Certificate for #5208 ⟨a, b | aabbaab=aaab⟩

Completion settings:

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

Axiom: aabbaab=aaab.

Referenced by [3].

Axiom: aaab=c.

Defines rule #5.

Referenced by [3], [5], [7].

Simplify [1] aabbaab=aaab.

Reduce RHS:

Defines rule #7.

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

Overlap of [3] aabbaab=c with [3] aabbaab=c:

Critical pair: aabbc=cbaab.

Flip LHS and RHS.

Referenced by [5], [9].

Overlap of [2] aaab=c with [3] aabbaab=c:

Critical pair: ac=cbaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [3] aabbaab=c with [5] aabbc=ac:

Critical pair: aabbac=cbc.

Defines rule #6.

Referenced by [8].

Overlap of [2] aaab=c with [5] aabbc=ac:

Critical pair: aac=cbc.

Defines rule #2.

Overlap of [3] aabbaab=c with [6] aabbac=cbc:

Critical pair: aabbcbc=cbac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Simplify [4] cbaab=aabbc.

Reduce RHS:

Defines rule #4.