WORST_CASE(?,O(n^1)) * Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__c() -> c() a__c() -> d() a__g(X) -> a__h(X) a__g(X) -> g(X) a__h(X) -> h(X) a__h(d()) -> a__g(c()) mark(c()) -> a__c() mark(d()) -> d() mark(g(X)) -> a__g(X) mark(h(X)) -> a__h(X) - Signature: {a__c/0,a__g/1,a__h/1,mark/1} / {c/0,d/0,g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__c,a__g,a__h,mark} and constructors {c,d,g,h} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 5. The enriched problem is compatible with follwoing automaton. a__c_0() -> 1 a__c_1() -> 1 a__g_0(2) -> 1 a__g_1(1) -> 1 a__g_1(2) -> 1 a__g_2(1) -> 1 a__g_3(3) -> 1 a__h_0(2) -> 1 a__h_1(2) -> 1 a__h_2(1) -> 1 a__h_2(2) -> 1 a__h_3(1) -> 1 a__h_4(3) -> 1 c_0() -> 2 c_1() -> 1 c_2() -> 1 c_3() -> 3 d_0() -> 2 d_1() -> 1 d_2() -> 1 g_0(2) -> 2 g_1(2) -> 1 g_2(1) -> 1 g_2(2) -> 1 g_3(1) -> 1 g_4(3) -> 1 h_0(2) -> 2 h_1(2) -> 1 h_2(2) -> 1 h_3(1) -> 1 h_3(2) -> 1 h_4(1) -> 1 h_5(3) -> 1 mark_0(2) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: a__c() -> c() a__c() -> d() a__g(X) -> a__h(X) a__g(X) -> g(X) a__h(X) -> h(X) a__h(d()) -> a__g(c()) mark(c()) -> a__c() mark(d()) -> d() mark(g(X)) -> a__g(X) mark(h(X)) -> a__h(X) - Signature: {a__c/0,a__g/1,a__h/1,mark/1} / {c/0,d/0,g/1,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__c,a__g,a__h,mark} and constructors {c,d,g,h} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))