/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:
            a() -> c()
            a() -> d()
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            gen(x,y,z) -> if(ge(z,x),x,y,z)
            generate(x,y) -> gen(x,y,0())
            head(cons(x,xs)) -> x
            head(nil()) -> error()
            if(false(),x,y,z) -> cons(y,gen(x,y,s(z)))
            if(true(),x,y,z) -> nil()
            ifsum(false(),b,xs,y) -> ifsum2(b,xs,y)
            ifsum(true(),b,xs,y) -> y
            ifsum2(false(),xs,y) -> sum2(cons(p(head(xs)),tail(xs)),s(y))
            ifsum2(true(),xs,y) -> sum2(tail(xs),y)
            isNil(cons(x,xs)) -> false()
            isNil(nil()) -> true()
            isZero(0()) -> true()
            isZero(s(0())) -> false()
            isZero(s(s(x))) -> isZero(s(x))
            p(0()) -> s(s(0()))
            p(s(0())) -> 0()
            p(s(s(x))) -> s(p(s(x)))
            sum(xs) -> sum2(xs,0())
            sum2(xs,y) -> ifsum(isNil(xs),isZero(head(xs)),xs,y)
            tail(cons(x,xs)) -> xs
            tail(nil()) -> nil()
            times(x,y) -> sum(generate(x,y))
        - Signature:
            {a/0,ge/2,gen/3,generate/2,head/1,if/4,ifsum/4,ifsum2/3,isNil/1,isZero/1,p/1,sum/1,sum2/2,tail/1
            ,times/2} / {0/0,c/0,cons/2,d/0,error/0,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,ge,gen,generate,head,if,ifsum,ifsum2,isNil,isZero,p,sum,sum2
            ,tail,times} and constructors {0,c,cons,d,error,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a() -> c()
            a() -> d()
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            gen(x,y,z) -> if(ge(z,x),x,y,z)
            generate(x,y) -> gen(x,y,0())
            head(cons(x,xs)) -> x
            head(nil()) -> error()
            if(false(),x,y,z) -> cons(y,gen(x,y,s(z)))
            if(true(),x,y,z) -> nil()
            ifsum(false(),b,xs,y) -> ifsum2(b,xs,y)
            ifsum(true(),b,xs,y) -> y
            ifsum2(false(),xs,y) -> sum2(cons(p(head(xs)),tail(xs)),s(y))
            ifsum2(true(),xs,y) -> sum2(tail(xs),y)
            isNil(cons(x,xs)) -> false()
            isNil(nil()) -> true()
            isZero(0()) -> true()
            isZero(s(0())) -> false()
            isZero(s(s(x))) -> isZero(s(x))
            p(0()) -> s(s(0()))
            p(s(0())) -> 0()
            p(s(s(x))) -> s(p(s(x)))
            sum(xs) -> sum2(xs,0())
            sum2(xs,y) -> ifsum(isNil(xs),isZero(head(xs)),xs,y)
            tail(cons(x,xs)) -> xs
            tail(nil()) -> nil()
            times(x,y) -> sum(generate(x,y))
        - Signature:
            {a/0,ge/2,gen/3,generate/2,head/1,if/4,ifsum/4,ifsum2/3,isNil/1,isZero/1,p/1,sum/1,sum2/2,tail/1
            ,times/2} / {0/0,c/0,cons/2,d/0,error/0,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,ge,gen,generate,head,if,ifsum,ifsum2,isNil,isZero,p,sum,sum2
            ,tail,times} and constructors {0,c,cons,d,error,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a() -> c()
            a() -> d()
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            gen(x,y,z) -> if(ge(z,x),x,y,z)
            generate(x,y) -> gen(x,y,0())
            head(cons(x,xs)) -> x
            head(nil()) -> error()
            if(false(),x,y,z) -> cons(y,gen(x,y,s(z)))
            if(true(),x,y,z) -> nil()
            ifsum(false(),b,xs,y) -> ifsum2(b,xs,y)
            ifsum(true(),b,xs,y) -> y
            ifsum2(false(),xs,y) -> sum2(cons(p(head(xs)),tail(xs)),s(y))
            ifsum2(true(),xs,y) -> sum2(tail(xs),y)
            isNil(cons(x,xs)) -> false()
            isNil(nil()) -> true()
            isZero(0()) -> true()
            isZero(s(0())) -> false()
            isZero(s(s(x))) -> isZero(s(x))
            p(0()) -> s(s(0()))
            p(s(0())) -> 0()
            p(s(s(x))) -> s(p(s(x)))
            sum(xs) -> sum2(xs,0())
            sum2(xs,y) -> ifsum(isNil(xs),isZero(head(xs)),xs,y)
            tail(cons(x,xs)) -> xs
            tail(nil()) -> nil()
            times(x,y) -> sum(generate(x,y))
        - Signature:
            {a/0,ge/2,gen/3,generate/2,head/1,if/4,ifsum/4,ifsum2/3,isNil/1,isZero/1,p/1,sum/1,sum2/2,tail/1
            ,times/2} / {0/0,c/0,cons/2,d/0,error/0,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,ge,gen,generate,head,if,ifsum,ifsum2,isNil,isZero,p,sum,sum2
            ,tail,times} and constructors {0,c,cons,d,error,false,nil,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),?)