Certificate for #539 ⟨a, b | abaab=aba⟩

Completion settings:

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

Axiom: abaab=aba.

Referenced by [3].

Axiom: aba=c.

Defines rule #4.

Referenced by [3], [4], [5], [6].

Simplify [1] abaab=aba.

Reduce RHS:

Referenced by [4].

Overlap of [3] abaab=c with [2] aba=c:

Critical pair: cab=c.

Referenced by [6], [7].

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

Critical pair: abc=cba.

Flip LHS and RHS.

Defines rule #3.

Overlap of [4] cab=c with [2] aba=c:

Critical pair: cc=ca.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Overlap of [4] cab=c with [6] ca=cc:

Critical pair: ccb=c.

Defines rule #1.