WORST_CASE(?,O(n^1)) * Step 1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: cond_prefix_s1_s2_2(False(),x2,x1) -> False() cond_prefix_s1_s2_2(True(),x2,x1) -> prefix#2(x2,x1) eq#2(0(),0()) -> True() eq#2(0(),S(x16)) -> False() eq#2(S(x16),0()) -> False() eq#2(S(x4),S(x2)) -> eq#2(x4,x2) main(x2,x1) -> prefix#2(x2,x1) prefix#2(Cons(x4,x2),Nil()) -> False() prefix#2(Cons(x8,x6),Cons(x4,x2)) -> cond_prefix_s1_s2_2(eq#2(x8,x4),x6,x2) prefix#2(Nil(),x2) -> True() - Signature: {cond_prefix_s1_s2_2/3,eq#2/2,main/2,prefix#2/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond_prefix_s1_s2_2,eq#2,main ,prefix#2} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 Cons_0(2,2) -> 2 False_0() -> 2 False_1() -> 1 False_2() -> 1 Nil_0() -> 2 S_0(2) -> 2 True_0() -> 2 True_1() -> 1 cond_prefix_s1_s2_2_0(2,2,2) -> 1 cond_prefix_s1_s2_2_1(1,2,2) -> 1 eq#2_0(2,2) -> 1 eq#2_1(2,2) -> 1 main_0(2,2) -> 1 prefix#2_0(2,2) -> 1 prefix#2_1(2,2) -> 1 prefix#2_2(2,2) -> 1 * Step 2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: cond_prefix_s1_s2_2(False(),x2,x1) -> False() cond_prefix_s1_s2_2(True(),x2,x1) -> prefix#2(x2,x1) eq#2(0(),0()) -> True() eq#2(0(),S(x16)) -> False() eq#2(S(x16),0()) -> False() eq#2(S(x4),S(x2)) -> eq#2(x4,x2) main(x2,x1) -> prefix#2(x2,x1) prefix#2(Cons(x4,x2),Nil()) -> False() prefix#2(Cons(x8,x6),Cons(x4,x2)) -> cond_prefix_s1_s2_2(eq#2(x8,x4),x6,x2) prefix#2(Nil(),x2) -> True() - Signature: {cond_prefix_s1_s2_2/3,eq#2/2,main/2,prefix#2/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {cond_prefix_s1_s2_2,eq#2,main ,prefix#2} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))