/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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

WORST_CASE(Omega(n^1),?)