/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            cadr(cons(x,cons(y,l))) -> y
            car(cons(x,l)) -> x
            cddr(cons(x,cons(y,l))) -> l
            cddr(cons(x,nil())) -> nil()
            cddr(nil()) -> nil()
            if(false(),b,l) -> if2(b,l)
            if(true(),b,l) -> s(0())
            if2(false(),l) -> prod(cons(times(car(l),cadr(l)),cddr(l)))
            if2(true(),l) -> car(l)
            ifplus(false(),x,y) -> s(plus(p(x),y))
            ifplus(true(),x,y) -> y
            iftimes(false(),x,y) -> plus(y,times(p(x),y))
            iftimes(true(),x,y) -> 0()
            isZero(0()) -> true()
            isZero(s(x)) -> false()
            p(0()) -> 0()
            p(s(x)) -> x
            plus(x,y) -> ifplus(isZero(x),x,y)
            prod(l) -> if(shorter(l,0()),shorter(l,s(0())),l)
            shorter(cons(x,l),0()) -> false()
            shorter(cons(x,l),s(y)) -> shorter(l,y)
            shorter(nil(),y) -> true()
            times(x,y) -> iftimes(isZero(x),x,y)
        - Signature:
            {cadr/1,car/1,cddr/1,if/3,if2/2,ifplus/3,iftimes/3,isZero/1,p/1,plus/2,prod/1,shorter/2,times/2} / {0/0
            ,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cadr,car,cddr,if,if2,ifplus,iftimes,isZero,p,plus,prod,shorter
            ,times} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            cadr(cons(x,cons(y,l))) -> y
            car(cons(x,l)) -> x
            cddr(cons(x,cons(y,l))) -> l
            cddr(cons(x,nil())) -> nil()
            cddr(nil()) -> nil()
            if(false(),b,l) -> if2(b,l)
            if(true(),b,l) -> s(0())
            if2(false(),l) -> prod(cons(times(car(l),cadr(l)),cddr(l)))
            if2(true(),l) -> car(l)
            ifplus(false(),x,y) -> s(plus(p(x),y))
            ifplus(true(),x,y) -> y
            iftimes(false(),x,y) -> plus(y,times(p(x),y))
            iftimes(true(),x,y) -> 0()
            isZero(0()) -> true()
            isZero(s(x)) -> false()
            p(0()) -> 0()
            p(s(x)) -> x
            plus(x,y) -> ifplus(isZero(x),x,y)
            prod(l) -> if(shorter(l,0()),shorter(l,s(0())),l)
            shorter(cons(x,l),0()) -> false()
            shorter(cons(x,l),s(y)) -> shorter(l,y)
            shorter(nil(),y) -> true()
            times(x,y) -> iftimes(isZero(x),x,y)
        - Signature:
            {cadr/1,car/1,cddr/1,if/3,if2/2,ifplus/3,iftimes/3,isZero/1,p/1,plus/2,prod/1,shorter/2,times/2} / {0/0
            ,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cadr,car,cddr,if,if2,ifplus,iftimes,isZero,p,plus,prod,shorter
            ,times} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            cadr(cons(x,cons(y,l))) -> y
            car(cons(x,l)) -> x
            cddr(cons(x,cons(y,l))) -> l
            cddr(cons(x,nil())) -> nil()
            cddr(nil()) -> nil()
            if(false(),b,l) -> if2(b,l)
            if(true(),b,l) -> s(0())
            if2(false(),l) -> prod(cons(times(car(l),cadr(l)),cddr(l)))
            if2(true(),l) -> car(l)
            ifplus(false(),x,y) -> s(plus(p(x),y))
            ifplus(true(),x,y) -> y
            iftimes(false(),x,y) -> plus(y,times(p(x),y))
            iftimes(true(),x,y) -> 0()
            isZero(0()) -> true()
            isZero(s(x)) -> false()
            p(0()) -> 0()
            p(s(x)) -> x
            plus(x,y) -> ifplus(isZero(x),x,y)
            prod(l) -> if(shorter(l,0()),shorter(l,s(0())),l)
            shorter(cons(x,l),0()) -> false()
            shorter(cons(x,l),s(y)) -> shorter(l,y)
            shorter(nil(),y) -> true()
            times(x,y) -> iftimes(isZero(x),x,y)
        - Signature:
            {cadr/1,car/1,cddr/1,if/3,if2/2,ifplus/3,iftimes/3,isZero/1,p/1,plus/2,prod/1,shorter/2,times/2} / {0/0
            ,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cadr,car,cddr,if,if2,ifplus,iftimes,isZero,p,plus,prod,shorter
            ,times} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          shorter(y,z){y -> cons(x,y),z -> s(z)} =
            shorter(cons(x,y),s(z)) ->^+ shorter(y,z)
              = C[shorter(y,z) = shorter(y,z){}]

WORST_CASE(Omega(n^1),?)