/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(X,nil()) -> mark(X)
 a____(nil(),X) -> mark(X)
 a__and(tt(),X) -> mark(X)
 a__isNePal(__(I,__(P,I))) -> tt()
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil()) -> nil()
 mark(tt()) -> tt()
 a____(X1,X2) -> __(X1,X2)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(X) -> isNePal(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [tt] = 4,
   
   [isNePal](x0) = x0 + 4,
   
   [a____](x0, x1) = x0 + x1 + 2,
   
   [nil] = 0,
   
   [a__and](x0, x1) = x0 + 4x1,
   
   [__](x0, x1) = x0 + x1 + 2,
   
   [and](x0, x1) = x0 + 4x1,
   
   [a__isNePal](x0) = x0 + 4,
   
   [mark](x0) = x0
  orientation:
   a____(__(X,Y),Z) = X + Y + Z + 4 >= X + Y + Z + 4 = a____(mark(X),a____(mark(Y),mark(Z)))
   
   a____(X,nil()) = X + 2 >= X = mark(X)
   
   a____(nil(),X) = X + 2 >= X = mark(X)
   
   a__and(tt(),X) = 4X + 4 >= X = mark(X)
   
   a__isNePal(__(I,__(P,I))) = 2I + P + 8 >= 4 = tt()
   
   mark(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = a____(mark(X1),mark(X2))
   
   mark(and(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = a__and(mark(X1),X2)
   
   mark(isNePal(X)) = X + 4 >= X + 4 = a__isNePal(mark(X))
   
   mark(nil()) = 0 >= 0 = nil()
   
   mark(tt()) = 4 >= 4 = tt()
   
   a____(X1,X2) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,X2)
   
   a__and(X1,X2) = X1 + 4X2 >= X1 + 4X2 = and(X1,X2)
   
   a__isNePal(X) = X + 4 >= X + 4 = isNePal(X)
  problem:
   a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
   mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
   mark(and(X1,X2)) -> a__and(mark(X1),X2)
   mark(isNePal(X)) -> a__isNePal(mark(X))
   mark(nil()) -> nil()
   mark(tt()) -> tt()
   a____(X1,X2) -> __(X1,X2)
   a__and(X1,X2) -> and(X1,X2)
   a__isNePal(X) -> isNePal(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [tt] = 0,
    
    [isNePal](x0) = 2x0 + 2,
    
    [a____](x0, x1) = 2x0 + x1 + 4,
    
    [nil] = 0,
    
    [a__and](x0, x1) = x0 + x1,
    
    [__](x0, x1) = 2x0 + x1 + 4,
    
    [and](x0, x1) = x0 + x1,
    
    [a__isNePal](x0) = 2x0 + 2,
    
    [mark](x0) = x0
   orientation:
    a____(__(X,Y),Z) = 4X + 2Y + Z + 12 >= 2X + 2Y + Z + 8 = a____(mark(X),a____(mark(Y),mark(Z)))
    
    mark(__(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = a____(mark(X1),mark(X2))
    
    mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = a__and(mark(X1),X2)
    
    mark(isNePal(X)) = 2X + 2 >= 2X + 2 = a__isNePal(mark(X))
    
    mark(nil()) = 0 >= 0 = nil()
    
    mark(tt()) = 0 >= 0 = tt()
    
    a____(X1,X2) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(X1,X2)
    
    a__and(X1,X2) = X1 + X2 >= X1 + X2 = and(X1,X2)
    
    a__isNePal(X) = 2X + 2 >= 2X + 2 = isNePal(X)
   problem:
    mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
    mark(and(X1,X2)) -> a__and(mark(X1),X2)
    mark(isNePal(X)) -> a__isNePal(mark(X))
    mark(nil()) -> nil()
    mark(tt()) -> tt()
    a____(X1,X2) -> __(X1,X2)
    a__and(X1,X2) -> and(X1,X2)
    a__isNePal(X) -> isNePal(X)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [tt] = 2,
     
     [isNePal](x0) = 2x0,
     
     [a____](x0, x1) = x0 + x1,
     
     [nil] = 0,
     
     [a__and](x0, x1) = 5x0 + 5x1,
     
     [__](x0, x1) = x0 + x1,
     
     [and](x0, x1) = 5x0 + x1,
     
     [a__isNePal](x0) = 2x0,
     
     [mark](x0) = 5x0
    orientation:
     mark(__(X1,X2)) = 5X1 + 5X2 >= 5X1 + 5X2 = a____(mark(X1),mark(X2))
     
     mark(and(X1,X2)) = 25X1 + 5X2 >= 25X1 + 5X2 = a__and(mark(X1),X2)
     
     mark(isNePal(X)) = 10X >= 10X = a__isNePal(mark(X))
     
     mark(nil()) = 0 >= 0 = nil()
     
     mark(tt()) = 10 >= 2 = tt()
     
     a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2)
     
     a__and(X1,X2) = 5X1 + 5X2 >= 5X1 + X2 = and(X1,X2)
     
     a__isNePal(X) = 2X >= 2X = isNePal(X)
    problem:
     mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
     mark(and(X1,X2)) -> a__and(mark(X1),X2)
     mark(isNePal(X)) -> a__isNePal(mark(X))
     mark(nil()) -> nil()
     a____(X1,X2) -> __(X1,X2)
     a__and(X1,X2) -> and(X1,X2)
     a__isNePal(X) -> isNePal(X)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [isNePal](x0) = 4x0,
      
