Certificate for #4593 ⟨a, b | aabaaaab=baa⟩

Completion settings:

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

Axiom: aabaaaab=baa.

Referenced by [3].

Axiom: baaaa=c.

Referenced by [3], [4].

Overlap of [1] aabaaaab=baa with [2] baaaa=c:

Critical pair: aacb=baa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5], [6], [7], [8], [9].

Overlap of [2] baaaa=c with [3] baa=aacb:

Critical pair: aacbaa=c.

Reduce LHS:

Referenced by [5], [6], [7], [8], [9], [10].

Overlap of [3] baa=aacb with [4] aacaacb=c:

Critical pair: bc=aacbcaacb.

Flip LHS and RHS.

Referenced by [8].

Overlap of [3] baa=aacb with [4] aacaacb=c:

Critical pair: bac=aacbacaacb.

Flip LHS and RHS.

Referenced by [9].

Overlap of [4] aacaacb=c with [3] baa=aacb:

Critical pair: aacaacaacb=caa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

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

Simplify [5] aacbcaacb=bc.

Reduce LHS:

Defines rule #1.

Simplify [6] aacbacaacb=bac.

Reduce LHS:

Defines rule #2.

Overlap of [4] aacaacb=c with [7] caa=aacc:

Critical pair: aaaacccb=c.

Defines rule #5.