/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^2)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^2)) + Considered Problem: - Strict TRS: domatch(patcs,Cons(x,xs),n) -> domatch[Ite](prefix(patcs,Cons(x,xs)),patcs,Cons(x,xs),n) domatch(Cons(x,xs),Nil(),n) -> Nil() domatch(Nil(),Nil(),n) -> Cons(n,Nil()) eqNatList(Cons(x,xs),Cons(y,ys)) -> eqNatList[Ite](!EQ(x,y),y,ys,x,xs) eqNatList(Cons(x,xs),Nil()) -> False() eqNatList(Nil(),Cons(y,ys)) -> False() eqNatList(Nil(),Nil()) -> True() notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() prefix(Cons(x,xs),Nil()) -> False() prefix(Cons(x',xs'),Cons(x,xs)) -> and(!EQ(x',x),prefix(xs',xs)) prefix(Nil(),cs) -> True() strmatch(patstr,str) -> domatch(patstr,str,Nil()) - Weak TRS: !EQ(0(),0()) -> True() !EQ(0(),S(y)) -> False() !EQ(S(x),0()) -> False() !EQ(S(x),S(y)) -> !EQ(x,y) and(False(),False()) -> False() and(False(),True()) -> False() and(True(),False()) -> False() and(True(),True()) -> True() domatch[Ite](False(),patcs,Cons(x,xs),n) -> domatch(patcs,xs,Cons(n,Cons(Nil(),Nil()))) domatch[Ite](True(),patcs,Cons(x,xs),n) -> Cons(n,domatch(patcs,xs,Cons(n,Cons(Nil(),Nil())))) eqNatList[Ite](False(),y,ys,x,xs) -> False() eqNatList[Ite](True(),y,ys,x,xs) -> eqNatList(xs,ys) - Signature: {!EQ/2,and/2,domatch/3,domatch[Ite]/4,eqNatList/2,eqNatList[Ite]/5,notEmpty/1,prefix/2,strmatch/2} / {0/0 ,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {!EQ,and,domatch,domatch[Ite],eqNatList,eqNatList[Ite] ,notEmpty,prefix,strmatch} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: domatch(patcs,Cons(x,xs),n) -> domatch[Ite](prefix(patcs,Cons(x,xs)),patcs,Cons(x,xs),n) domatch(Cons(x,xs),Nil(),n) -> Nil() domatch(Nil(),Nil(),n) -> Cons(n,Nil()) eqNatList(Cons(x,xs),Cons(y,ys)) -> eqNatList[Ite](!EQ(x,y),y,ys,x,xs) eqNatList(Cons(x,xs),Nil()) -> False() eqNatList(Nil(),Cons(y,ys)) -> False() eqNatList(Nil(),Nil()) -> True() notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() prefix(Cons(x,xs),Nil()) -> False() prefix(Cons(x',xs'),Cons(x,xs)) -> and(!EQ(x',x),prefix(xs',xs)) prefix(Nil(),cs) -> True() strmatch(patstr,str) -> domatch(patstr,str,Nil()) - Weak TRS: !EQ(0(),0()) -> True() !EQ(0(),S(y)) -> False() !EQ(S(x),0()) -> False() !EQ(S(x),S(y)) -> !EQ(x,y) and(False(),False()) -> False() and(False(),True()) -> False() and(True(),False()) -> False() and(True(),True()) -> True() domatch[Ite](False(),patcs,Cons(x,xs),n) -> domatch(patcs,xs,Cons(n,Cons(Nil(),Nil()))) domatch[Ite](True(),patcs,Cons(x,xs),n) -> Cons(n,domatch(patcs,xs,Cons(n,Cons(Nil(),Nil())))) eqNatList[Ite](False(),y,ys,x,xs) -> False() eqNatList[Ite](True(),y,ys,x,xs) -> eqNatList(xs,ys) - Signature: {!EQ/2,and/2,domatch/3,domatch[Ite]/4,eqNatList/2,eqNatList[Ite]/5,notEmpty/1,prefix/2,strmatch/2} / {0/0 ,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {!EQ,and,domatch,domatch[Ite],eqNatList,eqNatList[Ite] ,notEmpty,prefix,strmatch} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: prefix(y,u){y -> Cons(x,y),u -> Cons(z,u)} = prefix(Cons(x,y),Cons(z,u)) ->^+ and(!EQ(x,z),prefix(y,u)) = C[prefix(y,u) = prefix(y,u){}] ** Step 1.b:1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: