Certificate for #1858 ⟨a, b, c | aba=bb, cac=1⟩

Completion settings:

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

Axiom: aba=bb.

Referenced by [5].

Axiom: cac=1.

Referenced by [3], [4], [7].

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

Critical pair: ca=ac.

Defines rule #8.

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

Overlap of [2] cac=1 with [3] ca=ac:

Critical pair: acc=1.

Defines rule #6.

Referenced by [5], [8].

Overlap of [1] aba=bb with [4] acc=1:

Critical pair: ab=bbcc.

Defines rule #4.

Referenced by [6].

Overlap of [3] ca=ac with [5] ab=bbcc:

Critical pair: cbbcc=acb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [7].

Overlap of [2] cac=1 with [6] acb=cbbcc:

Critical pair: ccbbcc=b.

Defines rule #3.

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

Overlap of [7] ccbbcc=b with [3] ca=ac:

Critical pair: ccbbcac=ba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [7] ccbbcc=b with [7] ccbbcc=b:

Critical pair: ccbbb=bbbcc.

Defines rule #1.

Overlap of [7] ccbbcc=b with [7] ccbbcc=b:

Critical pair: ccbbcb=bcbbcc.

Defines rule #2.