* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: head(cons(x,l)) -> x head(nil()) -> undefined() if(false(),x,l,accu,orig) -> accu if(true(),x,l,accu,orig) -> rev(s(x),tail(l),cons(head(l),accu),orig) length(cons(x,l)) -> s(length(l)) length(nil()) -> 0() lt(x,0()) -> false() lt(0(),s(y)) -> true() lt(s(x),s(y)) -> lt(x,y) rev(x,l,accu,orig) -> if(lt(x,length(orig)),x,l,accu,orig) reverse(l) -> rev(0(),l,nil(),l) tail(cons(x,l)) -> l tail(nil()) -> nil() - Signature: {head/1,if/5,length/1,lt/2,rev/4,reverse/1,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0,undefined/0} - Obligation: innermost runtime complexity wrt. defined symbols {head,if,length,lt,rev,reverse,tail} and constructors {0 ,cons,false,nil,s,true,undefined} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: head(cons(x,l)) -> x head(nil()) -> undefined() if(false(),x,l,accu,orig) -> accu if(true(),x,l,accu,orig) -> rev(s(x),tail(l),cons(head(l),accu),orig) length(cons(x,l)) -> s(length(l)) length(nil()) -> 0() lt(x,0()) -> false() lt(0(),s(y)) -> true() lt(s(x),s(y)) -> lt(x,y) rev(x,l,accu,orig) -> if(lt(x,length(orig)),x,l,accu,orig) reverse(l) -> rev(0(),l,nil(),l) tail(cons(x,l)) -> l tail(nil()) -> nil() - Signature: {head/1,if/5,length/1,lt/2,rev/4,reverse/1,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0,undefined/0} - Obligation: innermost runtime complexity wrt. defined symbols {head,if,length,lt,rev,reverse,tail} and constructors {0 ,cons,false,nil,s,true,undefined} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: length(y){y -> cons(x,y)} = length(cons(x,y)) ->^+ s(length(y)) = C[length(y) = length(y){}] WORST_CASE(Omega(n^1),?)