domatch(patcs,Cons(x,xs),n) -> domatch[Ite](prefix(patcs,Cons(x,xs)),patcs,Cons(x,xs),n) domatch(Cons(x,xs),Nil(),n) -> Nil() domatch(Nil(),Nil(),n) -> Cons(n,Nil()) eqNatList(Cons(x,xs),Cons(y,ys)) -> eqNatList[Ite](!EQ(x,y),y,ys,x,xs) eqNatList(Cons(x,xs),Nil()) -> False() eqNatList(Nil(),Cons(y,ys)) -> False() eqNatList(Nil(),Nil()) -> True() notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() prefix(Cons(x,xs),Nil()) -> False() prefix(Cons(x',xs'),Cons(x,xs)) -> and(!EQ(x',x),prefix(xs',xs)) prefix(Nil(),cs) -> True() strmatch(patstr,str) -> domatch(patstr,str,Nil()) - Weak TRS: !EQ(0(),0()) -> True() !EQ(0(),S(y)) -> False() !EQ(S(x),0()) -> False() !EQ(S(x),S(y)) -> !EQ(x,y) and(False(),False()) -> False() and(False(),True()) -> False() and(True(),False()) -> False() and(True(),True()) -> True() domatch[Ite](False(),patcs,Cons(x,xs),n) -> domatch(patcs,xs,Cons(n,Cons(Nil(),Nil()))) domatch[Ite](True(),patcs,Cons(x,xs),n) -> Cons(n,domatch(patcs,xs,Cons(n,Cons(Nil(),Nil())))) eqNatList[Ite](False(),y,ys,x,xs) -> False() eqNatList[Ite](True(),y,ys,x,xs) -> eqNatList(xs,ys) - Signature: {!EQ/2,and/2,domatch/3,domatch[Ite]/4,eqNatList/2,eqNatList[Ite]/5,notEmpty/1,prefix/2,strmatch/2} / {0/0 ,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {!EQ,and,domatch,domatch[Ite],eqNatList,eqNatList[Ite] ,notEmpty,prefix,strmatch} and constructors {0,Cons,False,Nil,S,True} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- !EQ :: ["A"(0, 0) x "A"(1, 0)] -(0)-> "A"(1, 1) 0 :: [] -(0)-> "A"(0, 0) 0 :: [] -(0)-> "A"(1, 0) Cons :: ["A"(9, 0) x "A"(15, 6)] -(9)-> "A"(9, 6) Cons :: ["A"(11, 0) x "A"(15, 4)] -(11)-> "A"(11, 4) Cons :: ["A"(3, 0) x "A"(14, 11)] -(3)-> "A"(3, 11) Cons :: ["A"(7, 0) x "A"(14, 7)] -(7)-> "A"(7, 7) Cons :: ["A"(7, 0) x "A"(12, 5)] -(7)-> "A"(7, 5) Cons :: ["A"(0, 0) x "A"(0, 0)] -(0)-> "A"(0, 0) Cons :: ["A"(1, 0) x "A"(1, 0)] -(1)-> "A"(1, 0) Cons :: ["A"(4, 0) x "A"(10, 6)] -(4)-> "A"(4, 6) Cons :: ["A"(1, 0) x "A"(14, 13)] -(1)-> "A"(1, 13) False :: [] -(0)-> "A"(0, 1) False :: [] -(0)-> "A"(0, 0) False :: [] -(0)-> "A"(1, 0) False :: [] -(0)-> "A"(4, 0) False :: [] -(0)-> "A"(1, 2) False :: [] -(0)-> "A"(2, 1) Nil :: [] -(0)-> "A"(9, 6) Nil :: [] -(0)-> "A"(11, 4) Nil :: [] -(0)-> "A"(7, 7) Nil :: [] -(0)-> "A"(3, 11) Nil :: [] -(0)-> "A"(7, 5) Nil :: [] -(0)-> "A"(1, 0) Nil :: [] -(0)-> "A"(0, 0) Nil :: [] -(0)-> "A"(14, 4) Nil :: [] -(0)-> "A"(14, 15) Nil :: [] -(0)-> "A"(14, 6) Nil :: [] -(0)-> "A"(9, 5) Nil :: [] -(0)-> "A"(15, 15) Nil :: [] -(0)-> "A"(14, 12) Nil :: [] -(0)-> "A"(15, 14) S :: ["A"(1, 0)] -(0)-> "A"(1, 0) S :: ["A"(0, 0)] -(0)-> "A"(0, 0) True :: [] -(0)-> "A"(0, 0) True :: [] -(0)-> "A"(0, 1) True :: [] -(0)-> "A"(1, 0) True :: [] -(0)-> "A"(4, 0) True :: [] -(0)-> "A"(1, 1) and :: ["A"(0, 1) x "A"(0, 0)] -(0)-> "A"(0, 0) domatch :: ["A"(11, 4) x "A"(9, 6) x "A"(0, 0)] -(7)-> "A"(0, 0) domatch[Ite] :: ["A"(0, 0) x "A"(11, 4) x "A"(4, 6) x "A"(0, 0)] -(6)-> "A"(0, 0) eqNatList :: ["A"(3, 11) x "A"(7, 7)] -(10)-> "A"(4, 0) eqNatList[Ite] :: ["A"(1, 0) x "A"(0, 0) x "A"(7, 7) x "A"(0, 0) x "A"(7, 11)] -(13)-> "A"(4, 0) notEmpty :: ["A"(7, 5)] -(12)-> "A"(0, 0) prefix :: ["A"(0, 0) x "A"(1, 0)] -(1)-> "A"(0, 0) strmatch :: ["A"(15, 15) x "A"(15, 14)] -(8)-> "A"(0, 0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1, 0) "0_A" :: [] -(0)-> "A"(0, 1) "Cons_A" :: ["A"(1, 0) x "A"(1, 0)] -(1)-> "A"(1, 0) "Cons_A" :: ["A"(0, 0) x "A"(1, 1)] -(0)-> "A"(0, 1) "False_A" :: [] -(0)-> "A"(1, 0) "False_A" :: [] -(0)-> "A"(0, 1) "Nil_A" :: [] -(0)-> "A"(1, 0) "Nil_A" :: [] -(0)-> "A"(0, 1) "S_A" :: ["A"(1, 0)] -(0)-> "A"(1, 0) "S_A" :: ["A"(1, 0)] -(1)-> "A"(0, 1) "True_A" :: [] -(0)-> "A"(1, 0) "True_A" :: [] -(0)-> "A"(0, 1) WORST_CASE(Omega(n^1),O(n^2))