* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: active(f(X)) -> f(active(X)) active(f(X)) -> mark(g(h(f(X)))) active(h(X)) -> h(active(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(ok(X)) -> ok(g(X)) h(mark(X)) -> mark(h(X)) h(ok(X)) -> ok(h(X)) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/1,g/1,h/1,proper/1,top/1} / {mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {mark,ok} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: active(f(X)) -> f(active(X)) active(f(X)) -> mark(g(h(f(X)))) active(h(X)) -> h(active(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(ok(X)) -> ok(g(X)) h(mark(X)) -> mark(h(X)) h(ok(X)) -> ok(h(X)) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/1,g/1,h/1,proper/1,top/1} / {mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {mark,ok} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x){x -> mark(x)} = f(mark(x)) ->^+ mark(f(x)) = C[f(x) = f(x){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(f(X)) -> f(active(X)) active(f(X)) -> mark(g(h(f(X)))) active(h(X)) -> h(active(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(ok(X)) -> ok(g(X)) h(mark(X)) -> mark(h(X)) h(ok(X)) -> ok(h(X)) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/1,g/1,h/1,proper/1,top/1} / {mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {mark,ok} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. active_0(2) -> 1 active_1(2) -> 4 f_0(2) -> 1 f_1(2) -> 3 g_0(2) -> 1 g_1(2) -> 3 h_0(2) -> 1 h_1(2) -> 3 mark_0(2) -> 2 mark_1(3) -> 1 mark_1(3) -> 3 ok_0(2) -> 2 ok_1(3) -> 1 ok_1(3) -> 3 proper_0(2) -> 1 proper_1(2) -> 4 top_0(2) -> 1 top_1(4) -> 1 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(f(X)) -> f(active(X)) active(f(X)) -> mark(g(h(f(X)))) active(h(X)) -> h(active(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(ok(X)) -> ok(g(X)) h(mark(X)) -> mark(h(X)) h(ok(X)) -> ok(h(X)) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) proper(h(X)) -> h(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,f/1,g/1,h/1,proper/1,top/1} / {mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,f,g,h,proper,top} and constructors {mark,ok} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))