* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: e(g(X)) -> e(X) f(a()) -> f(c(a())) f(a()) -> f(d(a())) f(c(X)) -> X f(c(a())) -> f(d(b())) f(c(b())) -> f(d(a())) f(d(X)) -> X - Signature: {e/1,f/1} / {a/0,b/0,c/1,d/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {e,f} and constructors {a,b,c,d,g} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: e(g(X)) -> e(X) f(a()) -> f(c(a())) f(a()) -> f(d(a())) f(c(X)) -> X f(c(a())) -> f(d(b())) f(c(b())) -> f(d(a())) f(d(X)) -> X - Signature: {e/1,f/1} / {a/0,b/0,c/1,d/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {e,f} and constructors {a,b,c,d,g} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: e(x){x -> g(x)} = e(g(x)) ->^+ e(x) = C[e(x) = e(x){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: e(g(X)) -> e(X) f(a()) -> f(c(a())) f(a()) -> f(d(a())) f(c(X)) -> X f(c(a())) -> f(d(b())) f(c(b())) -> f(d(a())) f(d(X)) -> X - Signature: {e/1,f/1} / {a/0,b/0,c/1,d/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {e,f} and constructors {a,b,c,d,g} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. a_0() -> 1 a_0() -> 6 a_1() -> 6 a_1() -> 9 a_2() -> 6 a_2() -> 11 b_0() -> 2 b_0() -> 6 b_1() -> 6 b_1() -> 9 b_2() -> 6 b_2() -> 11 c_0(1) -> 3 c_0(1) -> 6 c_0(2) -> 3 c_0(2) -> 6 c_0(3) -> 3 c_0(3) -> 6 c_0(4) -> 3 c_0(4) -> 6 c_0(7) -> 3 c_0(7) -> 6 c_1(9) -> 8 d_0(1) -> 4 d_0(1) -> 6 d_0(2) -> 4 d_0(2) -> 6 d_0(3) -> 4 d_0(3) -> 6 d_0(4) -> 4 d_0(4) -> 6 d_0(7) -> 4 d_0(7) -> 6 d_1(9) -> 8 d_2(11) -> 10 e_0(1) -> 5 e_0(2) -> 5 e_0(3) -> 5 e_0(4) -> 5 e_0(7) -> 5 e_1(1) -> 5 e_1(2) -> 5 e_1(3) -> 5 e_1(4) -> 5 e_1(7) -> 5 f_0(1) -> 6 f_0(2) -> 6 f_0(3) -> 6 f_0(4) -> 6 f_0(7) -> 6 f_1(8) -> 6 f_2(10) -> 6 g_0(1) -> 6 g_0(1) -> 7 g_0(2) -> 6 g_0(2) -> 7 g_0(3) -> 6 g_0(3) -> 7 g_0(4) -> 6 g_0(4) -> 7 g_0(7) -> 6 g_0(7) -> 7 1 -> 6 2 -> 6 3 -> 6 4 -> 6 7 -> 6 9 -> 6 11 -> 6 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: e(g(X)) -> e(X) f(a()) -> f(c(a())) f(a()) -> f(d(a())) f(c(X)) -> X f(c(a())) -> f(d(b())) f(c(b())) -> f(d(a())) f(d(X)) -> X - Signature: {e/1,f/1} / {a/0,b/0,c/1,d/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {e,f} and constructors {a,b,c,d,g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))