/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:
            r1(cons(x,k),a) -> r1(k,cons(x,a))
            r1(empty(),a) -> a
            rev(ls) -> r1(ls,empty())
        - Signature:
            {r1/2,rev/1} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            r1(cons(x,k),a) -> r1(k,cons(x,a))
            r1(empty(),a) -> a
            rev(ls) -> r1(ls,empty())
        - Signature:
            {r1/2,rev/1} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          r1(y,z){y -> cons(x,y)} =
            r1(cons(x,y),z) ->^+ r1(y,cons(x,z))
              = C[r1(y,cons(x,z)) = r1(y,z){z -> cons(x,z)}]

** Step 1.b:1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            r1(cons(x,k),a) -> r1(k,cons(x,a))
            r1(empty(),a) -> a
            rev(ls) -> r1(ls,empty())
        - Signature:
            {r1/2,rev/1} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
    + Applied Processor:
        Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          cons :: ["A"(0) x "A"(15)] -(15)-> "A"(15)
          cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          empty :: [] -(0)-> "A"(15)
          empty :: [] -(0)-> "A"(8)
          r1 :: ["A"(15) x "A"(0)] -(3)-> "A"(0)
          rev :: ["A"(15)] -(12)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1)
          "empty_A" :: [] -(0)-> "A"(1)
        

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