caccca=acaccc:

Critical pair: caccacaccc=acacccccca.

Referenced by [30].

Simplify [22] b=cacccac.

Reduce RHS:

Defines rule #10.

Overlap of [28] caccacaccc=acacccccca with [18] cd=dc:

Critical pair: caccacaccdc=acaccccccad.

Reduce LHS:

Defines rule #9.