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

WORST_CASE(Omega(n^1),?)