* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: int(x,x) -> cons(x,nil()) int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) int(s(x),0()) -> nil() int(s(x),s(y)) -> intlist(int(x,y)) intlist(cons(x,y)) -> cons(s(x),intlist(y)) intlist(cons(x,nil())) -> cons(s(x),nil()) intlist(nil()) -> nil() - Signature: {int/2,intlist/1} / {0/0,cons/2,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {int,intlist} and constructors {0,cons,nil,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: int(x,x) -> cons(x,nil()) int(0(),s(y)) -> cons(0(),int(s(0()),s(y))) int(s(x),0()) -> nil() int(s(x),s(y)) -> intlist(int(x,y)) intlist(cons(x,y)) -> cons(s(x),intlist(y)) intlist(cons(x,nil())) -> cons(s(x),nil()) intlist(nil()) -> nil() - Signature: {int/2,intlist/1} / {0/0,cons/2,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {int,intlist} and constructors {0,cons,nil,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: int(x,y){x -> s(x),y -> s(y)} = int(s(x),s(y)) ->^+ intlist(int(x,y)) = C[int(x,y) = int(x,y){}] WORST_CASE(Omega(n^1),?)