(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
odd(Cons(x, xs)) → even(xs)
odd(Nil) → False
even(Cons(x, xs)) → odd(xs)
notEmpty(Cons(x, xs)) → True
notEmpty(Nil) → False
even(Nil) → True
evenodd(x) → even(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:
odd(Cons(x, xs)) → even(xs)
odd(Nil) → False
even(Cons(x, xs)) → odd(xs)
notEmpty(Cons(x, xs)) → True
notEmpty(Nil) → False
even(Nil) → True
evenodd(x) → even(x)
S is empty.
Rewrite Strategy: INNERMOST
(3) SlicingProof (LOWER BOUND(ID) transformation)
Sliced the following arguments:
Cons/0
(4) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
odd(Cons(xs)) → even(xs)
odd(Nil) → False
even(Cons(xs)) → odd(xs)
notEmpty(Cons(xs)) → True
notEmpty(Nil) → False
even(Nil) → True
evenodd(x) → even(x)
S is empty.
Rewrite Strategy: INNERMOST
(5) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
odd(Cons(Cons(xs2_0))) →+ odd(xs2_0)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [xs2_0 / Cons(Cons(xs2_0))].
The result substitution is [ ].
(6) BOUNDS(n^1, INF)