Certificate for #5123 ⟨a, b | aabaaab=abba⟩

Completion settings:

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

Axiom: aabaaab=abba.

Referenced by [3].

Axiom: abba=c.

Defines rule #1.

Referenced by [3], [4], [6], [7].

Simplify [1] aabaaab=abba.

Reduce RHS:

Defines rule #2.

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

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

Critical pair: abbc=cbba.

Flip LHS and RHS.

Defines rule #5.

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

Critical pair: aabac=caaab.

Flip LHS and RHS.

Defines rule #4.

Overlap of [3] aabaaab=c with [2] abba=c:

Critical pair: aabaac=cba.

Flip LHS and RHS.

Defines rule #3.

Overlap of [2] abba=c with [3] aabaaab=c:

Critical pair: abbc=cabaaab.

Flip LHS and RHS.

Defines rule #6.