(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) InfiniteLowerBoundProof (EQUIVALENT transformation)
The loop following loop proves infinite runtime complexity:
The rewrite sequence
nestimeql(Cons(x, xs)) →+ nestimeql(Cons(Nil, 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 [x / Nil, xs / immatcopy(xs)].
(2) BOUNDS(INF, INF)