Certificate for #2400 ⟨a, b, c | aab=a, cbbc=1⟩

Completion settings:

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

Axiom: aab=a.

Defines rule #1.

Referenced by [6], [10].

Axiom: cbbc=1.

Referenced by [4].

Axiom: bc=d.

Defines rule #4.

Referenced by [4], [5], [6], [9], [14].

Overlap of [2] cbbc=1 with [3] bc=d:

Critical pair: cbd=1.

Defines rule #7.

Referenced by [5], [7], [9], [12].

Overlap of [3] bc=d with [4] cbd=1:

Critical pair: b=dbd.

Flip LHS and RHS.

Defines rule #6.

Referenced by [7], [8], [13].

Overlap of [1] aab=a with [3] bc=d:

Critical pair: aad=ac.

Flip LHS and RHS.

Defines rule #3.

Overlap of [4] cbd=1 with [5] dbd=b:

Critical pair: cbb=bd.

Defines rule #5.

Referenced by [9], [11].

Overlap of [5] dbd=b with [5] dbd=b:

Critical pair: dbb=bbd.

Defines rule #2.

Overlap of [7] cbb=bd with [3] bc=d:

Critical pair: cbd=bdc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [10], [11], [13].

Overlap of [1] aab=a with [9] bdc=1:

Critical pair: aa=adc.

Flip LHS and RHS.

Defines rule #8.

Overlap of [7] cbb=bd with [9] bdc=1:

Critical pair: cb=bddc.

Flip LHS and RHS.

Referenced by [12], [13].

Overlap of [4] cbd=1 with [11] bddc=cb:

Critical pair: ccb=dc.

Defines rule #11.

Referenced by [16].

Overlap of [5] dbd=b with [11] bddc=cb:

Critical pair: dcb=bdc.

Reduce RHS:

Defines rule #10.

Referenced by [14].

Overlap of [13] dcb=1 with [3] bc=d:

Critical pair: dcd=c.

Defines rule #12.

Referenced by [15].

Overlap of [14] dcd=c with [14] dcd=c:

Critical pair: dcc=ccd.

Defines rule #14.

Referenced by [16].

Overlap of [15] dcc=ccd with [12] ccb=dc:

Critical pair: ddc=ccdb.

Defines rule #13.