(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(node(s(n), xs)) → f(addchild(select(xs), node(n, xs)))
select(cons(ap, xs)) → ap
select(cons(ap, xs)) → select(xs)
addchild(node(y, ys), node(n, xs)) → node(y, cons(node(n, xs), ys))
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:
f(node(s(n), xs)) → f(addchild(select(xs), node(n, xs)))
select(cons(ap, xs)) → ap
select(cons(ap, xs)) → select(xs)
addchild(node(y, ys), node(n, xs)) → node(y, cons(node(n, xs), ys))
S is empty.
Rewrite Strategy: INNERMOST
(3) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
f(node(s(n), cons(node(s(n131_0), ys48_0), xs4_0))) →+ f(node(n, cons(node(n131_0, cons(node(n, cons(node(s(n131_0), ys48_0), xs4_0)), ys48_0)), cons(node(s(n131_0), ys48_0), xs4_0))))
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [n / s(n), n131_0 / s(n131_0)].
The result substitution is [ys48_0 / cons(node(n, cons(node(s(n131_0), ys48_0), xs4_0)), ys48_0), xs4_0 / cons(node(s(n131_0), ys48_0), xs4_0)].
(4) BOUNDS(n^1, INF)