Certificate for #4820 ⟨a, b | abababab=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: abababab=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #3.

Referenced by [3], [5].

Simplify [1] abababab=aab.

Reduce RHS:

Defines rule #9.

Referenced by [4], [5], [6], [7].

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

Critical pair: abc=cab.

Defines rule #1.

Referenced by [6], [8].

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

Critical pair: ac=cababab.

Flip LHS and RHS.

Defines rule #8.

Referenced by [6], [7], [8], [9], [10].

Overlap of [3] abababab=c with [4] abc=cab:

Critical pair: abababcab=cc.

Reduce LHS:

Defines rule #4.

Referenced by [7], [8], [9], [10].

Overlap of [6] acab=cc with [3] abababab=c:

Critical pair: acc=ccababab.

Reduce RHS:

Defines rule #2.

Referenced by [10].

Overlap of [4] abc=cab with [5] cababab=ac:

Critical pair: abac=cabababab.

Reduce RHS:

Defines rule #6.

Overlap of [6] acab=cc with [5] cababab=ac:

Critical pair: aac=ccabab.

Defines rule #5.

Overlap of [7] acc=cac with [5] cababab=ac:

Critical pair: acac=cacababab.

Reduce RHS:

Defines rule #7.