NO

Problem:
 f(a(),b()) -> c()
 a() -> a'()
 b() -> b'()
 c() -> f(a'(),b())
 c() -> f(a(),b'())
 c() -> f(a(),b())

Proof:
 Uncurry Processor:
  a1(b()) -> c()
  a1(x1) -> a'1(x1)
  a() -> a'()
  b() -> b'()
  c() -> a'1(b())
  c() -> a1(b'())
  c() -> a1(b())
  f(a(),x0) -> a1(x0)
  f(a'(),x0) -> a'1(x0)
  Matrix Interpretation Processor:
   dimension: 3
   interpretation:
                [1 0 0]  
    [a'1](x0) = [0 0 0]x0
                [0 0 1]  ,
    
                 
    [a1](x0) = x0
                 ,
    
           [0]
    [b'] = [0]
           [0],
    
           [0]
    [a'] = [0]
           [0],
    
          [0]
    [c] = [0]
          [1],
    
                  [1 0 0]       
    [f](x0, x1) = [0 0 1]x0 + x1
                  [0 0 0]       ,
    
          [0]
    [b] = [0]
          [1],
    
          [1]
    [a] = [0]
          [1]
   orientation:
              [0]    [0]      
    a1(b()) = [0] >= [0] = c()
              [1]    [1]      
    
                   [1 0 0]            
    a1(x1) = x1 >= [0 0 0]x1 = a'1(x1)
                   [0 0 1]            
    
          [1]    [0]       
    a() = [0] >= [0] = a'()
          [1]    [0]       
    
          [0]    [0]       
    b() = [0] >= [0] = b'()
          [1]    [0]       
    
          [0]    [0]           
    c() = [0] >= [0] = a'1(b())
          [1]    [1]           
    
          [0]    [0]           
    c() = [0] >= [0] = a1(b'())
          [1]    [0]           
    
          [0]    [0]          
    c() = [0] >= [0] = a1(b())
          [1]    [1]          
    
                     [1]               
    f(a(),x0) = x0 + [1] >= x0 = a1(x0)
                     [0]               
    
                       [1 0 0]            
    f(a'(),x0) = x0 >= [0 0 0]x0 = a'1(x0)
                       [0 0 1]            
   problem:
    a1(b()) -> c()
    a1(x1) -> a'1(x1)
    b() -> b'()
    c() -> a'1(b())
    c() -> a1(b'())
    c() -> a1(b())
    f(a'(),x0) -> a'1(x0)
   Matrix Interpretation Processor:
    dimension: 3
    interpretation:
                 [1 0 0]  
     [a'1](x0) = [0 0 0]x0
                 [0 0 0]  ,
     
                [1 1 0]  
     [a1](x0) = [0 0 0]x0
                [0 0 0]  ,
     
            [0]
     [b'] = [0]
            [0],
     
            [0]
     [a'] = [0]
            [0],
     
           [0]
     [c] = [0]
           [0],
     
                   [1 0 0]     [1 0 0]     [1]
     [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                   [0 0 0]     [0 0 0]     [0],
     
           [0]
     [b] = [0]
           [1]
    orientation:
               [0]    [0]      
     a1(b()) = [0] >= [0] = c()
               [0]    [0]      
     
              [1 1 0]      [1 0 0]            
     a1(x1) = [0 0 0]x1 >= [0 0 0]x1 = a'1(x1)
              [0 0 0]      [0 0 0]            
     
           [0]    [0]       
     b() = [0] >= [0] = b'()
           [1]    [0]       
     
           [0]    [0]           
     c() = [0] >= [0] = a'1(b())
           [0]    [0]           
     
           [0]    [0]           
     c() = [0] >= [0] = a1(b'())
           [0]    [0]           
     
           [0]    [0]          
     c() = [0] >= [0] = a1(b())
           [0]    [0]          
     
                  [1 0 0]     [1]    [1 0 0]            
     f(a'(),x0) = [0 0 0]x0 + [0] >= [0 0 0]x0 = a'1(x0)
                  [0 0 0]     [0]    [0 0 0]            
    problem:
     a1(b()) -> c()
     a1(x1) -> a'1(x1)
     b() -> b'()
     c() -> a'1(b())
     c() -> a1(b'())
     c() -> a1(b())
    Matrix Interpretation Processor:
     dimension: 3
     interpretation:
                  [1 1 0]  
      [a'1](x0) = [0 0 0]x0
                  [0 0 0]  ,
      
