Certificate for #2425 ⟨a, b | aaabaa=abaa⟩

Completion settings:

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

Axiom: aaabaa=abaa.

Referenced by [3].

Axiom: abaa=c.

Defines rule #3.

Referenced by [3], [4], [5], [6], [7], [8], [9].

Simplify [1] aaabaa=abaa.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaabaa=c with [2] abaa=c:

Critical pair: aac=c.

Defines rule #1.

Referenced by [6], [7].

Overlap of [2] abaa=c with [2] abaa=c:

Critical pair: abac=cbaa.

Flip LHS and RHS.

Referenced by [10].

Overlap of [2] abaa=c with [4] aac=c:

Critical pair: abc=cc.

Defines rule #2.

Referenced by [8].

Overlap of [2] abaa=c with [4] aac=c:

Critical pair: abac=cac.

Defines rule #4.

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

Overlap of [2] abaa=c with [6] abc=cc:

Critical pair: abacc=cbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [2] abaa=c with [7] abac=cac:

Critical pair: abacac=cbac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Simplify [5] cbaa=abac.

Reduce RHS:

Defines rule #6.