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


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WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            div(0(),s(Y)) -> 0()
            div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y)))
            minus(X,0()) -> X
            minus(s(X),s(Y)) -> p(minus(X,Y))
            p(s(X)) -> X
        - Signature:
            {div/2,minus/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div,minus,p} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            div(0(),s(Y)) -> 0()
            div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y)))
            minus(X,0()) -> X
            minus(s(X),s(Y)) -> p(minus(X,Y))
            p(s(X)) -> X
        - Signature:
            {div/2,minus/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div,minus,p} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          minus(x,y){x -> s(x),y -> s(y)} =
            minus(s(x),s(y)) ->^+ p(minus(x,y))
              = C[minus(x,y) = minus(x,y){}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            div(0(),s(Y)) -> 0()
            div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y)))
            minus(X,0()) -> X
            minus(s(X),s(Y)) -> p(minus(X,Y))
            p(s(X)) -> X
        - Signature:
            {div/2,minus/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div,minus,p} and constructors {0,s}
    + Applied Processor:
        Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> "A"(2)
          0 :: [] -(0)-> "A"(0)
          div :: ["A"(2) x "A"(0)] -(1)-> "A"(0)
          minus :: ["A"(2) x "A"(0)] -(1)-> "A"(2)
          p :: ["A"(2)] -(0)-> "A"(2)
          s :: ["A"(0)] -(0)-> "A"(0)
          s :: ["A"(2)] -(2)-> "A"(2)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "0_A" :: [] -(0)-> "A"(0)
          "s_A" :: ["A"(0)] -(0)-> "A"(0)
        

WORST_CASE(Omega(n^1),O(n^1))