/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:
            div(0(),s(y)) -> 0()
            div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
            f(x,0(),b) -> x
            f(x,s(y),b) -> div(f(x,minus(s(y),s(0())),b),b)
            minus(x,x) -> 0()
            minus(x,0()) -> x
            minus(0(),x) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {div/2,f/3,minus/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {div,f,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:
            div(0(),s(y)) -> 0()
            div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
            f(x,0(),b) -> x
            f(x,s(y),b) -> div(f(x,minus(s(y),s(0())),b),b)
            minus(x,x) -> 0()
            minus(x,0()) -> x
            minus(0(),x) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {div/2,f/3,minus/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {div,f,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:
            div(0(),s(y)) -> 0()
            div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
            f(x,0(),b) -> x
            f(x,s(y),b) -> div(f(x,minus(s(y),s(0())),b),b)
            minus(x,x) -> 0()
            minus(x,0()) -> x
            minus(0(),x) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {div/2,f/3,minus/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {div,f,minus} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          minus(x,y){x -> s(x),y -> s(y)} =
            minus(s(x),s(y)) ->^+ minus(x,y)
              = C[minus(x,y) = minus(x,y){}]

WORST_CASE(Omega(n^1),?)