YES

Problem:
 main(Nil()) -> ParseFail(0())
 main(Cons(A(),Nil())) -> ParseFail(S(0()))
 main(Cons(A(),Cons(A(),x112))) -> ParseFail(S(S(0())))
 main(Cons(A(),Cons(B(),Nil()))) -> ParseSuccess()
 main(Cons(A(),Cons(B(),Cons(x120,x88)))) -> ParseFail(S(S(0())))
 main(Cons(A(),Cons(C(),x112))) -> ParseFail(S(S(0())))
 main(Cons(B(),x14)) -> ParseFail(S(0()))
 main(Cons(C(),x14)) -> ParseFail(S(0()))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
         [0]
   [C] = [0]
         [1],
   
                    [0]
   [ParseSuccess] = [0]
                    [0],
   
         [1]
   [B] = [0]
         [0],
   
             [1 0 0]  
   [S](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                    [1 0 1]     [1 0 0]  
   [Cons](x0, x1) = [0 0 0]x0 + [1 0 0]x1
                    [0 0 0]     [0 0 0]  ,
   
         [0]
   [A] = [0]
         [0],
   
                     [1 0 0]  
   [ParseFail](x0) = [0 0 0]x0
                     [0 0 0]  ,
   
         [0]
   [0] = [0]
         [0],
   
                [1 0 0]     [0]
   [main](x0) = [0 0 0]x0 + [0]
                [0 0 0]     [1],
   
           [0]
   [Nil] = [0]
           [0]
  orientation:
                 [0]    [0]                 
   main(Nil()) = [0] >= [0] = ParseFail(0())
                 [1]    [0]                 
   
                           [0]    [0]                    
   main(Cons(A(),Nil())) = [0] >= [0] = ParseFail(S(0()))
                           [1]    [0]                    
   
                                    [1 0 0]       [0]    [0]                       
   main(Cons(A(),Cons(A(),x112))) = [0 0 0]x112 + [0] >= [0] = ParseFail(S(S(0())))
                                    [0 0 0]       [1]    [0]                       
   
                                     [1]    [0]                 
   main(Cons(A(),Cons(B(),Nil()))) = [0] >= [0] = ParseSuccess()
                                     [1]    [0]                 
   
                                              [1 0 1]       [1 0 0]      [1]    [0]                       
   main(Cons(A(),Cons(B(),Cons(x120,x88)))) = [0 0 0]x120 + [0 0 0]x88 + [0] >= [0] = ParseFail(S(S(0())))
                                              [0 0 0]       [0 0 0]      [1]    [0]                       
   
                                    [1 0 0]       [1]    [0]                       
   main(Cons(A(),Cons(C(),x112))) = [0 0 0]x112 + [0] >= [0] = ParseFail(S(S(0())))
                                    [0 0 0]       [1]    [0]                       
   
                         [1 0 0]      [1]    [0]                    
   main(Cons(B(),x14)) = [0 0 0]x14 + [0] >= [0] = ParseFail(S(0()))
                         [0 0 0]      [1]    [0]                    
   
                         [1 0 0]      [1]    [0]                    
   main(Cons(C(),x14)) = [0 0 0]x14 + [0] >= [0] = ParseFail(S(0()))
                         [0 0 0]      [1]    [0]                    
  problem:
   main(Nil()) -> ParseFail(0())
   main(Cons(A(),Nil())) -> ParseFail(S(0()))
   main(Cons(A(),Cons(A(),x112))) -> ParseFail(S(S(0())))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]     [0]
    [S](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1],
    
                     [1 0 0]     [1 0 0]  
    [Cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                     [0 0 0]     [0 0 0]  ,
    
          [0]
    [A] = [0]
          [0],
    
                      [1 0 0]  
    [ParseFail](x0) = [0 0 0]x0
                      [0 0 0]  ,
    
          [0]
    [0] = [0]
          [0],
    
                 [1 0 0]     [1]
    [main](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
    
            [0]
    [Nil] = [0]
            [0]
   orientation:
                  [1]    [0]                 
    main(Nil()) = [0] >= [0] = ParseFail(0())
                  [0]    [0]                 
    
                            [1]    [0]                    
    main(Cons(A(),Nil())) = [0] >= [0] = ParseFail(S(0()))
                            [0]    [0]                    
    
                                     [1 0 0]       [1]    [0]                       
    main(Cons(A(),Cons(A(),x112))) = [0 0 0]x112 + [0] >= [0] = ParseFail(S(S(0())))
                                     [0 0 0]       [0]    [0]                       
   problem:
    
   Qed