* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(b()) -> mark(a()) active(f(X,X)) -> mark(f(a(),b())) active(f(X1,X2)) -> f(active(X1),X2) f(mark(X1),X2) -> mark(f(X1,X2)) f(ok(X1),ok(X2)) -> ok(f(X1,X2)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) proper(f(X1,X2)) -> f(proper(X1),proper(X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/2,proper/1,top/1} / {a/0,b/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,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(b()) -> mark(a()) active(f(X,X)) -> mark(f(a(),b())) active(f(X1,X2)) -> f(active(X1),X2) f(mark(X1),X2) -> mark(f(X1,X2)) f(ok(X1),ok(X2)) -> ok(f(X1,X2)) proper(a()) -> ok(a()) proper(b()) -> ok(b()) proper(f(X1,X2)) -> f(proper(X1),proper(X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/2,proper/1,top/1} / {a/0,b/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,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),?)