/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:
 g(A()) -> A()
 g(B()) -> A()
 g(B()) -> B()
 g(C()) -> A()
 g(C()) -> B()
 g(C()) -> C()
 foldf(x,nil()) -> x
 foldf(x,cons(y,z)) -> f(foldf(x,z),y)
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
 f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
 f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
 f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
           [0]
   [nil] = [0]
           [0],
   
                  [1 0 0]     [1 0 1]  
   [f'](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  ,
   
             [1 0 0]  
   [g](x0) = [0 0 0]x0
             [0 0 1]  ,
   
         [0]
   [C] = [0]
         [1],
   
                     [1 0 0]     [1 0 0]  
   [foldf](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                     [0 1 1]     [0 0 0]  ,
   
               [1 0 0]  
   [f''](x0) = [0 0 1]x0
               [0 0 0]  ,
   
         [0]
   [A] = [0]
         [0],
   
                 [1 0 0]     [1 0 1]  
   [f](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                 [0 0 0]     [0 0 0]  ,
   
                          [1 1 0]     [1 0 0]     [1 0 0]  
   [triple](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 1]x2
                          [0 0 0]     [0 0 0]     [0 0 0]  ,
   
                    [1 0 1]     [1 0 0]  
   [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                    [0 0 0]     [0 0 0]  ,
   
         [0]
   [B] = [0]
         [1]
  orientation:
            [0]    [0]      
   g(A()) = [0] >= [0] = A()
            [0]    [0]      
   
            [0]    [0]      
   g(B()) = [0] >= [0] = A()
            [1]    [0]      
   
            [0]    [0]      
   g(B()) = [0] >= [0] = B()
            [1]    [1]      
   
            [0]    [0]      
   g(C()) = [0] >= [0] = A()
            [1]    [0]      
   
            [0]    [0]      
   g(C()) = [0] >= [0] = B()
            [1]    [1]      
   
            [0]    [0]      
   g(C()) = [0] >= [0] = C()
            [1]    [1]      
   
                    [1 0 0]          
   foldf(x,nil()) = [0 1 0]x >= x = x
                    [0 1 1]          
   
                        [1 0 0]    [1 0 1]    [1 0 0]     [1 0 0]    [1 0 1]    [1 0 0]                   
   foldf(x,cons(y,z)) = [0 1 0]x + [0 0 0]y + [0 0 0]z >= [0 1 0]x + [0 0 0]y + [0 0 0]z = f(foldf(x,z),y)
                        [0 1 1]    [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]    [0 0 0]                   
   
            [1 0 0]    [1 0 1]     [1 0 0]    [1 0 1]              
   f(t,x) = [0 1 0]t + [0 0 0]x >= [0 1 0]t + [0 0 0]x = f'(t,g(x))
            [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]              
   
                           [1 1 0]    [1 0 0]    [1 0 0]    [1]    [1 1 0]    [1 0 0]    [1 0 0]    [1]                          
   f'(triple(a,b,c),C()) = [0 0 0]a + [0 0 0]b + [0 0 1]c + [0] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [0] = triple(a,b,cons(C(),c))
                           [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]                          
   
                           [1 1 0]    [1 0 0]    [1 0 0]    [1]    [1 1 0]    [1 0 0]    [1 0 0]                        
   f'(triple(a,b,c),B()) = [0 0 0]a + [0 0 0]b + [0 0 1]c + [0] >= [0 0 0]a + [0 0 0]b + [0 0 1]c = f(triple(a,b,c),A())
                           [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]                        
   
                           [1 1 0]    [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]    [1 0 0]                                             
   f'(triple(a,b,c),A()) = [0 0 0]a + [0 0 0]b + [0 0 1]c >= [0 0 0]a + [0 0 0]b + [0 0 1]c = f''(foldf(triple(cons(A(),a),nil(),c),b))
                           [0 0 0]    [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]    [0 0 0]                                             
   
