* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: active(f(X)) -> f(active(X)) active(f(f(a()))) -> mark(c(f(g(f(a()))))) active(g(X)) -> g(active(X)) c(ok(X)) -> ok(c(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(mark(X)) -> mark(g(X)) g(ok(X)) -> ok(g(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,c/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,c,f,g,proper,top} and constructors {a,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(f(a()))) -> mark(c(f(g(f(a()))))) active(g(X)) -> g(active(X)) c(ok(X)) -> ok(c(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(mark(X)) -> mark(g(X)) g(ok(X)) -> ok(g(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,c/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,c,f,g,proper,top} and constructors {a,mark,ok} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: c(x){x -> ok(x)} = c(ok(x)) ->^+ ok(c(x)) = C[c(x) = c(x){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: active(f(X)) -> f(active(X)) active(f(f(a()))) -> mark(c(f(g(f(a()))))) active(g(X)) -> g(active(X)) c(ok(X)) -> ok(c(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(mark(X)) -> mark(g(X)) g(ok(X)) -> ok(g(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,c/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,c,f,g,proper,top} and constructors {a,mark,ok} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. a_0() -> 2 a_1() -> 3 active_0(2) -> 1 active_1(2) -> 5 active_2(3) -> 6 c_0(2) -> 1 c_1(2) -> 3 f_0(2) -> 1 f_1(2) -> 4 g_0(2) -> 1 g_1(2) -> 4 mark_0(2) -> 2 mark_1(4) -> 1 mark_1(4) -> 4 ok_0(2) -> 2 ok_1(3) -> 1 ok_1(3) -> 3 ok_1(3) -> 5 ok_1(4) -> 1 ok_1(4) -> 4 proper_0(2) -> 1 proper_1(2) -> 5 top_0(2) -> 1 top_1(5) -> 1 top_2(6) -> 1 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(f(X)) -> f(active(X)) active(f(f(a()))) -> mark(c(f(g(f(a()))))) active(g(X)) -> g(active(X)) c(ok(X)) -> ok(c(X)) f(mark(X)) -> mark(f(X)) f(ok(X)) -> ok(f(X)) g(mark(X)) -> mark(g(X)) g(ok(X)) -> ok(g(X)) proper(a()) -> ok(a()) proper(c(X)) -> c(proper(X)) proper(f(X)) -> f(proper(X)) proper(g(X)) -> g(proper(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) - Signature: {active/1,c/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1} - Obligation: innermost runtime complexity wrt. defined symbols {active,c,f,g,proper,top} and constructors {a,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))