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

WORST_CASE(Omega(n^1),?)