                        [1 1 0]    [1 0 0]    [1 0 0]     [1 1 0]    [1 0 0]    [1 0 0]                              
   f''(triple(a,b,c)) = [0 0 0]a + [0 0 0]b + [0 0 0]c >= [0 0 0]a + [0 0 0]b + [0 0 0]c = foldf(triple(a,b,nil()),c)
                        [0 0 0]    [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]    [0 0 0]                              
  problem:
   g(A()) -> A()
   g(B()) -> A()
   g(B()) -> B()
   g(C()) -> A()
   g(C()) -> B()
   g(C()) -> C()
   foldf(x,nil()) -> x
   foldf(x,cons(y,z)) -> f(foldf(x,z),y)
   f(t,x) -> f'(t,g(x))
   f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
   f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
   f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [nil] = 0,
    
    [f'](x0, x1) = x0 + 4x1,
    
    [g](x0) = x0,
    
    [C] = 2,
    
    [foldf](x0, x1) = x0 + x1,
    
    [f''](x0) = x0,
    
    [A] = 0,
    
    [f](x0, x1) = x0 + 4x1,
    
    [triple](x0, x1, x2) = x0 + x1 + x2,
    
    [cons](x0, x1) = 4x0 + x1,
    
    [B] = 0
   orientation:
    g(A()) = 0 >= 0 = A()
    
    g(B()) = 0 >= 0 = A()
    
    g(B()) = 0 >= 0 = B()
    
    g(C()) = 2 >= 0 = A()
    
    g(C()) = 2 >= 0 = B()
    
    g(C()) = 2 >= 2 = C()
    
    foldf(x,nil()) = x >= x = x
    
    foldf(x,cons(y,z)) = x + 4y + z >= x + 4y + z = f(foldf(x,z),y)
    
    f(t,x) = t + 4x >= t + 4x = f'(t,g(x))
    
    f'(triple(a,b,c),C()) = a + b + c + 8 >= a + b + c + 8 = triple(a,b,cons(C(),c))
    
    f'(triple(a,b,c),A()) = a + b + c >= a + b + c = f''(foldf(triple(cons(A(),a),nil(),c),b))
    
    f''(triple(a,b,c)) = a + b + c >= a + b + c = foldf(triple(a,b,nil()),c)
   problem:
    g(A()) -> A()
    g(B()) -> A()
    g(B()) -> B()
    g(C()) -> C()
    foldf(x,nil()) -> x
    foldf(x,cons(y,z)) -> f(foldf(x,z),y)
    f(t,x) -> f'(t,g(x))
    f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
    f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
    f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [nil] = 0,
     
     [f'](x0, x1) = x0 + 4x1,
     
     [g](x0) = x0,
     
     [C] = 0,
     
     [foldf](x0, x1) = x0 + x1,
     
     [f''](x0) = x0,
     
     [A] = 0,
     
     [f](x0, x1) = x0 + 4x1,
     
     [triple](x0, x1, x2) = 2x0 + 2x1 + x2,
     
     [cons](x0, x1) = 6x0 + x1,
     
     [B] = 1
    orientation:
     g(A()) = 0 >= 0 = A()
     
     g(B()) = 1 >= 0 = A()
     
     g(B()) = 1 >= 1 = B()
     
     g(C()) = 0 >= 0 = C()
     
     foldf(x,nil()) = x >= x = x
     
     foldf(x,cons(y,z)) = x + 6y + z >= x + 4y + z = f(foldf(x,z),y)
     
     f(t,x) = t + 4x >= t + 4x = f'(t,g(x))
     
     f'(triple(a,b,c),C()) = 2a + 2b + c >= 2a + 2b + c = triple(a,b,cons(C(),c))
     
     f'(triple(a,b,c),A()) = 2a + 2b + c >= 2a + b + c = f''(foldf(triple(cons(A(),a),nil(),c),b))
     
     f''(triple(a,b,c)) = 2a + 2b + c >= 2a + 2b + c = foldf(triple(a,b,nil()),c)
    problem:
     g(A()) -> A()
     g(B()) -> B()
     g(C()) -> C()
     foldf(x,nil()) -> x
     foldf(x,cons(y,z)) -> f(foldf(x,z),y)
     f(t,x) -> f'(t,g(x))
     f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
     f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
     f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [nil] = 0,
      
