Certificate for #1876 ⟨a, b, c | aba=bc, cab=1⟩

Completion settings:

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

Axiom: aba=bc.

Referenced by [3], [4].

Axiom: cab=1.

Referenced by [3], [5].

Overlap of [2] cab=1 with [1] aba=bc:

Critical pair: cbc=a.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

Overlap of [1] aba=bc with [3] a=cbc:

Critical pair: cbcba=bc.

Reduce LHS:

Referenced by [6], [7].

Overlap of [2] cab=1 with [3] a=cbc:

Critical pair: ccbcb=1.

Defines rule #2.

Referenced by [6].

Overlap of [4] cbcbcbc=bc with [5] ccbcb=1:

Critical pair: cbcbcb=bccbcb.

Reduce RHS:

Defines rule #3.

Referenced by [7].

Overlap of [4] cbcbcbc=bc with [6] cbcbcb=b:

Critical pair: cbb=bcb.

Defines rule #1.