/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(),N) -> activate(N)
            U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U31(tt()) -> 0()
            U41(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__isNat(X)) -> isNat(X)
            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))
            and(tt(),X) -> activate(X)
            isNat(X) -> n__isNat(X)
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
            isNat(n__s(V1)) -> isNat(activate(V1))
            isNat(n__x(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
            plus(N,0()) -> U11(isNat(N),N)
            plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
            x(N,0()) -> U31(isNat(N))
            x(N,s(M)) -> U41(and(isNat(M),n__isNat(N)),M,N)
            x(X1,X2) -> n__x(X1,X2)
        - Signature:
            {0/0,U11/2,U21/3,U31/1,U41/3,activate/1,and/2,isNat/1,plus/2,s/1,x/2} / {n__0/0,n__isNat/1,n__plus/2,n__s/1
            ,n__x/2,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,U11,U21,U31,U41,activate,and,isNat,plus,s
            ,x} and constructors {n__0,n__isNat,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(),N) -> activate(N)
            U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U31(tt()) -> 0()
            U41(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__isNat(X)) -> isNat(X)
            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))
            and(tt(),X) -> activate(X)
            isNat(X) -> n__isNat(X)
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
            isNat(n__s(V1)) -> isNat(activate(V1))
            isNat(n__x(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
            plus(N,0()) -> U11(isNat(N),N)
            plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
            x(N,0()) -> U31(isNat(N))
            x(N,s(M)) -> U41(and(isNat(M),n__isNat(N)),M,N)
            x(X1,X2) -> n__x(X1,X2)
        - Signature:
            {0/0,U11/2,U21/3,U31/1,U41/3,activate/1,and/2,isNat/1,plus/2,s/1,x/2} / {n__0/0,n__isNat/1,n__plus/2,n__s/1
            ,n__x/2,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,U11,U21,U31,U41,activate,and,isNat,plus,s
            ,x} and constructors {n__0,n__isNat,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(),N) -> activate(N)
            U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U31(tt()) -> 0()
            U41(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__isNat(X)) -> isNat(X)
            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))
            and(tt(),X) -> activate(X)
            isNat(X) -> n__isNat(X)
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
            isNat(n__s(V1)) -> isNat(activate(V1))
            isNat(n__x(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
            plus(N,0()) -> U11(isNat(N),N)
            plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
            x(N,0()) -> U31(isNat(N))
            x(N,s(M)) -> U41(and(isNat(M),n__isNat(N)),M,N)
            x(X1,X2) -> n__x(X1,X2)
        - Signature:
            {0/0,U11/2,U21/3,U31/1,U41/3,activate/1,and/2,isNat/1,plus/2,s/1,x/2} / {n__0/0,n__isNat/1,n__plus/2,n__s/1
            ,n__x/2,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,U11,U21,U31,U41,activate,and,isNat,plus,s
            ,x} and constructors {n__0,n__isNat,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),?)