Certificate for #2777 ⟨a, b, c | abc=b, acca=1⟩

Completion settings:

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

Axiom: abc=b.

Referenced by [5], [8].

Axiom: acca=1.

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

Axiom: aa=d.

Defines rule #8.

Referenced by [4], [5], [7], [13].

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

Critical pair: ad=da.

Flip LHS and RHS.

Defines rule #6.

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

Critical pair: ab=dbc.

Referenced by [8], [14].

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

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #7.

Referenced by [13].

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

Critical pair: accd=a.

Referenced by [9].

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

Critical pair: dbcc=b.

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

Overlap of [2] acca=1 with [7] accd=a:

Critical pair: acca=ccd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [8] dbcc=b with [9] ccd=1:

Critical pair: db=bd.

Defines rule #1.

Referenced by [11], [14].

Overlap of [8] dbcc=b with [9] ccd=1:

Critical pair: dbc=bcd.

Reduce LHS:

Referenced by [14].

Overlap of [9] ccd=1 with [8] dbcc=b:

Critical pair: ccb=bcc.

Defines rule #3.

Overlap of [2] acca=1 with [6] cca=acc:

Critical pair: aacc=1.

Reduce LHS:

Referenced by [15].

Simplify [5] ab=dbc.

Reduce RHS:

Defines rule #5.

Overlap of [13] dcc=1 with [9] ccd=1:

Critical pair: dc=cd.

Defines rule #2.