/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:
            f0(x,y,z) -> d()
            f0(0(),y,x) -> f1(x,y,x)
            f1(x,y,z) -> c()
            f1(x,y,z) -> f2(x,y,z)
            f2(x,1(),z) -> f0(x,z,z)
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            ifPlus(false(),x,y) -> plus(p(x),y)
            ifPlus(true(),x,y) -> p(y)
            ifTimes(false(),i,x,y,z) -> timesIter(inc(i),x,y,plus(z,y))
            ifTimes(true(),i,x,y,z) -> z
            inc(x) -> s(x)
            inc(0()) -> s(0())
            inc(s(x)) -> s(inc(x))
            isZero(0()) -> true()
            isZero(s(0())) -> false()
            isZero(s(s(x))) -> isZero(s(x))
            p(0()) -> 0()
            p(s(x)) -> x
            p(s(s(x))) -> s(p(s(x)))
            plus(x,y) -> ifPlus(isZero(x),x,inc(y))
            times(x,y) -> timesIter(0(),x,y,0())
            timesIter(i,x,y,z) -> ifTimes(ge(i,x),i,x,y,z)
        - Signature:
            {f0/3,f1/3,f2/3,ge/2,ifPlus/3,ifTimes/5,inc/1,isZero/1,p/1,plus/2,times/2,timesIter/4} / {0/0,1/0,c/0,d/0
            ,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {f0,f1,f2,ge,ifPlus,ifTimes,inc,isZero,p,plus,times
            ,timesIter} and constructors {0,1,c,d,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f0(x,y,z) -> d()
            f0(0(),y,x) -> f1(x,y,x)
            f1(x,y,z) -> c()
            f1(x,y,z) -> f2(x,y,z)
            f2(x,1(),z) -> f0(x,z,z)
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            ifPlus(false(),x,y) -> plus(p(x),y)
            ifPlus(true(),x,y) -> p(y)
            ifTimes(false(),i,x,y,z) -> timesIter(inc(i),x,y,plus(z,y))
            ifTimes(true(),i,x,y,z) -> z
            inc(x) -> s(x)
            inc(0()) -> s(0())
            inc(s(x)) -> s(inc(x))
            isZero(0()) -> true()
            isZero(s(0())) -> false()
            isZero(s(s(x))) -> isZero(s(x))
            p(0()) -> 0()
            p(s(x)) -> x
            p(s(s(x))) -> s(p(s(x)))
            plus(x,y) -> ifPlus(isZero(x),x,inc(y))
            times(x,y) -> timesIter(0(),x,y,0())
            timesIter(i,x,y,z) -> ifTimes(ge(i,x),i,x,y,z)
        - Signature:
            {f0/3,f1/3,f2/3,ge/2,ifPlus/3,ifTimes/5,inc/1,isZero/1,p/1,plus/2,times/2,timesIter/4} / {0/0,1/0,c/0,d/0
            ,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {f0,f1,f2,ge,ifPlus,ifTimes,inc,isZero,p,plus,times
            ,timesIter} and constructors {0,1,c,d,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f0(x,y,z) -> d()
            f0(0(),y,x) -> f1(x,y,x)
            f1(x,y,z) -> c()
            f1(x,y,z) -> f2(x,y,z)
            f2(x,1(),z) -> f0(x,z,z)
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            ifPlus(false(),x,y) -> plus(p(x),y)
            ifPlus(true(),x,y) -> p(y)
            ifTimes(false(),i,x,y,z) -> timesIter(inc(i),x,y,plus(z,y))
            ifTimes(true(),i,x,y,z) -> z
            inc(x) -> s(x)
            inc(0()) -> s(0())
            inc(s(x)) -> s(inc(x))
            isZero(0()) -> true()
            isZero(s(0())) -> false()
            isZero(s(s(x))) -> isZero(s(x))
            p(0()) -> 0()
            p(s(x)) -> x
            p(s(s(x))) -> s(p(s(x)))
            plus(x,y) -> ifPlus(isZero(x),x,inc(y))
            times(x,y) -> timesIter(0(),x,y,0())
            timesIter(i,x,y,z) -> ifTimes(ge(i,x),i,x,y,z)
        - Signature:
            {f0/3,f1/3,f2/3,ge/2,ifPlus/3,ifTimes/5,inc/1,isZero/1,p/1,plus/2,times/2,timesIter/4} / {0/0,1/0,c/0,d/0
            ,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {f0,f1,f2,ge,ifPlus,ifTimes,inc,isZero,p,plus,times
            ,timesIter} and constructors {0,1,c,d,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),?)