/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),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y))
        - Signature:
            {dfib/2} / {s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dfib} and constructors {s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y))
        - Signature:
            {dfib/2} / {s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dfib} and constructors {s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 2.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y))
        - Signature:
            {dfib/2} / {s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dfib} and constructors {s}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "dfib") :: ["A"(3, 2, 1) x "A"(0, 0, 0)] -(4)-> "A"(0, 0, 0)
          F (TrsFun "main") :: ["A"(3, 1, 1) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "s") :: ["A"(5, 3, 1)] -(3)-> "A"(3, 2, 1)
          F (TrsFun "s") :: ["A"(8, 4, 1)] -(5)-> "A"(5, 3, 1)
          F (TrsFun "s") :: ["A"(5, 2, 0)] -(3)-> "A"(3, 2, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y))
          main(x1,x2) -> dfib(x1,x2)
        2. Weak:
          
        

** Step 2.b:1: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y))
        - Signature:
            {dfib/2} / {s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {dfib} and constructors {s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          dfib(s(x),y){x -> s(x)} =
            dfib(s(s(x)),y) ->^+ dfib(s(x),dfib(x,y))
              = C[dfib(s(x),dfib(x,y)) = dfib(s(x),y){y -> dfib(x,y)}]

WORST_CASE(Omega(n^1),?)