Certificate for #1592 ⟨a, b, c | aaa=bc, cab=1⟩

Completion settings:

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

Axiom: aaa=bc.

Defines rule #4.

Referenced by [3], [6].

Axiom: cab=1.

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

Overlap of [1] aaa=bc with [1] aaa=bc:

Critical pair: abc=bca.

Flip LHS and RHS.

Referenced by [4], [5].

Overlap of [2] cab=1 with [3] bca=abc:

Critical pair: caabc=ca.

Referenced by [7].

Overlap of [3] bca=abc with [2] cab=1:

Critical pair: b=abcb.

Flip LHS and RHS.

Referenced by [6], [9].

Overlap of [1] aaa=bc with [5] abcb=b:

Critical pair: aab=bcbcb.

Referenced by [7].

Simplify [4] caabc=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [8].

Overlap of [2] cab=1 with [7] ca=cbcbcbc:

Critical pair: cbcbcbcb=1.

Defines rule #1.

Referenced by [9].

Overlap of [5] abcb=b with [8] cbcbcbcb=1:

Critical pair: ab=bcbcbcb.

Defines rule #2.