      [f'](x0, x1) = x0 + 2x1,
      
      [g](x0) = 2x0,
      
      [C] = 0,
      
      [foldf](x0, x1) = x0 + x1,
      
      [f''](x0) = x0,
      
      [A] = 0,
      
      [f](x0, x1) = x0 + 4x1,
      
      [triple](x0, x1, x2) = 2x0 + x1 + 2x2,
      
      [cons](x0, x1) = 4x0 + x1,
      
      [B] = 4
     orientation:
      g(A()) = 0 >= 0 = A()
      
      g(B()) = 8 >= 4 = B()
      
      g(C()) = 0 >= 0 = C()
      
      foldf(x,nil()) = x >= x = x
      
      foldf(x,cons(y,z)) = x + 4y + z >= x + 4y + z = f(foldf(x,z),y)
      
      f(t,x) = t + 4x >= t + 4x = f'(t,g(x))
      
      f'(triple(a,b,c),C()) = 2a + b + 2c >= 2a + b + 2c = triple(a,b,cons(C(),c))
      
      f'(triple(a,b,c),A()) = 2a + b + 2c >= 2a + b + 2c = f''(foldf(triple(cons(A(),a),nil(),c),b))
      
      f''(triple(a,b,c)) = 2a + b + 2c >= 2a + b + c = foldf(triple(a,b,nil()),c)
     problem:
      g(A()) -> A()
      g(C()) -> C()
      foldf(x,nil()) -> x
      foldf(x,cons(y,z)) -> f(foldf(x,z),y)
      f(t,x) -> f'(t,g(x))
      f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
      f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
      f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [nil] = 0,
       
       [f'](x0, x1) = x0 + x1,
       
       [g](x0) = 2x0,
       
       [C] = 0,
       
       [foldf](x0, x1) = x0 + 2x1,
       
       [f''](x0) = x0,
       
       [A] = 4,
       
       [f](x0, x1) = x0 + 2x1,
       
       [triple](x0, x1, x2) = x0 + 2x1 + 2x2,
       
       [cons](x0, x1) = x0 + x1
      orientation:
       g(A()) = 8 >= 4 = A()
       
       g(C()) = 0 >= 0 = C()
       
       foldf(x,nil()) = x >= x = x
       
       foldf(x,cons(y,z)) = x + 2y + 2z >= x + 2y + 2z = f(foldf(x,z),y)
       
       f(t,x) = t + 2x >= t + 2x = f'(t,g(x))
       
       f'(triple(a,b,c),C()) = a + 2b + 2c >= a + 2b + 2c = triple(a,b,cons(C(),c))
       
       f'(triple(a,b,c),A()) = a + 2b + 2c + 4 >= a + 2b + 2c + 4 = f''(foldf(triple(cons(A(),a),nil(),c),b))
       
       f''(triple(a,b,c)) = a + 2b + 2c >= a + 2b + 2c = foldf(triple(a,b,nil()),c)
      problem:
       g(C()) -> C()
       foldf(x,nil()) -> x
       foldf(x,cons(y,z)) -> f(foldf(x,z),y)
       f(t,x) -> f'(t,g(x))
       f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
       f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
       f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [nil] = 0,
        
