/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:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2} / {0/0,s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {U11,U12,U21,U22,activate,plus,x} and constructors {0,s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2} / {0/0,s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {U11,U12,U21,U22,activate,plus,x} and constructors {0,s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2} / {0/0,s/1,tt/0}
        - Obligation:
             runtime complexity wrt. defined symbols {U11,U12,U21,U22,activate,plus,x} and constructors {0,s,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          U11(tt(),z,x_31){z -> s(z)} =
            U11(tt(),s(z),x_31) ->^+ s(U11(tt(),z,activate(activate(x_31))))
              = C[U11(tt(),z,activate(activate(x_31))) = U11(tt(),z,x_31){x_31 -> activate(activate(x_31))}]

WORST_CASE(Omega(n^1),?)