/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:
            ack(0(),x) -> s(x)
            ack(s(x),0()) -> ack(x,s(0()))
            ack(s(x),s(y)) -> ack(x,ack(s(x),y))
            d(x) -> if(le(x,nr()),x)
            if(false(),x) -> nil()
            if(true(),x) -> cons(x,d(s(x)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            nr() -> ack(s(s(s(s(s(s(0())))))),0())
            numbers() -> d(0())
        - Signature:
            {ack/2,d/1,if/2,le/2,nr/0,numbers/0} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {ack,d,if,le,nr,numbers} 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:
            ack(0(),x) -> s(x)
            ack(s(x),0()) -> ack(x,s(0()))
            ack(s(x),s(y)) -> ack(x,ack(s(x),y))
            d(x) -> if(le(x,nr()),x)
            if(false(),x) -> nil()
            if(true(),x) -> cons(x,d(s(x)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            nr() -> ack(s(s(s(s(s(s(0())))))),0())
            numbers() -> d(0())
        - Signature:
            {ack/2,d/1,if/2,le/2,nr/0,numbers/0} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {ack,d,if,le,nr,numbers} 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:
            ack(0(),x) -> s(x)
            ack(s(x),0()) -> ack(x,s(0()))
            ack(s(x),s(y)) -> ack(x,ack(s(x),y))
            d(x) -> if(le(x,nr()),x)
            if(false(),x) -> nil()
            if(true(),x) -> cons(x,d(s(x)))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            nr() -> ack(s(s(s(s(s(s(0())))))),0())
            numbers() -> d(0())
        - Signature:
            {ack/2,d/1,if/2,le/2,nr/0,numbers/0} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {ack,d,if,le,nr,numbers} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          ack(s(x),y){y -> s(y)} =
            ack(s(x),s(y)) ->^+ ack(x,ack(s(x),y))
              = C[ack(s(x),y) = ack(s(x),y){}]

WORST_CASE(Omega(n^1),?)