                 [1 1 1]  
      [a1](x0) = [0 0 0]x0
                 [0 0 0]  ,
      
             [0]
      [b'] = [0]
             [0],
      
            [1]
      [c] = [0]
            [0],
      
            [0]
      [b] = [1]
            [0]
     orientation:
                [1]    [1]      
      a1(b()) = [0] >= [0] = c()
                [0]    [0]      
      
               [1 1 1]      [1 1 0]            
      a1(x1) = [0 0 0]x1 >= [0 0 0]x1 = a'1(x1)
               [0 0 0]      [0 0 0]            
      
            [0]    [0]       
      b() = [1] >= [0] = b'()
            [0]    [0]       
      
            [1]    [1]           
      c() = [0] >= [0] = a'1(b())
            [0]    [0]           
      
            [1]    [0]           
      c() = [0] >= [0] = a1(b'())
            [0]    [0]           
      
            [1]    [1]          
      c() = [0] >= [0] = a1(b())
            [0]    [0]          
     problem:
      a1(b()) -> c()
      a1(x1) -> a'1(x1)
      b() -> b'()
      c() -> a'1(b())
      c() -> a1(b())
     Matrix Interpretation Processor:
      dimension: 3
      interpretation:
                   [1 0 0]  
       [a'1](x0) = [0 0 0]x0
                   [0 0 0]  ,
       
                  [1 0 1]     [0]
       [a1](x0) = [0 1 1]x0 + [0]
                  [0 0 1]     [1],
       
              [0]
       [b'] = [0]
              [0],
       
             [1]
       [c] = [0]
             [1],
       
             [1]
       [b] = [0]
             [0]
      orientation:
                 [1]    [1]      
       a1(b()) = [0] >= [0] = c()
                 [1]    [1]      
       
                [1 0 1]     [0]    [1 0 0]            
       a1(x1) = [0 1 1]x1 + [0] >= [0 0 0]x1 = a'1(x1)
                [0 0 1]     [1]    [0 0 0]            
       
             [1]    [0]       
       b() = [0] >= [0] = b'()
             [0]    [0]       
       
             [1]    [1]           
       c() = [0] >= [0] = a'1(b())
             [1]    [0]           
       
             [1]    [1]          
       c() = [0] >= [0] = a1(b())
             [1]    [1]          
      problem:
       a1(b()) -> c()
       a1(x1) -> a'1(x1)
       c() -> a'1(b())
       c() -> a1(b())
      Matrix Interpretation Processor:
       dimension: 3
       interpretation:
                    [1 0 0]  
        [a'1](x0) = [0 1 0]x0
                    [0 0 0]  ,
        
                   [1 1 0]  
        [a1](x0) = [0 1 1]x0
                   [0 0 0]  ,
        
              [1]
        [c] = [1]
              [0],
        
              [0]
        [b] = [1]
              [0]
       orientation:
                  [1]    [1]      
        a1(b()) = [1] >= [1] = c()
                  [0]    [0]      
        
                 [1 1 0]      [1 0 0]            
        a1(x1) = [0 1 1]x1 >= [0 1 0]x1 = a'1(x1)
                 [0 0 0]      [0 0 0]            
        
              [1]    [0]           
        c() = [1] >= [1] = a'1(b())
              [0]    [0]           
        
              [1]    [1]          
        c() = [1] >= [1] = a1(b())
              [0]    [0]          
       problem:
        a1(b()) -> c()
        a1(x1) -> a'1(x1)
        c() -> a1(b())
       Matrix Interpretation Processor:
        dimension: 3
        interpretation:
                     [1 0 0]  
         [a'1](x0) = [0 0 0]x0
                     [0 0 0]  ,
         
                    [1 0 0]     [1]
         [a1](x0) = [0 0 0]x0 + [0]
                    [0 0 0]     [0],
         
               [1]
         [c] = [0]
               [0],
         
               [0]
         [b] = [0]
               [0]
        orientation:
                   [1]    [1]      
         a1(b()) = [0] >= [0] = c()
                   [0]    [0]      
         
                  [1 0 0]     [1]    [1 0 0]            
         a1(x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 = a'1(x1)
                  [0 0 0]     [0]    [0 0 0]            
         
               [1]    [1]          
         c() = [0] >= [0] = a1(b())
               [0]    [0]          
        problem:
         a1(b()) -> c()
         c() -> a1(b())
        Unfolding Processor:
         loop length: 2
         terms:
          a1(b())
          c()
         context: []
         substitution:
          
         Qed