Certificate for #3755 ⟨a, b | ababaaaaab=a⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(c) = deg(e) = 0, c < e; deg(d) = deg(a) = 1, d < a; deg(b) = 2
• Auxiliary generators:
  1. ab=c
  2. aaaaa=d
  3. caaac=e

Axiom: ababaaaaab=a.

Referenced by [5].

Axiom: ab=c.

Defines rule #16.

Referenced by [5], [8].

Axiom: aaaaa=d.

Defines rule #12.

Referenced by [5], [8], [9], [11], [12], [13], [16], [17].

Axiom: caaac=e.

Defines rule #4.

Referenced by [6], [7], [11], [15], [18], [19], [20], [21].

Overlap of [1] ababaaaaab=a with [2] ab=c:

Critical pair: cabaaaaab=a.

Reduce LHS:

Referenced by [7], [12], [14].

Overlap of [4] caaac=e with [4] caaac=e:

Critical pair: caaae=eaaac.

Defines rule #5.

Overlap of [4] caaac=e with [5] ccdb=a:

Critical pair: caaaa=ecdb.

Flip LHS and RHS.

Referenced by [10].

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

Critical pair: aaaac=db.

Flip LHS and RHS.

Defines rule #15.

Referenced by [10], [12], [14].

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

Critical pair: ad=da.

Flip LHS and RHS.

Defines rule #3.

Referenced by [11], [13], [18], [20], [21].

Simplify [7] ecdb=caaaa.

Reduce LHS:

Defines rule #8.

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

Overlap of [10] ecaaaac=caaaa with [4] caaac=e:

Critical pair: ecaaaae=caaaaaaac.

Reduce RHS:

Referenced by [22].

Overlap of [10] ecaaaac=caaaa with [5] ccdb=a:

Critical pair: ecaaaaa=caaaacdb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [13], [16].

Overlap of [10] ecaaaac=caaaa with [12] caaaacaaaac=ecd:

Critical pair: eecd=caaaaaaaac.

Reduce RHS:

Flip LHS and RHS.

Referenced by [18].

Overlap of [5] ccdb=a with [8] db=aaaac:

Critical pair: ccaaaac=a.

Defines rule #7.

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

Overlap of [14] ccaaaac=a with [4] caaac=e:

Critical pair: ccaaaae=aaaac.

Defines rule #10.

Overlap of [14] ccaaaac=a with [12] caaaacaaaac=ecd:

Critical pair: cecd=aaaaac.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [18], [20], [21], [22].

Overlap of [14] ccaaaac=a with [14] ccaaaac=a:

Critical pair: ccaaaaa=acaaaac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

Referenced by [19], [20].

Overlap of [16] dc=cecd with [4] caaac=e:

Critical pair: de=cecdaaac.

Reduce RHS:

Defines rule #2.

Overlap of [4] caaac=e with [17] acaaaac=ccd:

Critical pair: caaccd=eaaaac.

Flip LHS and RHS.

Defines rule #6.

Referenced by [21].

Overlap of [17] acaaaac=ccd with [4] caaac=e:

Critical pair: acaaaae=ccdaaac.

Reduce RHS:

Defines rule #14.

Overlap of [19] eaaaac=caaccd with [4] caaac=e:

Critical pair: eaaaae=caaccdaaac.

Reduce RHS:

Defines rule #9.

Simplify [11] ecaaaae=caadc.

Reduce RHS:

Defines rule #11.