/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__U11(X1,X2) -> U11(X1,X2) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(X1,X2) -> U12(X1,X2) a__U12(tt(),L) -> s(a__length(mark(L))) a__U21(X1,X2,X3,X4) -> U21(X1,X2,X3,X4) a__U21(tt(),IL,M,N) -> a__U22(tt(),IL,M,N) a__U22(X1,X2,X3,X4) -> U22(X1,X2,X3,X4) a__U22(tt(),IL,M,N) -> a__U23(tt(),IL,M,N) a__U23(X1,X2,X3,X4) -> U23(X1,X2,X3,X4) a__U23(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__length(X) -> length(X) a__length(cons(N,L)) -> a__U11(tt(),L) a__length(nil()) -> 0() a__take(X1,X2) -> take(X1,X2) a__take(0(),IL) -> nil() a__take(s(M),cons(N,IL)) -> a__U21(tt(),IL,M,N) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U21(X1,X2,X3,X4)) -> a__U21(mark(X1),X2,X3,X4) mark(U22(X1,X2,X3,X4)) -> a__U22(mark(X1),X2,X3,X4) mark(U23(X1,X2,X3,X4)) -> a__U23(mark(X1),X2,X3,X4) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(nil()) -> nil() mark(s(X)) -> s(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() mark(zeros()) -> a__zeros() - Signature: {a__U11/2,a__U12/2,a__U21/4,a__U22/4,a__U23/4,a__length/1,a__take/2,a__zeros/0,mark/1} / {0/0,U11/2,U12/2 ,U21/4,U22/4,U23/4,cons/2,length/1,nil/0,s/1,take/2,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {a__U11,a__U12,a__U21,a__U22,a__U23,a__length,a__take,a__zeros ,mark} and constructors {0,U11,U12,U21,U22,U23,cons,length,nil,s,take,tt,zeros} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__U11(X1,X2) -> U11(X1,X2) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(X1,X2) -> U12(X1,X2) a__U12(tt(),L) -> s(a__length(mark(L))) a__U21(X1,X2,X3,X4) -> U21(X1,X2,X3,X4) a__U21(tt(),IL,M,N) -> a__U22(tt(),IL,M,N) a__U22(X1,X2,X3,X4) -> U22(X1,X2,X3,X4) a__U22(tt(),IL,M,N) -> a__U23(tt(),IL,M,N) a__U23(X1,X2,X3,X4) -> U23(X1,X2,X3,X4) a__U23(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__length(X) -> length(X) a__length(cons(N,L)) -> a__U11(tt(),L) a__length(nil()) -> 0() a__take(X1,X2) -> take(X1,X2) a__take(0(),IL) -> nil() a__take(s(M),cons(N,IL)) -> a__U21(tt(),IL,M,N) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U21(X1,X2,X3,X4)) -> a__U21(mark(X1),X2,X3,X4) mark(U22(X1,X2,X3,X4)) -> a__U22(mark(X1),X2,X3,X4) mark(U23(X1,X2,X3,X4)) -> a__U23(mark(X1),X2,X3,X4) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(nil()) -> nil() mark(s(X)) -> s(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() mark(zeros()) -> a__zeros() - Signature: {a__U11/2,a__U12/2,a__U21/4,a__U22/4,a__U23/4,a__length/1,a__take/2,a__zeros/0,mark/1} / {0/0,U11/2,U12/2 ,U21/4,U22/4,U23/4,cons/2,length/1,nil/0,s/1,take/2,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {a__U11,a__U12,a__U21,a__U22,a__U23,a__length,a__take,a__zeros ,mark} and constructors {0,U11,U12,U21,U22,U23,cons,length,nil,s,take,tt,zeros} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__U11(X1,X2) -> U11(X1,X2) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(X1,X2) -> U12(X1,X2) a__U12(tt(),L) -> s(a__length(mark(L))) a__U21(X1,X2,X3,X4) -> U21(X1,X2,X3,X4) a__U21(tt(),IL,M,N) -> a__U22(tt(),IL,M,N) a__U22(X1,X2,X3,X4) -> U22(X1,X2,X3,X4) a__U22(tt(),IL,M,N) -> a__U23(tt(),IL,M,N) a__U23(X1,X2,X3,X4) -> U23(X1,X2,X3,X4) a__U23(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__length(X) -> length(X) a__length(cons(N,L)) -> a__U11(tt(),L) a__length(nil()) -> 0() a__take(X1,X2) -> take(X1,X2) a__take(0(),IL) -> nil() a__take(s(M),cons(N,IL)) -> a__U21(tt(),IL,M,N) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(U21(X1,X2,X3,X4)) -> a__U21(mark(X1),X2,X3,X4) mark(U22(X1,X2,X3,X4)) -> a__U22(mark(X1),X2,X3,X4) mark(U23(X1,X2,X3,X4)) -> a__U23(mark(X1),X2,X3,X4) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(nil()) -> nil() mark(s(X)) -> s(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() mark(zeros()) -> a__zeros() - Signature: {a__U11/2,a__U12/2,a__U21/4,a__U22/4,a__U23/4,a__length/1,a__take/2,a__zeros/0,mark/1} / {0/0,U11/2,U12/2 ,U21/4,U22/4,U23/4,cons/2,length/1,nil/0,s/1,take/2,tt/0,zeros/0} - Obligation: runtime complexity wrt. defined symbols {a__U11,a__U12,a__U21,a__U22,a__U23,a__length,a__take,a__zeros ,mark} and constructors {0,U11,U12,U21,U22,U23,cons,length,nil,s,take,tt,zeros} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: mark(x){x -> U11(x,y)} = mark(U11(x,y)) ->^+ a__U11(mark(x),y) = C[mark(x) = mark(x){}] WORST_CASE(Omega(n^1),?)