Certificate for #4376 ⟨a, b | aaaaaaba=aab⟩

Completion settings:

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

Axiom: aaaaaaba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #5.

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

Simplify [1] aaaaaaba=aab.

Reduce RHS:

Referenced by [4].

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

Critical pair: aaaaca=c.

Defines rule #2.

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

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

Critical pair: aaaacc=cab.

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: aaaacc=caaaca.

Defines rule #1.

Referenced by [7].

Simplify [5] cab=aaaacc.

Reduce RHS:

Defines rule #4.

Referenced by [8].

Overlap of [4] aaaaca=c with [7] cab=caaaca:

Critical pair: aaaacaaaca=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.