        [f'](x0, x1) = x0 + 4x1,
        
        [g](x0) = x0,
        
        [C] = 3,
        
        [foldf](x0, x1) = x0 + 4x1 + 3,
        
        [f''](x0) = x0 + 3,
        
        [A] = 2,
        
        [f](x0, x1) = x0 + 4x1,
        
        [triple](x0, x1, x2) = x0 + 4x1 + 4x2 + 5,
        
        [cons](x0, x1) = x0 + x1
       orientation:
        g(C()) = 3 >= 3 = C()
        
        foldf(x,nil()) = x + 3 >= x = x
        
        foldf(x,cons(y,z)) = x + 4y + 4z + 3 >= x + 4y + 4z + 3 = f(foldf(x,z),y)
        
        f(t,x) = t + 4x >= t + 4x = f'(t,g(x))
        
        f'(triple(a,b,c),C()) = a + 4b + 4c + 17 >= a + 4b + 4c + 17 = triple(a,b,cons(C(),c))
        
        f'(triple(a,b,c),A()) = a + 4b + 4c + 13 >= a + 4b + 4c + 13 = f''(foldf(triple(cons(A(),a),nil(),c),b))
        
        f''(triple(a,b,c)) = a + 4b + 4c + 8 >= a + 4b + 4c + 8 = foldf(triple(a,b,nil()),c)
       problem:
        g(C()) -> C()
        foldf(x,cons(y,z)) -> f(foldf(x,z),y)
        f(t,x) -> f'(t,g(x))
        f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
        f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
        f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)
       Matrix Interpretation Processor: dim=1
        
        interpretation:
         [nil] = 1,
         
         [f'](x0, x1) = x0 + 4x1,
         
         [g](x0) = x0,
         
         [C] = 4,
         
         [foldf](x0, x1) = x0 + 2x1,
         
         [f''](x0) = x0 + 4,
         
         [A] = 3,
         
         [f](x0, x1) = x0 + 4x1,
         
         [triple](x0, x1, x2) = x0 + 2x1 + 2x2,
         
         [cons](x0, x1) = 2x0 + x1
        orientation:
         g(C()) = 4 >= 4 = C()
         
         foldf(x,cons(y,z)) = x + 4y + 2z >= x + 4y + 2z = f(foldf(x,z),y)
         
         f(t,x) = t + 4x >= t + 4x = f'(t,g(x))
         
         f'(triple(a,b,c),C()) = a + 2b + 2c + 16 >= a + 2b + 2c + 16 = triple(a,b,cons(C(),c))
         
         f'(triple(a,b,c),A()) = a + 2b + 2c + 12 >= a + 2b + 2c + 12 = f''(foldf(triple(cons(A(),a),nil(),c),b))
         
         f''(triple(a,b,c)) = a + 2b + 2c + 4 >= a + 2b + 2c + 2 = foldf(triple(a,b,nil()),c)
        problem:
         g(C()) -> C()
         foldf(x,cons(y,z)) -> f(foldf(x,z),y)
         f(t,x) -> f'(t,g(x))
         f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
         f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
        Matrix Interpretation Processor: dim=1
         
         interpretation:
          [nil] = 0,
          
          [f'](x0, x1) = x0 + 4x1,
          
          [g](x0) = x0,
          
          [C] = 6,
          
          [foldf](x0, x1) = x0 + 4x1 + 2,
          
          [f''](x0) = x0,
          
          [A] = 1,
          
          [f](x0, x1) = x0 + 4x1,
          
          [triple](x0, x1, x2) = x0 + 4x1 + 4x2 + 5,
          
          [cons](x0, x1) = x0 + x1
         orientation:
          g(C()) = 6 >= 6 = C()
          
          foldf(x,cons(y,z)) = x + 4y + 4z + 2 >= x + 4y + 4z + 2 = f(foldf(x,z),y)
          
          f(t,x) = t + 4x >= t + 4x = f'(t,g(x))
          
          f'(triple(a,b,c),C()) = a + 4b + 4c + 29 >= a + 4b + 4c + 29 = triple(a,b,cons(C(),c))
          
