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

WORST_CASE(Omega(n^1),?)