Certificate for #5872 ⟨a, b | ababab=abbba⟩

Completion settings:

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

Axiom: ababab=abbba.

Referenced by [3].

Axiom: abbba=c.

Defines rule #3.

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

Simplify [1] ababab=abbba.

Reduce RHS:

Defines rule #4.

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

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

Critical pair: abbbc=cbbba.

Flip LHS and RHS.

Defines rule #5.

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

Critical pair: abc=cab.

Flip LHS and RHS.

Defines rule #1.

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

Critical pair: ababc=cbba.

Flip LHS and RHS.

Defines rule #2.

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

Critical pair: abbbc=cbabab.

Flip LHS and RHS.

Defines rule #6.