Certificate for #5299 ⟨a, b | aaa=aa, aba=ab⟩

Completion settings:

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

Axiom: aaa=aa.

Defines rule #2.

Referenced by [4].

Axiom: aba=ab.

Defines rule #4.

Referenced by [5], [6].

Axiom: abb=c.

Defines rule #6.

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

Overlap of [1] aaa=aa with [3] abb=c:

Critical pair: aac=aabb.

Reduce RHS:

Defines rule #3.

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

Critical pair: abab=abba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [2] aba=ab with [3] abb=c:

Critical pair: abc=abbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.