* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__f(X) -> cons(mark(X),f(g(X))) a__f(X) -> f(X) a__g(X) -> g(X) a__g(0()) -> s(0()) a__g(s(X)) -> s(s(a__g(mark(X)))) a__sel(X1,X2) -> sel(X1,X2) a__sel(0(),cons(X,Y)) -> mark(X) a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z)) mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> a__g(mark(X)) mark(s(X)) -> s(mark(X)) mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) - Signature: {a__f/1,a__g/1,a__sel/2,mark/1} / {0/0,cons/2,f/1,g/1,s/1,sel/2} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,a__g,a__sel,mark} and constructors {0,cons,f,g,s ,sel} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__f(X) -> cons(mark(X),f(g(X))) a__f(X) -> f(X) a__g(X) -> g(X) a__g(0()) -> s(0()) a__g(s(X)) -> s(s(a__g(mark(X)))) a__sel(X1,X2) -> sel(X1,X2) a__sel(0(),cons(X,Y)) -> mark(X) a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z)) mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> a__g(mark(X)) mark(s(X)) -> s(mark(X)) mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) - Signature: {a__f/1,a__g/1,a__sel/2,mark/1} / {0/0,cons/2,f/1,g/1,s/1,sel/2} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,a__g,a__sel,mark} and constructors {0,cons,f,g,s ,sel} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: mark(x){x -> cons(x,y)} = mark(cons(x,y)) ->^+ cons(mark(x),y) = C[mark(x) = mark(x){}] WORST_CASE(Omega(n^1),?)