* Step 1: Sum WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: even(Cons(x,xs)) -> odd(xs) even(Nil()) -> True() evenodd(x) -> even(x) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() odd(Cons(x,xs)) -> even(xs) odd(Nil()) -> False() - Signature: {even/1,evenodd/1,notEmpty/1,odd/1} / {Cons/2,False/0,Nil/0,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {even,evenodd,notEmpty,odd} and constructors {Cons,False ,Nil,True} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: even(Cons(x,xs)) -> odd(xs) even(Nil()) -> True() evenodd(x) -> even(x) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() odd(Cons(x,xs)) -> even(xs) odd(Nil()) -> False() - Signature: {even/1,evenodd/1,notEmpty/1,odd/1} / {Cons/2,False/0,Nil/0,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {even,evenodd,notEmpty,odd} and constructors {Cons,False ,Nil,True} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. Cons_0(2,2) -> 2 False_0() -> 2 False_1() -> 1 Nil_0() -> 2 True_0() -> 2 True_1() -> 1 even_0(2) -> 1 even_1(2) -> 1 evenodd_0(2) -> 1 notEmpty_0(2) -> 1 odd_0(2) -> 1 odd_1(2) -> 1 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: even(Cons(x,xs)) -> odd(xs) even(Nil()) -> True() evenodd(x) -> even(x) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() odd(Cons(x,xs)) -> even(xs) odd(Nil()) -> False() - Signature: {even/1,evenodd/1,notEmpty/1,odd/1} / {Cons/2,False/0,Nil/0,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {even,evenodd,notEmpty,odd} and constructors {Cons,False ,Nil,True} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))