WORST_CASE(?,O(n^1)) * Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__c() -> a__f(g(c())) a__c() -> c() a__f(X) -> f(X) a__f(g(X)) -> g(X) mark(c()) -> a__c() mark(f(X)) -> a__f(X) mark(g(X)) -> g(X) - Signature: {a__c/0,a__f/1,mark/1} / {c/0,f/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__c,a__f,mark} and constructors {c,f,g} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. a__c_0() -> 1 a__c_1() -> 1 a__f_0(2) -> 1 a__f_1(2) -> 1 a__f_1(3) -> 1 a__f_2(5) -> 1 c_0() -> 2 c_1() -> 1 c_1() -> 4 c_2() -> 1 c_2() -> 6 f_0(2) -> 2 f_1(2) -> 1 f_2(2) -> 1 f_2(3) -> 1 f_3(5) -> 1 g_0(2) -> 2 g_1(2) -> 1 g_1(4) -> 3 g_2(4) -> 1 g_2(6) -> 5 g_3(6) -> 1 mark_0(2) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: a__c() -> a__f(g(c())) a__c() -> c() a__f(X) -> f(X) a__f(g(X)) -> g(X) mark(c()) -> a__c() mark(f(X)) -> a__f(X) mark(g(X)) -> g(X) - Signature: {a__c/0,a__f/1,mark/1} / {c/0,f/1,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__c,a__f,mark} and constructors {c,f,g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))