(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
from(X) → cons(X, from(s(X)))
length(nil) → 0
length(cons(X, Y)) → s(length1(Y))
length1(X) → length(X)
Rewrite Strategy: FULL
(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:
from(X) → cons(X, from(s(X)))
length(nil) → 0
length(cons(X, Y)) → s(length1(Y))
length1(X) → length(X)
S is empty.
Rewrite Strategy: FULL
(3) SlicingProof (LOWER BOUND(ID) transformation)
Sliced the following arguments:
from/0
cons/0
(4) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
from → cons(from)
length(nil) → 0
length(cons(Y)) → s(length1(Y))
length1(X) → length(X)
S is empty.
Rewrite Strategy: FULL
(5) InfiniteLowerBoundProof (EQUIVALENT transformation)
The loop following loop proves infinite runtime complexity:
The rewrite sequence
from →+ cons(from)
gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
The pumping substitution is [ ].
The result substitution is [ ].
(6) BOUNDS(INF, INF)