WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: append(l1,l2) -> ifappend(l1,l2,l1) hd(cons(x,l)) -> x ifappend(l1,l2,cons(x,l)) -> cons(x,append(l,l2)) ifappend(l1,l2,nil()) -> l2 is_empty(cons(x,l)) -> false() is_empty(nil()) -> true() tl(cons(x,l)) -> l - Signature: {append/2,hd/1,ifappend/3,is_empty/1,tl/1} / {cons/2,false/0,nil/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,hd,ifappend,is_empty,tl} and constructors {cons ,false,nil,true} + Applied Processor: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(cons) = {2} Following symbols are considered usable: {append,hd,ifappend,is_empty,tl} TcT has computed the following interpretation: p(append) = 2 + 8*x1 + 8*x2 p(cons) = 2 + x1 + x2 p(false) = 15 p(hd) = 1 + 6*x1 p(ifappend) = 8*x2 + 8*x3 p(is_empty) = 15 + x1 p(nil) = 2 p(tl) = 10 + 4*x1 p(true) = 13 Following rules are strictly oriented: append(l1,l2) = 2 + 8*l1 + 8*l2 > 8*l1 + 8*l2 = ifappend(l1,l2,l1) hd(cons(x,l)) = 13 + 6*l + 6*x > x = x ifappend(l1,l2,cons(x,l)) = 16 + 8*l + 8*l2 + 8*x > 4 + 8*l + 8*l2 + x = cons(x,append(l,l2)) ifappend(l1,l2,nil()) = 16 + 8*l2 > l2 = l2 is_empty(cons(x,l)) = 17 + l + x > 15 = false() is_empty(nil()) = 17 > 13 = true() tl(cons(x,l)) = 18 + 4*l + 4*x > l = l Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))