Certificate for #1118 ⟨a, b | ababab=aab⟩

Completion settings:

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

Axiom: ababab=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #3.

Referenced by [3], [5], [7].

Simplify [1] ababab=aab.

Reduce RHS:

Defines rule #7.

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

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

Critical pair: abc=cab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [5], [7], [8].

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

Critical pair: ac=cabab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

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

Overlap of [3] ababab=c with [5] ababc=ac:

Critical pair: abac=cc.

Defines rule #5.

Overlap of [2] aab=c with [5] ababc=ac:

Critical pair: aac=cabc.

Reduce RHS:

Defines rule #4.

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

Critical pair: cac=abcabc.

Reduce RHS:

Defines rule #2.