Certificate for #12342 ⟨a, b | aaba=aa, babb=a⟩

Completion settings:

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

Axiom: aaba=aa.

Defines rule #3.

Referenced by [4], [5].

Axiom: babb=a.

Defines rule #6.

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

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

Critical pair: baba=aabb.

Flip LHS and RHS.

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

Overlap of [1] aaba=aa with [2] babb=a:

Critical pair: aaa=aabb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [1] aaba=aa with [4] baba=aaa:

Critical pair: aaaaa=aaba.

Reduce RHS:

Defines rule #1.

Overlap of [4] baba=aaa with [2] babb=a:

Critical pair: baa=aaabb.

Reduce RHS:

Defines rule #2.

Simplify [3] aabb=baba.

Reduce RHS:

Defines rule #5.