Certificate for #2783 ⟨a, b, c | abc=b, baca=1⟩

Completion settings:

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

Axiom: abc=b.

Referenced by [5], [6].

Axiom: baca=1.

Referenced by [4].

Axiom: ca=d.

Referenced by [4], [5], [6], [8], [9].

Overlap of [2] baca=1 with [3] ca=d:

Critical pair: bad=1.

Referenced by [7], [11], [12].

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

Critical pair: abd=ba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [11], [12].

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

Critical pair: cb=dbc.

Flip LHS and RHS.

Referenced by [10].

Overlap of [4] bad=1 with [5] ba=abd:

Critical pair: abdd=1.

Defines rule #2.

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

Overlap of [3] ca=d with [7] abdd=1:

Critical pair: c=dbdd.

Defines rule #5.

Referenced by [9], [10].

Overlap of [3] ca=d with [8] c=dbdd:

Critical pair: dbdda=d.

Referenced by [12].

Simplify [6] dbc=cb.

Reduce LHS:

Reduce RHS:

Referenced by [11].

Overlap of [4] bad=1 with [10] dbdbdd=dbddb:

Critical pair: badbddb=bdbdd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [4] bad=1 with [9] dbdda=d:

Critical pair: bad=bdda.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.