Certificate for #4456 ⟨a, b | aaaabbaa=aab⟩

Completion settings:

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

Axiom: aaaabbaa=aab.

Referenced by [3].

Axiom: aabb=c.

Referenced by [3], [4].

Overlap of [1] aaaabbaa=aab with [2] aabb=c:

Critical pair: aacaa=aab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [4], [5], [6].

Overlap of [2] aabb=c with [3] aab=aacaa:

Critical pair: aacaab=c.

Reduce LHS:

Defines rule #2.

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

Overlap of [4] aacaacaa=c with [3] aab=aacaa:

Critical pair: aacaacaacaa=cb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [4] aacaacaa=c with [3] aab=aacaa:

Critical pair: aacaacaaacaa=cab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [4] aacaacaa=c with [4] aacaacaa=c:

Critical pair: aacc=ccaa.

Flip LHS and RHS.

Defines rule #1.

Referenced by [9].

Overlap of [4] aacaacaa=c with [4] aacaacaa=c:

Critical pair: aacaacac=cacaacaa.

Flip LHS and RHS.

Defines rule #3.

Simplify [5] cb=ccaa.

Reduce RHS:

Defines rule #4.