/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:
            d(x) -> if(le(x,s(s(s(s(s(s(s(s(s(0())))))))))),x)
            digits() -> d(0())
            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)
        - Signature:
            {d/1,digits/0,if/2,le/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {d,digits,if,le} 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:
            d(x) -> if(le(x,s(s(s(s(s(s(s(s(s(0())))))))))),x)
            digits() -> d(0())
            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)
        - Signature:
            {d/1,digits/0,if/2,le/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {d,digits,if,le} 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:
            d(x) -> if(le(x,s(s(s(s(s(s(s(s(s(0())))))))))),x)
            digits() -> d(0())
            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)
        - Signature:
            {d/1,digits/0,if/2,le/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {d,digits,if,le} and constructors {0,cons,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),?)