/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(x,y) -> if1(ge(x,y),x,y)
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
            if(false(),x,y) -> 0()
            if(true(),x,y) -> s(minus(x,y))
            if1(false(),x,y) -> if3(gt(x,0()),x,y)
            if1(true(),x,y) -> if2(gt(y,0()),x,y)
            if2(false(),x,y) -> x
            if2(true(),x,y) -> gcd(minus(x,y),y)
            if3(false(),x,y) -> y
            if3(true(),x,y) -> gcd(x,minus(y,x))
            minus(s(x),y) -> if(gt(s(x),y),x,y)
        - Signature:
            {gcd/2,ge/2,gt/2,if/3,if1/3,if2/3,if3/3,minus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {gcd,ge,gt,if,if1,if2,if3,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(x,y) -> if1(ge(x,y),x,y)
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
            if(false(),x,y) -> 0()
            if(true(),x,y) -> s(minus(x,y))
            if1(false(),x,y) -> if3(gt(x,0()),x,y)
            if1(true(),x,y) -> if2(gt(y,0()),x,y)
            if2(false(),x,y) -> x
            if2(true(),x,y) -> gcd(minus(x,y),y)
            if3(false(),x,y) -> y
            if3(true(),x,y) -> gcd(x,minus(y,x))
            minus(s(x),y) -> if(gt(s(x),y),x,y)
        - Signature:
            {gcd/2,ge/2,gt/2,if/3,if1/3,if2/3,if3/3,minus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {gcd,ge,gt,if,if1,if2,if3,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(x,y) -> if1(ge(x,y),x,y)
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            gt(0(),y) -> false()
            gt(s(x),0()) -> true()
            gt(s(x),s(y)) -> gt(x,y)
            if(false(),x,y) -> 0()
            if(true(),x,y) -> s(minus(x,y))
            if1(false(),x,y) -> if3(gt(x,0()),x,y)
            if1(true(),x,y) -> if2(gt(y,0()),x,y)
            if2(false(),x,y) -> x
            if2(true(),x,y) -> gcd(minus(x,y),y)
            if3(false(),x,y) -> y
            if3(true(),x,y) -> gcd(x,minus(y,x))
            minus(s(x),y) -> if(gt(s(x),y),x,y)
        - Signature:
            {gcd/2,ge/2,gt/2,if/3,if1/3,if2/3,if3/3,minus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {gcd,ge,gt,if,if1,if2,if3,minus} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          ge(x,y){x -> s(x),y -> s(y)} =
            ge(s(x),s(y)) ->^+ ge(x,y)
              = C[ge(x,y) = ge(x,y){}]

WORST_CASE(Omega(n^1),?)