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