/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:
            check(0()) -> zero()
            check(s(0())) -> odd()
            check(s(s(0()))) -> even()
            check(s(s(s(x)))) -> check(s(x))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if(even(),x,y,z,u) -> plus(timesIter(half(x),y,half(z)),timesIter(half(x),y,half(s(z))))
            if(odd(),x,y,z,u) -> timesIter(p(x),y,u)
            if(zero(),x,y,z,u) -> z
            p(0()) -> 0()
            p(s(x)) -> x
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(x,y) -> timesIter(x,y,0())
            timesIter(x,y,z) -> if(check(x),x,y,z,plus(z,y))
        - Signature:
            {check/1,half/1,if/5,p/1,plus/2,times/2,timesIter/3} / {0/0,even/0,odd/0,s/1,zero/0}
        - Obligation:
             runtime complexity wrt. defined symbols {check,half,if,p,plus,times,timesIter} and constructors {0,even,odd
            ,s,zero}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            check(0()) -> zero()
            check(s(0())) -> odd()
            check(s(s(0()))) -> even()
            check(s(s(s(x)))) -> check(s(x))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if(even(),x,y,z,u) -> plus(timesIter(half(x),y,half(z)),timesIter(half(x),y,half(s(z))))
            if(odd(),x,y,z,u) -> timesIter(p(x),y,u)
            if(zero(),x,y,z,u) -> z
            p(0()) -> 0()
            p(s(x)) -> x
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(x,y) -> timesIter(x,y,0())
            timesIter(x,y,z) -> if(check(x),x,y,z,plus(z,y))
        - Signature:
            {check/1,half/1,if/5,p/1,plus/2,times/2,timesIter/3} / {0/0,even/0,odd/0,s/1,zero/0}
        - Obligation:
             runtime complexity wrt. defined symbols {check,half,if,p,plus,times,timesIter} and constructors {0,even,odd
            ,s,zero}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            check(0()) -> zero()
            check(s(0())) -> odd()
            check(s(s(0()))) -> even()
            check(s(s(s(x)))) -> check(s(x))
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if(even(),x,y,z,u) -> plus(timesIter(half(x),y,half(z)),timesIter(half(x),y,half(s(z))))
            if(odd(),x,y,z,u) -> timesIter(p(x),y,u)
            if(zero(),x,y,z,u) -> z
            p(0()) -> 0()
            p(s(x)) -> x
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(x,y) -> timesIter(x,y,0())
            timesIter(x,y,z) -> if(check(x),x,y,z,plus(z,y))
        - Signature:
            {check/1,half/1,if/5,p/1,plus/2,times/2,timesIter/3} / {0/0,even/0,odd/0,s/1,zero/0}
        - Obligation:
             runtime complexity wrt. defined symbols {check,half,if,p,plus,times,timesIter} and constructors {0,even,odd
            ,s,zero}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          check(s(x)){x -> s(s(x))} =
            check(s(s(s(x)))) ->^+ check(s(x))
              = C[check(s(x)) = check(s(x)){}]

WORST_CASE(Omega(n^1),?)