/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- tct-trs: Prelude.head: empty list tct-trs: Prelude.head: empty list tct-trs: Prelude.head: empty list tct-trs: Prelude.head: empty list WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: U11(tt(),L) -> U12(tt(),activate(L)) U12(tt(),L) -> s(length(activate(L))) U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__zeros()) -> zeros() length(cons(N,L)) -> U11(tt(),activate(L)) length(nil()) -> 0() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {U11/2,U12/2,U21/4,U22/4,U23/4,activate/1,length/1,take/2,zeros/0} / {0/0,cons/2,n__take/2,n__zeros/0,nil/0 ,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,U21,U22,U23,activate,length,take ,zeros} and constructors {0,cons,n__take,n__zeros,nil,s,tt} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: U11(tt(),L) -> U12(tt(),activate(L)) U12(tt(),L) -> s(length(activate(L))) U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__zeros()) -> zeros() length(cons(N,L)) -> U11(tt(),activate(L)) length(nil()) -> 0() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {U11/2,U12/2,U21/4,U22/4,U23/4,activate/1,length/1,take/2,zeros/0} / {0/0,cons/2,n__take/2,n__zeros/0,nil/0 ,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,U21,U22,U23,activate,length,take ,zeros} and constructors {0,cons,n__take,n__zeros,nil,s,tt} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 2.a:1: Ara. MAYBE + Considered Problem: - Strict TRS: U11(tt(),L) -> U12(tt(),activate(L)) U12(tt(),L) -> s(length(activate(L))) U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__zeros()) -> zeros() length(cons(N,L)) -> U11(tt(),activate(L)) length(nil()) -> 0() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {U11/2,U12/2,U21/4,U22/4,U23/4,activate/1,length/1,take/2,zeros/0} / {0/0,cons/2,n__take/2,n__zeros/0,nil/0 ,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,U21,U22,U23,activate,length,take ,zeros} and constructors {0,cons,n__take,n__zeros,nil,s,tt} + Applied Processor: Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False} + Details: Signatures used: ---------------- F (TrsFun "0") :: [] -(0)-> "A"(0, 0, 0) F (TrsFun "U11") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "U12") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "U21") :: ["A"(0, 0, 1) x "A"(0, 0, 0) x "A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "U22") :: ["A"(0, 0, 0) x "A"(0, 0, 0) x "A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "U23") :: ["A"(0, 0, 0) x "A"(0, 0, 0) x "A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "activate") :: ["A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "cons") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0) F (TrsFun "length") :: ["A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "main") :: [] -(1)-> "A"(0, 0, 0) F (TrsFun "n__take") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0) F (TrsFun "n__zeros") :: [] -(0)-> "A"(0, 0, 0) F (TrsFun "nil") :: [] -(0)-> "A"(0, 0, 0) F (TrsFun "s") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0) F (TrsFun "take") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0) F (TrsFun "tt") :: [] -(0)-> "A"(0, 0, 0) F (TrsFun "tt") :: [] -(0)-> "A"(0, 0, 1) F (TrsFun "zeros") :: [] -(1)-> "A"(0, 0, 0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- Following Still Strict Rules were Typed as: ------------------------------------------- 1. Strict: U11(tt(),L) -> U12(tt(),activate(L)) U12(tt(),L) -> s(length(activate(L))) U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__zeros()) -> zeros() length(cons(N,L)) -> U11(tt(),activate(L)) length(nil()) -> 0() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() main() -> zeros() 2. Weak: ** Step 2.b:1: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: U11(tt(),L) -> U12(tt(),activate(L)) U12(tt(),L) -> s(length(activate(L))) U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) activate(X) -> X activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__zeros()) -> zeros() length(cons(N,L)) -> U11(tt(),activate(L)) length(nil()) -> 0() take(X1,X2) -> n__take(X1,X2) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> cons(0(),n__zeros()) zeros() -> n__zeros() - Signature: {U11/2,U12/2,U21/4,U22/4,U23/4,activate/1,length/1,take/2,zeros/0} / {0/0,cons/2,n__take/2,n__zeros/0,nil/0 ,s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U12,U21,U22,U23,activate,length,take ,zeros} and constructors {0,cons,n__take,n__zeros,nil,s,tt} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: activate(x){x -> n__take(x,y)} = activate(n__take(x,y)) ->^+ take(activate(x),activate(y)) = C[activate(x) = activate(x){}] WORST_CASE(Omega(n^1),?)