* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: append(cons(x,xs),ys) -> cons(x,append(xs,ys)) append(nil(),ys) -> ys dropLast(cons(x,cons(y,ys))) -> cons(x,dropLast(cons(y,ys))) dropLast(cons(x,nil())) -> nil() dropLast(nil()) -> nil() if(false(),xs,ys,zs) -> rev(xs,ys) if(true(),xs,ys,zs) -> zs isEmpty(cons(x,xs)) -> false() isEmpty(nil()) -> true() last(cons(x,cons(y,ys))) -> last(cons(y,ys)) last(cons(x,nil())) -> x rev(xs,ys) -> if(isEmpty(xs),dropLast(xs),append(ys,last(xs)),ys) reverse(xs) -> rev(xs,nil()) - Signature: {append/2,dropLast/1,if/4,isEmpty/1,last/1,rev/2,reverse/1} / {cons/2,false/0,nil/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,dropLast,if,isEmpty,last,rev ,reverse} and constructors {cons,false,nil,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: append(cons(x,xs),ys) -> cons(x,append(xs,ys)) append(nil(),ys) -> ys dropLast(cons(x,cons(y,ys))) -> cons(x,dropLast(cons(y,ys))) dropLast(cons(x,nil())) -> nil() dropLast(nil()) -> nil() if(false(),xs,ys,zs) -> rev(xs,ys) if(true(),xs,ys,zs) -> zs isEmpty(cons(x,xs)) -> false() isEmpty(nil()) -> true() last(cons(x,cons(y,ys))) -> last(cons(y,ys)) last(cons(x,nil())) -> x rev(xs,ys) -> if(isEmpty(xs),dropLast(xs),append(ys,last(xs)),ys) reverse(xs) -> rev(xs,nil()) - Signature: {append/2,dropLast/1,if/4,isEmpty/1,last/1,rev/2,reverse/1} / {cons/2,false/0,nil/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,dropLast,if,isEmpty,last,rev ,reverse} and constructors {cons,false,nil,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: append(y,z){y -> cons(x,y)} = append(cons(x,y),z) ->^+ cons(x,append(y,z)) = C[append(y,z) = append(y,z){}] WORST_CASE(Omega(n^1),?)