(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
select(x', revprefix, Cons(x, xs)) → mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs))
revapp(Cons(x, xs), rest) → revapp(xs, Cons(x, rest))
permute(Cons(x, xs)) → select(x, Nil, xs)
mapconsapp(x', Cons(x, xs), rest) → Cons(Cons(x', x), mapconsapp(x', xs, rest))
select(x, revprefix, Nil) → mapconsapp(x, permute(revapp(revprefix, Nil)), Nil)
revapp(Nil, rest) → rest
permute(Nil) → Cons(Nil, Nil)
mapconsapp(x, Nil, rest) → rest
goal(xs) → permute(xs)
Rewrite Strategy: INNERMOST
(1) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(2n):
The rewrite sequence
permute(Cons(x, Cons(x23981_0, Cons(x24266_0, xs24267_0)))) →+ mapconsapp(x, permute(Cons(x23981_0, Cons(x24266_0, xs24267_0))), mapconsapp(x23981_0, permute(Cons(x, Cons(x24266_0, xs24267_0))), select(x24266_0, Cons(x23981_0, Cons(x, Nil)), xs24267_0)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
The pumping substitution is [xs24267_0 / Cons(x24266_0, xs24267_0)].
The result substitution is [x / x23981_0, x23981_0 / x24266_0].
The rewrite sequence
permute(Cons(x, Cons(x23981_0, Cons(x24266_0, xs24267_0)))) →+ mapconsapp(x, permute(Cons(x23981_0, Cons(x24266_0, xs24267_0))), mapconsapp(x23981_0, permute(Cons(x, Cons(x24266_0, xs24267_0))), select(x24266_0, Cons(x23981_0, Cons(x, Nil)), xs24267_0)))
gives rise to a decreasing loop by considering the right hand sides subterm at position [2,1].
The pumping substitution is [xs24267_0 / Cons(x24266_0, xs24267_0)].
The result substitution is [x23981_0 / x24266_0].
(2) BOUNDS(2^n, INF)