/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:
            D(b(x,y)) -> b(D(x),D(y))
            D(c(x,y)) -> b(c(y,D(x)),c(x,D(y)))
            D(constant()) -> h()
            D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2())))
            D(ln(x)) -> div(D(x),x)
            D(m(x,y)) -> m(D(x),D(y))
            D(opp(x)) -> opp(D(x))
            D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
            D(t()) -> s(h())
            b(x,h()) -> x
            b(b(x,y),z) -> b(x,b(y,z))
            b(h(),x) -> x
            b(s(x),s(y)) -> s(s(b(x,y)))
        - Signature:
            {D/1,b/2} / {1/0,2/0,c/2,constant/0,div/2,h/0,ln/1,m/2,opp/1,pow/2,s/1,t/0}
        - Obligation:
             runtime complexity wrt. defined symbols {D,b} and constructors {1,2,c,constant,div,h,ln,m,opp,pow,s,t}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            D(b(x,y)) -> b(D(x),D(y))
            D(c(x,y)) -> b(c(y,D(x)),c(x,D(y)))
            D(constant()) -> h()
            D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2())))
            D(ln(x)) -> div(D(x),x)
            D(m(x,y)) -> m(D(x),D(y))
            D(opp(x)) -> opp(D(x))
            D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
            D(t()) -> s(h())
            b(x,h()) -> x
            b(b(x,y),z) -> b(x,b(y,z))
            b(h(),x) -> x
            b(s(x),s(y)) -> s(s(b(x,y)))
        - Signature:
            {D/1,b/2} / {1/0,2/0,c/2,constant/0,div/2,h/0,ln/1,m/2,opp/1,pow/2,s/1,t/0}
        - Obligation:
             runtime complexity wrt. defined symbols {D,b} and constructors {1,2,c,constant,div,h,ln,m,opp,pow,s,t}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            D(b(x,y)) -> b(D(x),D(y))
            D(c(x,y)) -> b(c(y,D(x)),c(x,D(y)))
            D(constant()) -> h()
            D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2())))
            D(ln(x)) -> div(D(x),x)
            D(m(x,y)) -> m(D(x),D(y))
            D(opp(x)) -> opp(D(x))
            D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
            D(t()) -> s(h())
            b(x,h()) -> x
            b(b(x,y),z) -> b(x,b(y,z))
            b(h(),x) -> x
            b(s(x),s(y)) -> s(s(b(x,y)))
        - Signature:
            {D/1,b/2} / {1/0,2/0,c/2,constant/0,div/2,h/0,ln/1,m/2,opp/1,pow/2,s/1,t/0}
        - Obligation:
             runtime complexity wrt. defined symbols {D,b} and constructors {1,2,c,constant,div,h,ln,m,opp,pow,s,t}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          D(x){x -> c(x,y)} =
            D(c(x,y)) ->^+ b(c(y,D(x)),c(x,D(y)))
              = C[D(x) = D(x){}]

WORST_CASE(Omega(n^1),?)