Certificate for #1815 ⟨a, b, c | aba=ab, bcc=1⟩

Completion settings:

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

Axiom: aba=ab.

Referenced by [4].

Axiom: bcc=1.

Defines rule #2.

Referenced by [6], [8].

Axiom: ab=d.

Referenced by [4], [5], [6], [7], [9].

Simplify [1] aba=ab.

Reduce RHS:

Referenced by [5].

Overlap of [4] aba=d with [3] ab=d:

Critical pair: da=d.

Referenced by [7].

Overlap of [3] ab=d with [2] bcc=1:

Critical pair: a=dcc.

Defines rule #5.

Referenced by [9].

Overlap of [5] da=d with [3] ab=d:

Critical pair: dd=db.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

Overlap of [7] db=dd with [2] bcc=1:

Critical pair: d=ddcc.

Flip LHS and RHS.

Defines rule #1.

Overlap of [3] ab=d with [6] a=dcc:

Critical pair: dccb=d.

Defines rule #4.