Certificate for #14698 ⟨a, b | aabb=a, baaaa=b⟩

Completion settings:

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

Axiom: aabb=a.

Referenced by [3], [4], [5], [6], [8], [9], [10], [11], [13].

Axiom: baaaa=b.

Referenced by [3], [4], [5], [7].

Overlap of [1] aabb=a with [2] baaaa=b:

Critical pair: aabb=aaaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] baaaa=b with [1] aabb=a:

Critical pair: baaa=bbb.

Referenced by [5], [7], [8].

Overlap of [2] baaaa=b with [1] aabb=a:

Critical pair: baaaa=babb.

Reduce LHS:

Referenced by [7].

Overlap of [3] aaaaa=a with [1] aabb=a:

Critical pair: aaaa=abb.

Referenced by [9].

Overlap of [2] baaaa=b with [4] baaa=bbb:

Critical pair: bbba=b.

Reduce LHS:

Referenced by [12].

Overlap of [4] baaa=bbb with [1] aabb=a:

Critical pair: baa=bbbbb.

Referenced by [10].

Overlap of [6] aaaa=abb with [1] aabb=a:

Critical pair: aaa=abbbb.

Referenced by [11].

Overlap of [8] baa=bbbbb with [1] aabb=a:

Critical pair: ba=bbbbbbb.

Defines rule #3.

Referenced by [12].

Overlap of [9] aaa=abbbb with [1] aabb=a:

Critical pair: aa=abbbbbb.

Defines rule #4.

Referenced by [13].

Overlap of [7] babb=b with [10] ba=bbbbbbb:

Critical pair: bbbbbbbbb=b.

Defines rule #1.

Overlap of [1] aabb=a with [11] aa=abbbbbb:

Critical pair: abbbbbbbb=a.

Defines rule #2.