Runti Compl Full Rewri 10127 pair #381903842

details

property	value
status	complete
benchmark	Ex4_DLMMU04_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n045.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	295.176803827 seconds
cpu usage	807.711112733
max memory	1.9935899648E10

stage attributes

key	value
output-size	5108
starexec-result	WORST_CASE(Omega(n^1),?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__length(X)) -> length(X)
            activate(n__nil()) -> nil()
            activate(n__s(X)) -> s(X)
            activate(n__take(X1,X2)) -> take(X1,X2)
            activate(n__zeros()) -> zeros()
            and(tt(),T) -> T
            cons(X1,X2) -> n__cons(X1,X2)
            isNat(n__0()) -> tt()
            isNat(n__length(L)) -> isNatList(activate(L))
            isNat(n__s(N)) -> isNat(activate(N))
            isNatIList(IL) -> isNatList(activate(IL))
            isNatIList(n__cons(N,IL)) -> and(isNat(activate(N)),isNatIList(activate(IL)))
            isNatIList(n__zeros()) -> tt()
            isNatList(n__cons(N,L)) -> and(isNat(activate(N)),isNatList(activate(L)))
            isNatList(n__nil()) -> tt()
            isNatList(n__take(N,IL)) -> and(isNat(activate(N)),isNatIList(activate(IL)))
            length(X) -> n__length(X)
            length(cons(N,L)) -> uLength(and(isNat(N),isNatList(activate(L))),activate(L))
            nil() -> n__nil()
            s(X) -> n__s(X)
            take(X1,X2) -> n__take(X1,X2)
            take(0(),IL) -> uTake1(isNatIList(IL))
            take(s(M),cons(N,IL)) -> uTake2(and(isNat(M),and(isNat(N),isNatIList(activate(IL)))),M,N,activate(IL))
            uLength(tt(),L) -> s(length(activate(L)))
            uTake1(tt()) -> nil()
            uTake2(tt(),M,N,IL) -> cons(activate(N),n__take(activate(M),activate(IL)))
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {0/0,activate/1,and/2,cons/2,isNat/1,isNatIList/1,isNatList/1,length/1,nil/0,s/1,take/2,uLength/2,uTake1/1
            ,uTake2/4,zeros/0} / {n__0/0,n__cons/2,n__length/1,n__nil/0,n__s/1,n__take/2,n__zeros/0,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,and,cons,isNat,isNatIList,isNatList,length,nil,s,take
            ,uLength,uTake1,uTake2,zeros} and constructors {n__0,n__cons,n__length,n__nil,n__s,n__take,n__zeros,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__length(X)) -> length(X)
            activate(n__nil()) -> nil()
            activate(n__s(X)) -> s(X)
            activate(n__take(X1,X2)) -> take(X1,X2)
            activate(n__zeros()) -> zeros()
            and(tt(),T) -> T
            cons(X1,X2) -> n__cons(X1,X2)
            isNat(n__0()) -> tt()
            isNat(n__length(L)) -> isNatList(activate(L))
            isNat(n__s(N)) -> isNat(activate(N))
            isNatIList(IL) -> isNatList(activate(IL))
            isNatIList(n__cons(N,IL)) -> and(isNat(activate(N)),isNatIList(activate(IL)))
            isNatIList(n__zeros()) -> tt()
            isNatList(n__cons(N,L)) -> and(isNat(activate(N)),isNatList(activate(L)))
            isNatList(n__nil()) -> tt()
            isNatList(n__take(N,IL)) -> and(isNat(activate(N)),isNatIList(activate(IL)))
            length(X) -> n__length(X)
            length(cons(N,L)) -> uLength(and(isNat(N),isNatList(activate(L))),activate(L))
            nil() -> n__nil()
            s(X) -> n__s(X)
            take(X1,X2) -> n__take(X1,X2)
            take(0(),IL) -> uTake1(isNatIList(IL))
            take(s(M),cons(N,IL)) -> uTake2(and(isNat(M),and(isNat(N),isNatIList(activate(IL)))),M,N,activate(IL))
            uLength(tt(),L) -> s(length(activate(L)))
            uTake1(tt()) -> nil()
            uTake2(tt(),M,N,IL) -> cons(activate(N),n__take(activate(M),activate(IL)))
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {0/0,activate/1,and/2,cons/2,isNat/1,isNatIList/1,isNatList/1,length/1,nil/0,s/1,take/2,uLength/2,uTake1/1
            ,uTake2/4,zeros/0} / {n__0/0,n__cons/2,n__length/1,n__nil/0,n__s/1,n__take/2,n__zeros/0,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,and,cons,isNat,isNatIList,isNatList,length,nil,s,take
            ,uLength,uTake1,uTake2,zeros} and constructors {n__0,n__cons,n__length,n__nil,n__s,n__take,n__zeros,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          isNat(x){x -> n__s(x)} =
            isNat(n__s(x)) ->^+ isNat(x)
              = C[isNat(x) = isNat(x){}]

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