      [a____](x0, x1) = 2x0 + 2x1 + 2,
      
      [nil] = 0,
      
      [a__and](x0, x1) = 4x0 + 2x1,
      
      [__](x0, x1) = 2x0 + 2x1 + 1,
      
      [and](x0, x1) = 4x0 + x1,
      
      [a__isNePal](x0) = 4x0,
      
      [mark](x0) = 2x0
     orientation:
      mark(__(X1,X2)) = 4X1 + 4X2 + 2 >= 4X1 + 4X2 + 2 = a____(mark(X1),mark(X2))
      
      mark(and(X1,X2)) = 8X1 + 2X2 >= 8X1 + 2X2 = a__and(mark(X1),X2)
      
      mark(isNePal(X)) = 8X >= 8X = a__isNePal(mark(X))
      
      mark(nil()) = 0 >= 0 = nil()
      
      a____(X1,X2) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 + 1 = __(X1,X2)
      
      a__and(X1,X2) = 4X1 + 2X2 >= 4X1 + X2 = and(X1,X2)
      
      a__isNePal(X) = 4X >= 4X = isNePal(X)
     problem:
      mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
      mark(and(X1,X2)) -> a__and(mark(X1),X2)
      mark(isNePal(X)) -> a__isNePal(mark(X))
      mark(nil()) -> nil()
      a__and(X1,X2) -> and(X1,X2)
      a__isNePal(X) -> isNePal(X)
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [isNePal](x0) = x0,
       
       [a____](x0, x1) = 3x0 + 5x1,
       
       [nil] = 0,
       
       [a__and](x0, x1) = 2x0 + 4x1 + 2,
       
       [__](x0, x1) = 3x0 + 5x1 + 7,
       
       [and](x0, x1) = 2x0 + 2x1 + 2,
       
       [a__isNePal](x0) = x0,
       
       [mark](x0) = 2x0 + 2
      orientation:
       mark(__(X1,X2)) = 6X1 + 10X2 + 16 >= 6X1 + 10X2 + 16 = a____(mark(X1),mark(X2))
       
       mark(and(X1,X2)) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = a__and(mark(X1),X2)
       
       mark(isNePal(X)) = 2X + 2 >= 2X + 2 = a__isNePal(mark(X))
       
       mark(nil()) = 2 >= 0 = nil()
       
       a__and(X1,X2) = 2X1 + 4X2 + 2 >= 2X1 + 2X2 + 2 = and(X1,X2)
       
       a__isNePal(X) = X >= X = isNePal(X)
      problem:
       mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
       mark(and(X1,X2)) -> a__and(mark(X1),X2)
       mark(isNePal(X)) -> a__isNePal(mark(X))
       a__and(X1,X2) -> and(X1,X2)
       a__isNePal(X) -> isNePal(X)
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [isNePal](x0) = 4x0 + 4,
        
        [a____](x0, x1) = 7x0 + x1 + 4,
        
        [a__and](x0, x1) = x0 + 3x1,
        
        [__](x0, x1) = 7x0 + x1 + 6,
        
        [and](x0, x1) = x0 + x1,
        
        [a__isNePal](x0) = 4x0 + 4,
        
        [mark](x0) = 3x0 + 2
       orientation:
        mark(__(X1,X2)) = 21X1 + 3X2 + 20 >= 21X1 + 3X2 + 20 = a____(mark(X1),mark(X2))
        
        mark(and(X1,X2)) = 3X1 + 3X2 + 2 >= 3X1 + 3X2 + 2 = a__and(mark(X1),X2)
        
        mark(isNePal(X)) = 12X + 14 >= 12X + 12 = a__isNePal(mark(X))
        
        a__and(X1,X2) = X1 + 3X2 >= X1 + X2 = and(X1,X2)
        
        a__isNePal(X) = 4X + 4 >= 4X + 4 = isNePal(X)
       problem:
        mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
        mark(and(X1,X2)) -> a__and(mark(X1),X2)
        a__and(X1,X2) -> and(X1,X2)
        a__isNePal(X) -> isNePal(X)
       Matrix Interpretation Processor: dim=1
        
        interpretation:
         [isNePal](x0) = x0,
         
         [a____](x0, x1) = 3x0 + 4x1 + 1,
         
         [a__and](x0, x1) = x0 + 4x1 + 4,
         
         [__](x0, x1) = 6x0 + 6x1 + 5,
         
         [and](x0, x1) = x0 + 2x1 + 4,
         
         [a__isNePal](x0) = x0 + 4,
         
         [mark](x0) = 4x0 + 3
        orientation:
         mark(__(X1,X2)) = 24X1 + 24X2 + 23 >= 12X1 + 16X2 + 22 = a____(mark(X1),mark(X2))
         
         mark(and(X1,X2)) = 4X1 + 8X2 + 19 >= 4X1 + 4X2 + 7 = a__and(mark(X1),X2)
         
         a__and(X1,X2) = X1 + 4X2 + 4 >= X1 + 2X2 + 4 = and(X1,X2)
         
         a__isNePal(X) = X + 4 >= X = isNePal(X)
        problem:
         a__and(X1,X2) -> and(X1,X2)
        Matrix Interpretation Processor: dim=3
         
         interpretation:
                             [1 0 0]     [1 0 0]     [1]
          [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                             [0 0 0]     [0 0 1]     [0],
          
                          [1 0 0]     [1 0 0]  
          [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                          [0 0 0]     [0 0 0]  
         orientation:
                          [1 0 0]     [1 0 0]     [1]    [1 0 0]     [1 0 0]               
          a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2)
                          [0 0 0]     [0 0 1]     [0]    [0 0 0]     [0 0 0]               
         problem:
          
         Qed