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

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

** Step 1.b:1: NaturalPI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a(b(x)) -> b(b(a(x)))
        - Signature:
            {a/1} / {b/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a} and constructors {b}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          uargs(b) = {1}
        
        Following symbols are considered usable:
          {a}
        TcT has computed the following interpretation:
          p(a) = 8 + 4*x1
          p(b) = 1 + x1  
        
        Following rules are strictly oriented:
        a(b(x)) = 12 + 4*x  
                > 10 + 4*x  
                = b(b(a(x)))
        
        
        Following rules are (at-least) weakly oriented:
        
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a(b(x)) -> b(b(a(x)))
        - Signature:
            {a/1} / {b/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a} and constructors {b}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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