/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(?,O(n^1))
* Step 1: Sum.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(s(x),y,y) -> f(y,x,s(x))
            g(x,y) -> x
            g(x,y) -> y
        - Signature:
            {f/3,g/2} / {s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(s(x),y,y) -> f(y,x,s(x))
            g(x,y) -> x
            g(x,y) -> y
        - Signature:
            {f/3,g/2} / {s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(f) = [8] x1 + [4] x2 + [4] x3 + [6]
          p(g) = [2] x1 + [2] x2 + [0]         
          p(s) = [1] x1 + [2]                  
        
        Following rules are strictly oriented:
        f(s(x),y,y) = [8] x + [8] y + [22]
                    > [8] x + [8] y + [14]
                    = f(y,x,s(x))         
        
        
        Following rules are (at-least) weakly oriented:
        g(x,y) =  [2] x + [2] y + [0]
               >= [1] x + [0]        
               =  x                  
        
        g(x,y) =  [2] x + [2] y + [0]
               >= [1] y + [0]        
               =  y                  
        
* Step 3: NaturalPI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(x,y) -> x
            g(x,y) -> y
        - Weak TRS:
            f(s(x),y,y) -> f(y,x,s(x))
        - Signature:
            {f/3,g/2} / {s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {s}
    + 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:
          none
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
          p(f) = 6 + x1 + x2    
          p(g) = 9 + 8*x1 + 8*x2
          p(s) = x1             
        
        Following rules are strictly oriented:
        g(x,y) = 9 + 8*x + 8*y
               > x            
               = x            
        
        g(x,y) = 9 + 8*x + 8*y
               > y            
               = y            
        
        
        Following rules are (at-least) weakly oriented:
        f(s(x),y,y) =  6 + x + y  
                    >= 6 + x + y  
                    =  f(y,x,s(x))
        
* Step 4: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(s(x),y,y) -> f(y,x,s(x))
            g(x,y) -> x
            g(x,y) -> y
        - Signature:
            {f/3,g/2} / {s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,g} and constructors {s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))