The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

immatcopy(Cons(x, xs)) → Cons(Nil, immatcopy(xs))
nestimeql(Nil) → number42(Nil)
nestimeql(Cons(x, xs)) → nestimeql(immatcopy(Cons(x, xs)))
immatcopy(Nil) → Nil
number42(x) → Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil))))))))))))))))))))))))))))))))))))))))))
goal(x) → nestimeql(x)

Rewrite Strategy: INNERMOST

(1) CpxTrsToCpxRelTrsProof (BOTH BOUNDS(ID, ID) transformation)

Transformed TRS to relative TRS where S is empty.

(2) Obligation:

Runtime Complexity Relative TRS:
The TRS R consists of the following rules:

immatcopy(Cons(x, xs)) → Cons(Nil, immatcopy(xs))
nestimeql(Nil) → number42(Nil)
nestimeql(Cons(x, xs)) → nestimeql(immatcopy(Cons(x, xs)))
immatcopy(Nil) → Nil
number42(x) → Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil))))))))))))))))))))))))))))))))))))))))))
goal(x) → nestimeql(x)

S is empty.
Rewrite Strategy: INNERMOST

(3) SlicingProof (LOWER BOUND(ID) transformation)

Sliced the following arguments:
Cons/0
number42/0

(4) Obligation:

Runtime Complexity Relative TRS:
The TRS R consists of the following rules:

immatcopy(Cons(xs)) → Cons(immatcopy(xs))
nestimeql(Nil) → number42
nestimeql(Cons(xs)) → nestimeql(immatcopy(Cons(xs)))
immatcopy(Nil) → Nil
number42 → Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Cons(Nil))))))))))))))))))))))))))))))))))))))))))
goal(x) → nestimeql(x)

S is empty.
Rewrite Strategy: INNERMOST

(5) InfiniteLowerBoundProof (EQUIVALENT transformation)

The loop following loop proves infinite runtime complexity:
The rewrite sequence
nestimeql(Cons(xs)) →⁺ nestimeql(Cons(immatcopy(xs)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [ ].
The result substitution is [xs / immatcopy(xs)].

(6) BOUNDS(INF, INF)