Certificate for #6364 ⟨a, b | aab=a, babbb=a⟩

Completion settings:

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

Axiom: aab=a.

Referenced by [3], [4], [5], [6], [7], [8], [9].

Axiom: babbb=a.

Referenced by [3], [4].

Overlap of [1] aab=a with [2] babbb=a:

Critical pair: aaa=aabbb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [4], [5].

Overlap of [2] babbb=a with [2] babbb=a:

Critical pair: babba=aabbb.

Reduce LHS:

Reduce RHS:

Referenced by [6].

Overlap of [1] aab=a with [3] abb=aaa:

Critical pair: aaaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8], [9].

Overlap of [4] baaaa=aaa with [1] aab=a:

Critical pair: baaa=aaab.

Reduce RHS:

Referenced by [7], [8].

Overlap of [6] baaa=aa with [1] aab=a:

Critical pair: baa=aab.

Reduce RHS:

Referenced by [8], [9].

Overlap of [6] baaa=aa with [5] ab=aaaa:

Critical pair: baaaaaa=aab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [7] baa=a with [1] aab=a:

Critical pair: ba=ab.

Reduce RHS:

Defines rule #2.