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

WORST_CASE(Omega(n^1),?)