* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(c()) -> mark(a()) active(c()) -> mark(b()) active(f(X1,X2,X3)) -> f(X1,X2,active(X3)) active(f(a(),b(),X)) -> mark(f(X,X,X)) f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3)) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) proper(c()) -> ok(c()) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/3,proper/1,top/1} / {a/0,b/0,c/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,proper,top} and constructors {a,b,c,mark,ok} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(c()) -> mark(a()) active(c()) -> mark(b()) active(f(X1,X2,X3)) -> f(X1,X2,active(X3)) active(f(a(),b(),X)) -> mark(f(X,X,X)) f(X1,X2,mark(X3)) -> mark(f(X1,X2,X3)) f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) proper(c()) -> ok(c()) proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/3,proper/1,top/1} / {a/0,b/0,c/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,proper,top} and constructors {a,b,c,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),?)