Certificate for #3255 ⟨a, b, c | bb=aa, acca=1⟩

Completion settings:

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

Axiom: bb=aa.

Referenced by [4].

Axiom: acca=1.

Referenced by [7], [8], [9], [10], [12].

Axiom: aa=d.

Defines rule #7.

Referenced by [4], [5], [8], [9].

Simplify [1] bb=aa.

Reduce RHS:

Defines rule #8.

Referenced by [6].

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

Critical pair: ad=da.

Flip LHS and RHS.

Defines rule #3.

Referenced by [9].

Overlap of [4] bb=d with [4] bb=d:

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #5.

Referenced by [11].

Overlap of [2] acca=1 with [2] acca=1:

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #4.

Referenced by [9].

Overlap of [2] acca=1 with [3] aa=d:

Critical pair: accd=a.

Referenced by [10].

Overlap of [3] aa=d with [2] acca=1:

Critical pair: a=dcca.

Reduce RHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [2] acca=1 with [8] accd=a:

Critical pair: acca=ccd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [11], [13], [15].

Overlap of [10] ccd=1 with [6] db=bd:

Critical pair: ccbd=b.

Referenced by [14].

Overlap of [2] acca=1 with [9] adcc=a:

Critical pair: acca=dcc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [12] dcc=1 with [10] ccd=1:

Critical pair: dc=cd.

Defines rule #1.

Referenced by [14], [15].

Overlap of [11] ccbd=b with [13] dc=cd:

Critical pair: ccbcd=bc.

Referenced by [15].

Overlap of [14] ccbcd=bc with [13] dc=cd:

Critical pair: ccbccd=bcc.

Reduce LHS:

Defines rule #6.