/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(),V2) -> U12(isNat(activate(V2)))
            U12(tt()) -> tt()
            U21(tt()) -> tt()
            U31(tt(),V2) -> U32(isNat(activate(V2)))
            U32(tt()) -> tt()
            U41(tt(),N) -> activate(N)
            U51(tt(),M,N) -> U52(isNat(activate(N)),activate(M),activate(N))
            U52(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U61(tt()) -> 0()
            U71(tt(),M,N) -> U72(isNat(activate(N)),activate(M),activate(N))
            U72(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
            activate(n__s(X)) -> s(activate(X))
            activate(n__x(X1,X2)) -> x(activate(X1),activate(X2))
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
            isNat(n__s(V1)) -> U21(isNat(activate(V1)))
            isNat(n__x(V1,V2)) -> U31(isNat(activate(V1)),activate(V2))
            plus(N,0()) -> U41(isNat(N),N)
            plus(N,s(M)) -> U51(isNat(M),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
            x(N,0()) -> U61(isNat(N))
            x(N,s(M)) -> U71(isNat(M),M,N)
            x(X1,X2) -> n__x(X1,X2)
        - Signature:
            {0/0,U11/2,U12/1,U21/1,U31/2,U32/1,U41/2,U51/3,U52/3,U61/1,U71/3,U72/3,activate/1,isNat/1,plus/2,s/1
            ,x/2} / {n__0/0,n__plus/2,n__s/1,n__x/2,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,U11,U12,U21,U31,U32,U41,U51,U52,U61,U71,U72,activate,isNat,plus
            ,s,x} and constructors {n__0,n__plus,n__s,n__x,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            U11(tt(),V2) -> U12(isNat(activate(V2)))
            U12(tt()) -> tt()
            U21(tt()) -> tt()
            U31(tt(),V2) -> U32(isNat(activate(V2)))
            U32(tt()) -> tt()
            U41(tt(),N) -> activate(N)
            U51(tt(),M,N) -> U52(isNat(activate(N)),activate(M),activate(N))
            U52(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U61(tt()) -> 0()
            U71(tt(),M,N) -> U72(isNat(activate(N)),activate(M),activate(N))
            U72(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
            activate(n__s(X)) -> s(activate(X))
            activate(n__x(X1,X2)) -> x(activate(X1),activate(X2))
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
            isNat(n__s(V1)) -> U21(isNat(activate(V1)))
            isNat(n__x(V1,V2)) -> U31(isNat(activate(V1)),activate(V2))
            plus(N,0()) -> U41(isNat(N),N)
            plus(N,s(M)) -> U51(isNat(M),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
            x(N,0()) -> U61(isNat(N))
            x(N,s(M)) -> U71(isNat(M),M,N)
            x(X1,X2) -> n__x(X1,X2)
        - Signature:
            {0/0,U11/2,U12/1,U21/1,U31/2,U32/1,U41/2,U51/3,U52/3,U61/1,U71/3,U72/3,activate/1,isNat/1,plus/2,s/1
            ,x/2} / {n__0/0,n__plus/2,n__s/1,n__x/2,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,U11,U12,U21,U31,U32,U41,U51,U52,U61,U71,U72,activate,isNat,plus
            ,s,x} and constructors {n__0,n__plus,n__s,n__x,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            U11(tt(),V2) -> U12(isNat(activate(V2)))
            U12(tt()) -> tt()
            U21(tt()) -> tt()
            U31(tt(),V2) -> U32(isNat(activate(V2)))
            U32(tt()) -> tt()
            U41(tt(),N) -> activate(N)
            U51(tt(),M,N) -> U52(isNat(activate(N)),activate(M),activate(N))
            U52(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U61(tt()) -> 0()
            U71(tt(),M,N) -> U72(isNat(activate(N)),activate(M),activate(N))
            U72(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2))
            activate(n__s(X)) -> s(activate(X))
            activate(n__x(X1,X2)) -> x(activate(X1),activate(X2))
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> U11(isNat(activate(V1)),activate(V2))
            isNat(n__s(V1)) -> U21(isNat(activate(V1)))
            isNat(n__x(V1,V2)) -> U31(isNat(activate(V1)),activate(V2))
            plus(N,0()) -> U41(isNat(N),N)
            plus(N,s(M)) -> U51(isNat(M),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
            x(N,0()) -> U61(isNat(N))
            x(N,s(M)) -> U71(isNat(M),M,N)
            x(X1,X2) -> n__x(X1,X2)
        - Signature:
            {0/0,U11/2,U12/1,U21/1,U31/2,U32/1,U41/2,U51/3,U52/3,U61/1,U71/3,U72/3,activate/1,isNat/1,plus/2,s/1
            ,x/2} / {n__0/0,n__plus/2,n__s/1,n__x/2,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,U11,U12,U21,U31,U32,U41,U51,U52,U61,U71,U72,activate,isNat,plus
            ,s,x} and constructors {n__0,n__plus,n__s,n__x,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__plus(x,y)} =
            activate(n__plus(x,y)) ->^+ plus(activate(x),activate(y))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)