Certificate for #358 ⟨a, b, c | aba=b, acb=1⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [4].

Axiom: acb=1.

Defines rule #9.

Referenced by [6], [7], [12], [13], [15].

Axiom: ab=d.

Defines rule #2.

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

Overlap of [1] aba=b with [3] ab=d:

Critical pair: da=b.

Defines rule #7.

Referenced by [5], [6], [10], [15].

Overlap of [4] da=b with [3] ab=d:

Critical pair: dd=bb.

Defines rule #6.

Referenced by [10], [11].

Overlap of [4] da=b with [2] acb=1:

Critical pair: d=bcb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8], [9], [13].

Overlap of [2] acb=1 with [6] bcb=d:

Critical pair: acd=cb.

Defines rule #14.

Referenced by [12], [15].

Overlap of [3] ab=d with [6] bcb=d:

Critical pair: ad=dcb.

Defines rule #8.

Overlap of [6] bcb=d with [6] bcb=d:

Critical pair: bcd=dcb.

Defines rule #12.

Overlap of [5] dd=bb with [4] da=b:

Critical pair: db=bba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [12], [14].

Overlap of [5] dd=bb with [5] dd=bb:

Critical pair: dbb=bbd.

Flip LHS and RHS.

Defines rule #1.

Overlap of [2] acb=1 with [10] bba=db:

Critical pair: acdb=ba.

Reduce LHS:

Defines rule #4.

Referenced by [13], [14].

Overlap of [12] cbb=ba with [6] bcb=d:

Critical pair: cbd=bacb.

Reduce RHS:

Defines rule #11.

Overlap of [12] cbb=ba with [10] bba=db:

Critical pair: cdb=baa.

Defines rule #10.

Overlap of [7] acd=cb with [4] da=b:

Critical pair: acb=cba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.