/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:
            din(der(der(X))) -> u41(din(der(X)),X)
            din(der(plus(X,Y))) -> u21(din(der(X)),X,Y)
            din(der(times(X,Y))) -> u31(din(der(X)),X,Y)
            u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX)
            u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY))
            u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX)
            u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX)))
            u41(dout(DX),X) -> u42(din(der(DX)),X,DX)
            u42(dout(DDX),X,DX) -> dout(DDX)
        - Signature:
            {din/1,u21/3,u22/4,u31/3,u32/4,u41/2,u42/3} / {der/1,dout/1,plus/2,times/2}
        - Obligation:
             runtime complexity wrt. defined symbols {din,u21,u22,u31,u32,u41,u42} and constructors {der,dout,plus
            ,times}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            din(der(der(X))) -> u41(din(der(X)),X)
            din(der(plus(X,Y))) -> u21(din(der(X)),X,Y)
            din(der(times(X,Y))) -> u31(din(der(X)),X,Y)
            u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX)
            u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY))
            u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX)
            u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX)))
            u41(dout(DX),X) -> u42(din(der(DX)),X,DX)
            u42(dout(DDX),X,DX) -> dout(DDX)
        - Signature:
            {din/1,u21/3,u22/4,u31/3,u32/4,u41/2,u42/3} / {der/1,dout/1,plus/2,times/2}
        - Obligation:
             runtime complexity wrt. defined symbols {din,u21,u22,u31,u32,u41,u42} and constructors {der,dout,plus
            ,times}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            din(der(der(X))) -> u41(din(der(X)),X)
            din(der(plus(X,Y))) -> u21(din(der(X)),X,Y)
            din(der(times(X,Y))) -> u31(din(der(X)),X,Y)
            u21(dout(DX),X,Y) -> u22(din(der(Y)),X,Y,DX)
            u22(dout(DY),X,Y,DX) -> dout(plus(DX,DY))
            u31(dout(DX),X,Y) -> u32(din(der(Y)),X,Y,DX)
            u32(dout(DY),X,Y,DX) -> dout(plus(times(X,DY),times(Y,DX)))
            u41(dout(DX),X) -> u42(din(der(DX)),X,DX)
            u42(dout(DDX),X,DX) -> dout(DDX)
        - Signature:
            {din/1,u21/3,u22/4,u31/3,u32/4,u41/2,u42/3} / {der/1,dout/1,plus/2,times/2}
        - Obligation:
             runtime complexity wrt. defined symbols {din,u21,u22,u31,u32,u41,u42} and constructors {der,dout,plus
            ,times}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          din(der(x)){x -> der(x)} =
            din(der(der(x))) ->^+ u41(din(der(x)),x)
              = C[din(der(x)) = din(der(x)){}]

WORST_CASE(Omega(n^1),?)