Certificate for #4582 ⟨a, b | aaabbbba=aab⟩

Completion settings:

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

Axiom: aaabbbba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #4.

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

Simplify [1] aaabbbba=aab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaabbbba=c with [2] aab=c:

Critical pair: acbbba=c.

Defines rule #3.

Referenced by [5], [6].

Overlap of [4] acbbba=c with [2] aab=c:

Critical pair: acbbbc=cab.

Referenced by [6], [7].

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

Critical pair: acbbbc=ccbbba.

Reduce LHS:

Defines rule #1.

Referenced by [7].

Simplify [5] acbbbc=cab.

Reduce RHS:

Defines rule #2.