/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^1)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: comp_f_g#1(plus_x(x3),comp_f_g(x1,x2),0()) -> plus_x#1(x3,comp_f_g#1(x1,x2,0())) comp_f_g#1(plus_x(x3),id(),0()) -> plus_x#1(x3,0()) foldr#3(Cons(x32,x6)) -> comp_f_g(x32,foldr#3(x6)) foldr#3(Nil()) -> id() foldr_f#3(Cons(x16,x5),x24) -> comp_f_g#1(x16,foldr#3(x5),x24) foldr_f#3(Nil(),0()) -> 0() main(x3) -> foldr_f#3(map#2(x3),0()) map#2(Cons(x16,x6)) -> Cons(plus_x(x16),map#2(x6)) map#2(Nil()) -> Nil() plus_x#1(0(),x6) -> x6 plus_x#1(S(x8),x10) -> S(plus_x#1(x8,x10)) - Signature: {comp_f_g#1/3,foldr#3/1,foldr_f#3/2,main/1,map#2/1,plus_x#1/2} / {0/0,Cons/2,Nil/0,S/1,comp_f_g/2,id/0 ,plus_x/1} - Obligation: innermost runtime complexity wrt. defined symbols {comp_f_g#1,foldr#3,foldr_f#3,main,map#2 ,plus_x#1} and constructors {0,Cons,Nil,S,comp_f_g,id,plus_x} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: comp_f_g#1(plus_x(x3),comp_f_g(x1,x2),0()) -> plus_x#1(x3,comp_f_g#1(x1,x2,0())) comp_f_g#1(plus_x(x3),id(),0()) -> plus_x#1(x3,0()) foldr#3(Cons(x32,x6)) -> comp_f_g(x32,foldr#3(x6)) foldr#3(Nil()) -> id() foldr_f#3(Cons(x16,x5),x24) -> comp_f_g#1(x16,foldr#3(x5),x24) foldr_f#3(Nil(),0()) -> 0() main(x3) -> foldr_f#3(map#2(x3),0()) map#2(Cons(x16,x6)) -> Cons(plus_x(x16),map#2(x6)) map#2(Nil()) -> Nil() plus_x#1(0(),x6) -> x6 plus_x#1(S(x8),x10) -> S(plus_x#1(x8,x10)) - Signature: {comp_f_g#1/3,foldr#3/1,foldr_f#3/2,main/1,map#2/1,plus_x#1/2} / {0/0,Cons/2,Nil/0,S/1,comp_f_g/2,id/0 ,plus_x/1} - Obligation: innermost runtime complexity wrt. defined symbols {comp_f_g#1,foldr#3,foldr_f#3,main,map#2 ,plus_x#1} and constructors {0,Cons,Nil,S,comp_f_g,id,plus_x} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: foldr#3(y){y -> Cons(x,y)} = foldr#3(Cons(x,y)) ->^+ comp_f_g(x,foldr#3(y)) = C[foldr#3(y) = foldr#3(y){}] ** Step 1.b:1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: comp_f_g#1(plus_x(x3),comp_f_g(x1,x2),0()) -> plus_x#1(x3,comp_f_g#1(x1,x2,0())) comp_f_g#1(plus_x(x3),id(),0()) -> plus_x#1(x3,0()) foldr#3(Cons(x32,x6)) -> comp_f_g(x32,foldr#3(x6)) foldr#3(Nil()) -> id() foldr_f#3(Cons(x16,x5),x24) -> comp_f_g#1(x16,foldr#3(x5),x24) foldr_f#3(Nil(),0()) -> 0() main(x3) -> foldr_f#3(map#2(x3),0()) map#2(Cons(x16,x6)) -> Cons(plus_x(x16),map#2(x6)) map#2(Nil()) -> Nil() plus_x#1(0(),x6) -> x6 plus_x#1(S(x8),x10) -> S(plus_x#1(x8,x10)) - Signature: {comp_f_g#1/3,foldr#3/1,foldr_f#3/2,main/1,map#2/1,plus_x#1/2} / {0/0,Cons/2,Nil/0,S/1,comp_f_g/2,id/0 ,plus_x/1} - Obligation: innermost runtime complexity wrt. defined symbols {comp_f_g#1,foldr#3,foldr_f#3,main,map#2 ,plus_x#1} and constructors {0,Cons,Nil,S,comp_f_g,id,plus_x} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(0) 0 :: [] -(0)-> "A"(7) 0 :: [] -(0)-> "A"(3) 0 :: [] -(0)-> "A"(4) 0 :: [] -(0)-> "A"(8) 0 :: [] -(0)-> "A"(12) Cons :: ["A"(12) x "A"(12)] -(12)-> "A"(12) Cons :: ["A"(13) x "A"(13)] -(13)-> "A"(13) Nil :: [] -(0)-> "A"(12) Nil :: [] -(0)-> "A"(13) Nil :: [] -(0)-> "A"(14) S :: ["A"(3)] -(3)-> "A"(3) S :: ["A"(0)] -(0)-> "A"(0) comp_f_g :: ["A"(3) x "A"(3)] -(3)-> "A"(3) comp_f_g#1 :: ["A"(3) x "A"(3) x "A"(0)] -(11)-> "A"(0) foldr#3 :: ["A"(12)] -(2)-> "A"(3) foldr_f#3 :: ["A"(12) x "A"(7)] -(5)-> "A"(0) id :: [] -(0)-> "A"(3) id :: [] -(0)-> "A"(7) main :: ["A"(14)] -(16)-> "A"(0) map#2 :: ["A"(13)] -(1)-> "A"(12) plus_x :: ["A"(3)] -(0)-> "A"(3) plus_x :: ["A"(12)] -(0)-> "A"(12) plus_x#1 :: ["A"(3) x "A"(0)] -(2)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "Cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "S_A" :: ["A"(1)] -(1)-> "A"(1) "comp_f_g_A" :: ["A"(0) x "A"(0)] -(1)-> "A"(1) "id_A" :: [] -(0)-> "A"(1) "plus_x_A" :: ["A"(0)] -(0)-> "A"(1) WORST_CASE(Omega(n^1),O(n^1))