WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: add(0(),X) -> X add(s(),Y) -> s() from(X) -> cons(X) fst(0(),Z) -> nil() fst(s(),cons(Y)) -> cons(Y) len(cons(X)) -> s() len(nil()) -> 0() - Signature: {add/2,from/1,fst/2,len/1} / {0/0,cons/1,nil/0,s/0} - Obligation: innermost runtime complexity wrt. defined symbols {add,from,fst,len} and constructors {0,cons,nil,s} + Applied Processor: NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(stronglyLinear): The following argument positions are considered usable: none Following symbols are considered usable: {add,from,fst,len} TcT has computed the following interpretation: p(0) = 4 p(add) = 2 + x1 + x2 p(cons) = 1 p(from) = 9 p(fst) = 8 + x1 + x2 p(len) = 1 + x1 p(nil) = 10 p(s) = 0 Following rules are strictly oriented: add(0(),X) = 6 + X > X = X add(s(),Y) = 2 + Y > 0 = s() from(X) = 9 > 1 = cons(X) fst(0(),Z) = 12 + Z > 10 = nil() fst(s(),cons(Y)) = 9 > 1 = cons(Y) len(cons(X)) = 2 > 0 = s() len(nil()) = 11 > 4 = 0() Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))