/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,X3,X4) -> U11(X1,X2,X3,X4) a__U11(tt(),N,X,XS) -> a__U12(a__splitAt(mark(N),mark(XS)),X) a__U12(X1,X2) -> U12(X1,X2) a__U12(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS)) a__afterNth(N,XS) -> a__snd(a__splitAt(mark(N),mark(XS))) a__afterNth(X1,X2) -> afterNth(X1,X2) a__and(X1,X2) -> and(X1,X2) a__and(tt(),X) -> mark(X) a__fst(X) -> fst(X) a__fst(pair(X,Y)) -> mark(X) a__head(X) -> head(X) a__head(cons(N,XS)) -> mark(N) a__natsFrom(N) -> cons(mark(N),natsFrom(s(N))) a__natsFrom(X) -> natsFrom(X) a__sel(N,XS) -> a__head(a__afterNth(mark(N),mark(XS))) a__sel(X1,X2) -> sel(X1,X2) a__snd(X) -> snd(X) a__snd(pair(X,Y)) -> mark(Y) a__splitAt(X1,X2) -> splitAt(X1,X2) a__splitAt(0(),XS) -> pair(nil(),mark(XS)) a__splitAt(s(N),cons(X,XS)) -> a__U11(tt(),N,X,XS) a__tail(X) -> tail(X) a__tail(cons(N,XS)) -> mark(XS) a__take(N,XS) -> a__fst(a__splitAt(mark(N),mark(XS))) a__take(X1,X2) -> take(X1,X2) mark(0()) -> 0() mark(U11(X1,X2,X3,X4)) -> a__U11(mark(X1),X2,X3,X4) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(fst(X)) -> a__fst(mark(X)) mark(head(X)) -> a__head(mark(X)) mark(natsFrom(X)) -> a__natsFrom(mark(X)) mark(nil()) -> nil() mark(pair(X1,X2)) -> pair(mark(X1),mark(X2)) mark(s(X)) -> s(mark(X)) mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) mark(snd(X)) -> a__snd(mark(X)) mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2)) mark(tail(X)) -> a__tail(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() - Signature: {a__U11/4,a__U12/2,a__afterNth/2,a__and/2,a__fst/1,a__head/1,a__natsFrom/1,a__sel/2,a__snd/1,a__splitAt/2 ,a__tail/1,a__take/2,mark/1} / {0/0,U11/4,U12/2,afterNth/2,and/2,cons/2,fst/1,head/1,natsFrom/1,nil/0,pair/2 ,s/1,sel/2,snd/1,splitAt/2,tail/1,take/2,tt/0} - Obligation: runtime complexity wrt. defined symbols {a__U11,a__U12,a__afterNth,a__and,a__fst,a__head,a__natsFrom,a__sel ,a__snd,a__splitAt,a__tail,a__take,mark} and constructors {0,U11,U12,afterNth,and,cons,fst,head,natsFrom,nil ,pair,s,sel,snd,splitAt,tail,take,tt} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__U11(X1,X2,X3,X4) -> U11(X1,X2,X3,X4) a__U11(tt(),N,X,XS) -> a__U12(a__splitAt(mark(N),mark(XS)),X) a__U12(X1,X2) -> U12(X1,X2) a__U12(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS)) a__afterNth(N,XS) -> a__snd(a__splitAt(mark(N),mark(XS))) a__afterNth(X1,X2) -> afterNth(X1,X2) a__and(X1,X2) -> and(X1,X2) a__and(tt(),X) -> mark(X) a__fst(X) -> fst(X) a__fst(pair(X,Y)) -> mark(X) a__head(X) -> head(X) a__head(cons(N,XS)) -> mark(N) a__natsFrom(N) -> cons(mark(N),natsFrom(s(N))) a__natsFrom(X) -> natsFrom(X) a__sel(N,XS) -> a__head(a__afterNth(mark(N),mark(XS))) a__sel(X1,X2) -> sel(X1,X2) a__snd(X) -> snd(X) a__snd(pair(X,Y)) -> mark(Y) a__splitAt(X1,X2) -> splitAt(X1,X2) a__splitAt(0(),XS) -> pair(nil(),mark(XS)) a__splitAt(s(N),cons(X,XS)) -> a__U11(tt(),N,X,XS) a__tail(X) -> tail(X) a__tail(cons(N,XS)) -> mark(XS) a__take(N,XS) -> a__fst(a__splitAt(mark(N),mark(XS))) a__take(X1,X2) -> take(X1,X2) mark(0()) -> 