Certificate for #7837 ⟨a, b, c | ab=1, cac=bba⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #7.

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

Axiom: cac=bba.

Flip LHS and RHS.

Referenced by [4].

Axiom: ac=d.

Defines rule #8.

Referenced by [4], [5], [8].

Simplify [2] bba=cac.

Reduce RHS:

Referenced by [5], [9].

Overlap of [1] ab=1 with [4] bba=cd:

Critical pair: acd=ba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [6], [7], [8], [10].

Overlap of [1] ab=1 with [5] ba=dd:

Critical pair: add=a.

Defines rule #6.

Referenced by [12].

Overlap of [5] ba=dd with [1] ab=1:

Critical pair: b=ddb.

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [5] ba=dd with [3] ac=d:

Critical pair: bd=ddc.

Flip LHS and RHS.

Defines rule #4.

Referenced by [9], [12].

Overlap of [7] ddb=b with [4] bba=cd:

Critical pair: ddcd=bba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [7] ddb=b with [5] ba=dd:

Critical pair: dddd=ba.

Reduce RHS:

Defines rule #1.

Overlap of [9] cd=bdd with [7] ddb=b:

Critical pair: cb=bdddb.

Reduce RHS:

Defines rule #5.

Overlap of [6] add=a with [8] ddc=bd:

Critical pair: adbd=adc.

Flip LHS and RHS.

Defines rule #9.