/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:
            a() -> b()
            a() -> c()
            head(cons(x,xs)) -> x
            head(nil()) -> error()
            ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
            ifPlus(true(),x,y,z) -> y
            ifSum(false(),xs,x,y) -> sumIter(tail(xs),y)
            ifSum(true(),xs,x,y) -> x
            isempty(cons(x,xs)) -> false()
            isempty(nil()) -> true()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            plus(x,y) -> plusIter(x,y,0())
            plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
            sum(xs) -> sumIter(xs,0())
            sumIter(xs,x) -> ifSum(isempty(xs),xs,x,plus(x,head(xs)))
            tail(cons(x,xs)) -> xs
            tail(nil()) -> nil()
        - Signature:
            {a/0,head/1,ifPlus/4,ifSum/4,isempty/1,le/2,plus/2,plusIter/3,sum/1,sumIter/2,tail/1} / {0/0,b/0,c/0,cons/2
            ,error/0,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,head,ifPlus,ifSum,isempty,le,plus,plusIter,sum,sumIter
            ,tail} and constructors {0,b,c,cons,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() -> b()
            a() -> c()
            head(cons(x,xs)) -> x
            head(nil()) -> error()
            ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
            ifPlus(true(),x,y,z) -> y
            ifSum(false(),xs,x,y) -> sumIter(tail(xs),y)
            ifSum(true(),xs,x,y) -> x
            isempty(cons(x,xs)) -> false()
            isempty(nil()) -> true()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            plus(x,y) -> plusIter(x,y,0())
            plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
            sum(xs) -> sumIter(xs,0())
            sumIter(xs,x) -> ifSum(isempty(xs),xs,x,plus(x,head(xs)))
            tail(cons(x,xs)) -> xs
            tail(nil()) -> nil()
        - Signature:
            {a/0,head/1,ifPlus/4,ifSum/4,isempty/1,le/2,plus/2,plusIter/3,sum/1,sumIter/2,tail/1} / {0/0,b/0,c/0,cons/2
            ,error/0,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,head,ifPlus,ifSum,isempty,le,plus,plusIter,sum,sumIter
            ,tail} and constructors {0,b,c,cons,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() -> b()
            a() -> c()
            head(cons(x,xs)) -> x
            head(nil()) -> error()
            ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
            ifPlus(true(),x,y,z) -> y
            ifSum(false(),xs,x,y) -> sumIter(tail(xs),y)
            ifSum(true(),xs,x,y) -> x
            isempty(cons(x,xs)) -> false()
            isempty(nil()) -> true()
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            plus(x,y) -> plusIter(x,y,0())
            plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
            sum(xs) -> sumIter(xs,0())
            sumIter(xs,x) -> ifSum(isempty(xs),xs,x,plus(x,head(xs)))
            tail(cons(x,xs)) -> xs
            tail(nil()) -> nil()
        - Signature:
            {a/0,head/1,ifPlus/4,ifSum/4,isempty/1,le/2,plus/2,plusIter/3,sum/1,sumIter/2,tail/1} / {0/0,b/0,c/0,cons/2
            ,error/0,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,head,ifPlus,ifSum,isempty,le,plus,plusIter,sum,sumIter
            ,tail} and constructors {0,b,c,cons,error,false,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          le(x,y){x -> s(x),y -> s(y)} =
            le(s(x),s(y)) ->^+ le(x,y)
              = C[le(x,y) = le(x,y){}]

WORST_CASE(Omega(n^1),?)