          f'(triple(a,b,c),A()) = a + 4b + 4c + 9 >= a + 4b + 4c + 8 = f''(foldf(triple(cons(A(),a),nil(),c),b))
         problem:
          g(C()) -> C()
          foldf(x,cons(y,z)) -> f(foldf(x,z),y)
          f(t,x) -> f'(t,g(x))
          f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
         Matrix Interpretation Processor: dim=1
          
          interpretation:
           [f'](x0, x1) = x0 + 6x1,
           
           [g](x0) = x0,
           
           [C] = 2,
           
           [foldf](x0, x1) = x0 + 4x1,
           
           [f](x0, x1) = x0 + 7x1,
           
           [triple](x0, x1, x2) = 2x0 + 2x1 + x2 + 3,
           
           [cons](x0, x1) = 4x0 + x1
          orientation:
           g(C()) = 2 >= 2 = C()
           
           foldf(x,cons(y,z)) = x + 16y + 4z >= x + 7y + 4z = f(foldf(x,z),y)
           
           f(t,x) = t + 7x >= t + 6x = f'(t,g(x))
           
           f'(triple(a,b,c),C()) = 2a + 2b + c + 15 >= 2a + 2b + c + 11 = triple(a,b,cons(C(),c))
          problem:
           g(C()) -> C()
           foldf(x,cons(y,z)) -> f(foldf(x,z),y)
           f(t,x) -> f'(t,g(x))
          Matrix Interpretation Processor: dim=3
           
           interpretation:
                           [1 0 0]     [1 0 1]  
            [f'](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                           [0 0 1]     [0 0 0]  ,
            
                      [1 0 1]     [0]
            [g](x0) = [0 0 0]x0 + [1]
                      [0 1 0]     [0],
            
                  [0]
            [C] = [1]
                  [1],
            
                              [1 0 0]     [1 0 0]     [0]
            [foldf](x0, x1) = [1 0 0]x0 + [0 0 1]x1 + [1]
                              [0 0 0]     [0 1 0]     [1],
            
                          [1 0 0]     [1 1 1]     [0]
            [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                          [0 0 1]     [0 0 0]     [0],
            
                             [1 1 1]     [1 0 0]     [1]
            [cons](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [0]
                             [0 0 1]     [0 0 0]     [0]
           orientation:
                     [1]    [0]      
            g(C()) = [1] >= [1] = C()
                     [1]    [1]      
            
                                 [1 0 0]    [1 1 1]    [1 0 0]    [1]    [1 0 0]    [1 1 1]    [1 0 0]    [0]                  
            foldf(x,cons(y,z)) = [1 0 0]x + [0 0 1]y + [0 0 0]z + [1] >= [0 0 0]x + [0 0 0]y + [0 0 0]z + [1] = f(foldf(x,z),y)
                                 [0 0 0]    [0 0 0]    [0 1 0]    [1]    [0 0 0]    [0 0 0]    [0 1 0]    [1]                  
            
                     [1 0 0]    [1 1 1]    [0]    [1 0 0]    [1 1 1]              
            f(t,x) = [0 0 0]t + [0 0 0]x + [1] >= [0 0 0]t + [0 0 0]x = f'(t,g(x))
                     [0 0 1]    [0 0 0]    [0]    [0 0 1]    [0 0 0]              
           problem:
            f(t,x) -> f'(t,g(x))
           Matrix Interpretation Processor: dim=3
            
            interpretation:
                            [1 0 0]     [1 0 0]     [0]
             [f'](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                            [0 0 0]     [0 0 0]     [0],
             
                       [1 0 0]  
             [g](x0) = [0 0 0]x0
                       [0 0 0]  ,
             
                           [1 0 0]     [1 0 0]     [1]
             [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                           [0 0 0]     [0 0 0]     [0]
            orientation:
                      [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [0]             
             f(t,x) = [0 0 0]t + [0 0 0]x + [1] >= [0 0 0]t + [0 0 0]x + [1] = f'(t,g(x))
                      [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]             
            problem:
             
            Qed