Certificate for #1586 ⟨a, b, c | aaa=bc, acc=1⟩

Completion settings:

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

Axiom: aaa=bc.

Referenced by [3], [4], [5].

Axiom: acc=1.

Referenced by [4], [7], [9].

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

Critical pair: abc=bca.

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] aaa=bc with [2] acc=1:

Critical pair: aa=bccc.

Referenced by [5], [6], [7], [8].

Overlap of [1] aaa=bc with [4] aa=bccc:

Critical pair: bccca=bc.

Referenced by [8].

Overlap of [3] bca=abc with [4] aa=bccc:

Critical pair: bcbccc=abca.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [10].

Overlap of [4] aa=bccc with [2] acc=1:

Critical pair: a=bccccc.

Defines rule #4.

Referenced by [8], [9].

Overlap of [4] aa=bccc with [4] aa=bccc:

Critical pair: abccc=bccca.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [2] acc=1 with [7] a=bccccc:

Critical pair: bccccccc=1.

Defines rule #3.

Overlap of [8] bcccccbccc=bc with [8] bcccccbccc=bc:

Critical pair: bcccccbc=bcccbccc.

Reduce RHS:

Defines rule #2.