Certificate for #366 ⟨a, b, c | aba=b, cbc=1⟩

Completion settings:

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

Axiom: aba=b.

Defines rule #5.

Referenced by [4], [9].

Axiom: cbc=1.

Referenced by [3], [5].

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

Critical pair: cb=bc.

Flip LHS and RHS.

Defines rule #1.

Referenced by [5], [7], [8].

Overlap of [1] aba=b with [1] aba=b:

Critical pair: abb=bba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [6].

Overlap of [2] cbc=1 with [3] bc=cb:

Critical pair: ccb=1.

Defines rule #2.

Referenced by [6], [8], [9], [10].

Overlap of [5] ccb=1 with [4] bba=abb:

Critical pair: ccabb=ba.

Referenced by [7].

Overlap of [6] ccabb=ba with [3] bc=cb:

Critical pair: ccabcb=bac.

Reduce LHS:

Referenced by [8].

Overlap of [7] ccacbb=bac with [3] bc=cb:

Critical pair: ccacbcb=bacc.

Reduce LHS:

Referenced by [9].

Overlap of [8] ccab=bacc with [1] aba=b:

Critical pair: ccb=bacca.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [5] ccb=1 with [9] bacca=1:

Critical pair: cc=acca.

Flip LHS and RHS.

Referenced by [11].

Overlap of [9] bacca=1 with [10] acca=cc:

Critical pair: bacccc=cca.

Flip LHS and RHS.

Defines rule #3.