Certificate for #5619 ⟨a, b, c | aa=a, aba=cc⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #1.

Referenced by [4], [5].

Axiom: aba=cc.

Flip LHS and RHS.

Defines rule #5.

Referenced by [3].

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

Critical pair: caba=abac.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

Overlap of [1] aa=a with [3] abac=caba:

Critical pair: acaba=abac.

Reduce RHS:

Defines rule #2.

Referenced by [5].

Overlap of [3] abac=caba with [4] acaba=caba:

Critical pair: abcaba=cabaaba.

Reduce RHS:

Defines rule #3.