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

WORST_CASE(Omega(n^1),?)