0() mark(U11(X1,X2,X3,X4)) -> a__U11(mark(X1),X2,X3,X4) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(fst(X)) -> a__fst(mark(X)) mark(head(X)) -> a__head(mark(X)) mark(natsFrom(X)) -> a__natsFrom(mark(X)) mark(nil()) -> nil() mark(pair(X1,X2)) -> pair(mark(X1),mark(X2)) mark(s(X)) -> s(mark(X)) mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) mark(snd(X)) -> a__snd(mark(X)) mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2)) mark(tail(X)) -> a__tail(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() - Signature: {a__U11/4,a__U12/2,a__afterNth/2,a__and/2,a__fst/1,a__head/1,a__natsFrom/1,a__sel/2,a__snd/1,a__splitAt/2 ,a__tail/1,a__take/2,mark/1} / {0/0,U11/4,U12/2,afterNth/2,and/2,cons/2,fst/1,head/1,natsFrom/1,nil/0,pair/2 ,s/1,sel/2,snd/1,splitAt/2,tail/1,take/2,tt/0} - Obligation: runtime complexity wrt. defined symbols {a__U11,a__U12,a__afterNth,a__and,a__fst,a__head,a__natsFrom,a__sel ,a__snd,a__splitAt,a__tail,a__take,mark} and constructors {0,U11,U12,afterNth,and,cons,fst,head,natsFrom,nil ,pair,s,sel,snd,splitAt,tail,take,tt} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__U11(X1,X2,X3,X4) -> U11(X1,X2,X3,X4) a__U11(tt(),N,X,XS) -> a__U12(a__splitAt(mark(N),mark(XS)),X) a__U12(X1,X2) -> U12(X1,X2) a__U12(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS)) a__afterNth(N,XS) -> a__snd(a__splitAt(mark(N),mark(XS))) a__afterNth(X1,X2) -> afterNth(X1,X2) a__and(X1,X2) -> and(X1,X2) a__and(tt(),X) -> mark(X) a__fst(X) -> fst(X) a__fst(pair(X,Y)) -> mark(X) a__head(X) -> head(X) a__head(cons(N,XS)) -> mark(N) a__natsFrom(N) -> cons(mark(N),natsFrom(s(N))) a__natsFrom(X) -> natsFrom(X) a__sel(N,XS) -> a__head(a__afterNth(mark(N),mark(XS))) a__sel(X1,X2) -> sel(X1,X2) a__snd(X) -> snd(X) a__snd(pair(X,Y)) -> mark(Y) a__splitAt(X1,X2) -> splitAt(X1,X2) a__splitAt(0(),XS) -> pair(nil(),mark(XS)) a__splitAt(s(N),cons(X,XS)) -> a__U11(tt(),N,X,XS) a__tail(X) -> tail(X) a__tail(cons(N,XS)) -> mark(XS) a__take(N,XS) -> a__fst(a__splitAt(mark(N),mark(XS))) a__take(X1,X2) -> take(X1,X2) mark(0()) -> 0() mark(U11(X1,X2,X3,X4)) -> a__U11(mark(X1),X2,X3,X4) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(fst(X)) -> a__fst(mark(X)) mark(head(X)) -> a__head(mark(X)) mark(natsFrom(X)) -> a__natsFrom(mark(X)) mark(nil()) -> nil() mark(pair(X1,X2)) -> pair(mark(X1),mark(X2)) mark(s(X)) -> s(mark(X)) mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2)) mark(snd(X)) -> a__snd(mark(X)) mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2)) mark(tail(X)) -> a__tail(mark(X)) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(tt()) -> tt() - Signature: {a__U11/4,a__U12/2,a__afterNth/2,a__and/2,a__fst/1,a__head/1,a__natsFrom/1,a__sel/2,a__snd/1,a__splitAt/2 ,a__tail/1,a__take/2,mark/1} / {0/0,U11/4,U12/2,afterNth/2,and/2,cons/2,fst/1,head/1,natsFrom/1,nil/0,pair/2 ,s/1,sel/2,snd/1,splitAt/2,tail/1,take/2,tt/0} - Obligation: runtime complexity wrt. defined symbols {a__U11,a__U12,a__afterNth,a__and,a__fst,a__head,a__natsFrom,a__sel ,a__snd,a__splitAt,a__tail,a__take,mark} and constructors {0,U11,U12,afterNth,and,cons,fst,head,natsFrom,nil ,pair,s,sel,snd,splitAt,tail,take,tt} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: mark(x){x -> U11(x,y,z,u)} = mark(U11(x,y,z,u)) ->^+ a__U11(mark(x),y,z,u) = C[mark(x) = mark(x){}] WORST_CASE(Omega(n^1),?)