* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: +(X,0()) -> X +(X,s(Y)) -> s(+(X,Y)) double(X) -> +(X,X) f(0(),s(0()),X) -> f(X,double(X),X) g(X,Y) -> X g(X,Y) -> Y - Signature: {+/2,double/1,f/3,g/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,double,f,g} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: +(X,0()) -> X +(X,s(Y)) -> s(+(X,Y)) double(X) -> +(X,X) f(0(),s(0()),X) -> f(X,double(X),X) g(X,Y) -> X g(X,Y) -> Y - Signature: {+/2,double/1,f/3,g/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,double,f,g} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: +(x,y){y -> s(y)} = +(x,s(y)) ->^+ s(+(x,y)) = C[+(x,y) = +(x,y){}] WORST_CASE(Omega(n^1),?)