Certificate for #2799 ⟨a, b, c | abc=b, ccaa=1⟩

Completion settings:

• Auxiliary generators:
  1. d = baa
• Reduction order:
  • Left-to-right shortlex with b < a < c < d

Axiom: abc=b.

Defines rule #5.

Referenced by [4], [5], [6], [7], [8], [14], [16].

Axiom: ccaa=1.

Defines rule #14.

Referenced by [5], [6], [7], [10], [11].

Axiom: baa=d.

Defines rule #3.

Referenced by [4], [7], [8], [9], [15].

Overlap of [3] baa=d with [1] abc=b:

Critical pair: bab=dbc.

Flip LHS and RHS.

Referenced by [7], [9].

Overlap of [1] abc=b with [2] ccaa=1:

Critical pair: ab=bcaa.

Flip LHS and RHS.

Defines rule #11.

Referenced by [8], [9], [12], [13].

Overlap of [2] ccaa=1 with [1] abc=b:

Critical pair: ccab=bc.

Defines rule #13.

Referenced by [16].

Overlap of [4] dbc=bab with [2] ccaa=1:

Critical pair: db=babcaa.

Reduce RHS:

Defines rule #1.

Overlap of [1] abc=b with [5] bcaa=ab:

Critical pair: aab=baa.

Reduce RHS:

Defines rule #6.

Referenced by [10], [11], [12], [13], [14], [15].

Overlap of [4] dbc=bab with [5] bcaa=ab:

Critical pair: dab=babaa.

Reduce RHS:

Defines rule #9.

Overlap of [2] ccaa=1 with [8] aab=d:

Critical pair: ccd=b.

Defines rule #8.

Overlap of [2] ccaa=1 with [8] aab=d:

Critical pair: ccad=ab.

Defines rule #15.

Overlap of [5] bcaa=ab with [8] aab=d:

Critical pair: bcd=abb.

Flip LHS and RHS.

Defines rule #4.

Overlap of [5] bcaa=ab with [8] aab=d:

Critical pair: bcad=abab.

Flip LHS and RHS.

Defines rule #12.

Overlap of [8] aab=d with [1] abc=b:

Critical pair: ab=dc.

Flip LHS and RHS.

Defines rule #2.

Overlap of [8] aab=d with [3] baa=d:

Critical pair: aad=daa.

Flip LHS and RHS.

Defines rule #10.

Overlap of [6] ccab=bc with [1] abc=b:

Critical pair: ccb=bcc.

Defines rule #7.