* Step 1: ToInnermost 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: runtime complexity wrt. defined symbols {e,f} and constructors {a,b,c,d,g} + Applied Processor: ToInnermost + Details: switch to innermost, as the system is overlay and right linear and does not contain weak rules * Step 2: 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 = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. a_0() -> 1 a_0() -> 2 a_1() -> 1 a_1() -> 4 a_2() -> 1 a_2() -> 6 b_0() -> 1 b_0() -> 2 b_1() -> 1 b_1() -> 4 b_2() -> 1 b_2() -> 6 c_0(2) -> 1 c_0(2) -> 2 c_1(4) -> 3 d_0(2) -> 1 d_0(2) -> 2 d_1(4) -> 3 d_2(6) -> 5 e_0(2) -> 1 e_1(2) -> 1 f_0(2) -> 1 f_1(3) -> 1 f_2(5) -> 1 g_0(2) -> 1 g_0(2) -> 2 2 -> 1 4 -> 1 6 -> 1 * Step 3: 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(?,O(n^1))