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