Certificate for #7539 ⟨a, b, c | ab=1, bbcc=cb⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #1.

Referenced by [5], [7].

Axiom: bbcc=cb.

Referenced by [4].

Axiom: cb=d.

Defines rule #9.

Referenced by [4], [6], [8], [9], [10].

Simplify [2] bbcc=cb.

Reduce RHS:

Referenced by [5], [6], [13].

Overlap of [1] ab=1 with [4] bbcc=d:

Critical pair: ad=bcc.

Flip LHS and RHS.

Referenced by [6], [7], [8], [9], [13], [14].

Overlap of [3] cb=d with [4] bbcc=d:

Critical pair: cd=dbcc.

Reduce RHS:

Defines rule #8.

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

Overlap of [1] ab=1 with [5] bcc=ad:

Critical pair: aad=cc.

Flip LHS and RHS.

Defines rule #12.

Referenced by [8], [10], [11], [12], [14].

Overlap of [3] cb=d with [5] bcc=ad:

Critical pair: cad=dcc.

Reduce RHS:

Defines rule #10.

Overlap of [5] bcc=ad with [3] cb=d:

Critical pair: bcd=adb.

Reduce LHS:

Defines rule #3.

Overlap of [7] cc=aad with [3] cb=d:

Critical pair: cd=aadb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [15].

Overlap of [7] cc=aad with [6] cd=dad:

Critical pair: cdad=aadd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [7] cc=aad with [7] cc=aad:

Critical pair: caad=aadc.

Defines rule #11.

Overlap of [4] bbcc=d with [5] bcc=ad:

Critical pair: bad=d.

Defines rule #2.

Overlap of [5] bcc=ad with [7] cc=aad:

Critical pair: baad=ad.

Defines rule #6.

Referenced by [15].

Overlap of [10] aadb=dad with [14] baad=ad:

Critical pair: aadad=dadaad.

Defines rule #7.