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

WORST_CASE(Omega(n^1),?)