/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()
            U11(tt(),V1,V2) -> U12(isNat(activate(V1)),activate(V2))
            U12(tt(),V2) -> U13(isNat(activate(V2)))
            U13(tt()) -> tt()
            U21(tt(),V1) -> U22(isNat(activate(V1)))
            U22(tt()) -> tt()
            U31(tt(),N) -> activate(N)
            U41(tt(),M,N) -> s(plus(activate(N),activate(M)))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__and(X1,X2)) -> and(X1,X2)
            activate(n__isNatKind(X)) -> isNatKind(X)
            activate(n__plus(X1,X2)) -> plus(X1,X2)
            activate(n__s(X)) -> s(X)
            and(X1,X2) -> n__and(X1,X2)
            and(tt(),X) -> activate(X)
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
                                        ,activate(V1)
                                        ,activate(V2))
            isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
            isNatKind(X) -> n__isNatKind(X)
            isNatKind(n__0()) -> tt()
            isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
            isNatKind(n__s(V1)) -> isNatKind(activate(V1))
            plus(N,0()) -> U31(and(isNat(N),n__isNatKind(N)),N)
            plus(N,s(M)) -> U41(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
        - Signature:
            {0/0,U11/3,U12/2,U13/1,U21/2,U22/1,U31/2,U41/3,activate/1,and/2,isNat/1,isNatKind/1,plus/2,s/1} / {n__0/0
            ,n__and/2,n__isNatKind/1,n__plus/2,n__s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,U11,U12,U13,U21,U22,U31,U41,activate,and,isNat,isNatKind,plus
            ,s} and constructors {n__0,n__and,n__isNatKind,n__plus,n__s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            U11(tt(),V1,V2) -> U12(isNat(activate(V1)),activate(V2))
            U12(tt(),V2) -> U13(isNat(activate(V2)))
            U13(tt()) -> tt()
            U21(tt(),V1) -> U22(isNat(activate(V1)))
            U22(tt()) -> tt()
            U31(tt(),N) -> activate(N)
            U41(tt(),M,N) -> s(plus(activate(N),activate(M)))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__and(X1,X2)) -> and(X1,X2)
            activate(n__isNatKind(X)) -> isNatKind(X)
            activate(n__plus(X1,X2)) -> plus(X1,X2)
            activate(n__s(X)) -> s(X)
            and(X1,X2) -> n__and(X1,X2)
            and(tt(),X) -> activate(X)
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
                                        ,activate(V1)
                                        ,activate(V2))
            isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
            isNatKind(X) -> n__isNatKind(X)
            isNatKind(n__0()) -> tt()
            isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2)))
            isNatKind(n__s(V1)) -> isNatKind(activate(V1))
            plus(N,0()) -> U31(and(isNat(N),n__isNatKind(N)),N)
            plus(N,s(M)) -> U41(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
        - Signature:
            {0/0,U11/3,U12/2,U13/1,U21/2,U22/1,U31/2,U41/3,activate/1,and/2,isNat/1,isNatKind/1,plus/2,s/1} / {n__0/0
            ,n__and/2,n__isNatKind/1,n__plus/2,n__s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,U11,U12,U13,U21,U22,U31,U41,activate,and,isNat,isNatKind,plus
            ,s} and constructors {n__0,n__and,n__isNatKind,n__plus,n__s,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__and(tt(),x)} =
            activate(n__and(tt(),x)) ->^+ activate(x)
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)