YES

Problem:
 t(f(x1)) -> t(c(n(x1)))
 n(f(x1)) -> f(n(x1))
 o(f(x1)) -> f(o(x1))
 n(s(x1)) -> f(s(x1))
 o(s(x1)) -> f(s(x1))
 c(f(x1)) -> f(c(x1))
 c(n(x1)) -> n(c(x1))
 c(o(x1)) -> o(c(x1))
 c(o(x1)) -> o(x1)

Proof:
 Arctic Interpretation Processor:
  dimension: 2
  interpretation:
             [3  -&]  
   [s](x0) = [3  0 ]x0,
   
             [3  2 ]  
   [o](x0) = [-& 1 ]x0,
   
             [0  -&]  
   [c](x0) = [0  -&]x0,
   
             [0 0]  
   [n](x0) = [0 0]x0,
   
             [0 0]  
   [t](x0) = [0 0]x0,
   
             [0  0 ]  
   [f](x0) = [-& 0 ]x0
  orientation:
              [0 0]      [0 0]                
   t(f(x1)) = [0 0]x1 >= [0 0]x1 = t(c(n(x1)))
   
              [0 0]      [0 0]             
   n(f(x1)) = [0 0]x1 >= [0 0]x1 = f(n(x1))
   
              [3  3 ]      [3  2 ]             
   o(f(x1)) = [-& 1 ]x1 >= [-& 1 ]x1 = f(o(x1))
   
              [3 0]      [3 0]             
   n(s(x1)) = [3 0]x1 >= [3 0]x1 = f(s(x1))
   
              [6 2]      [3 0]             
   o(s(x1)) = [4 1]x1 >= [3 0]x1 = f(s(x1))
   
              [0 0]      [0  -&]             
   c(f(x1)) = [0 0]x1 >= [0  -&]x1 = f(c(x1))
   
              [0 0]      [0  -&]             
   c(n(x1)) = [0 0]x1 >= [0  -&]x1 = n(c(x1))
   
              [3 2]      [3  -&]             
   c(o(x1)) = [3 2]x1 >= [1  -&]x1 = o(c(x1))
   
              [3 2]      [3  2 ]          
   c(o(x1)) = [3 2]x1 >= [-& 1 ]x1 = o(x1)
  problem:
   t(f(x1)) -> t(c(n(x1)))
   n(f(x1)) -> f(n(x1))
   o(f(x1)) -> f(o(x1))
   n(s(x1)) -> f(s(x1))
   c(f(x1)) -> f(c(x1))
   c(n(x1)) -> n(c(x1))
   c(o(x1)) -> o(c(x1))
   c(o(x1)) -> o(x1)
  String Reversal Processor:
   f(t(x1)) -> n(c(t(x1)))
   f(n(x1)) -> n(f(x1))
   f(o(x1)) -> o(f(x1))
   s(n(x1)) -> s(f(x1))
   f(c(x1)) -> c(f(x1))
   n(c(x1)) -> c(n(x1))
   o(c(x1)) -> c(o(x1))
   o(c(x1)) -> o(x1)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 1 0]  
     [s](x0) = [1 1 0]x0
               [0 0 0]  ,
     
               [1 0 0]     [0]
     [o](x0) = [1 0 0]x0 + [1]
               [0 0 0]     [0],
     
               [1 0 1]  
     [c](x0) = [0 0 0]x0
               [0 0 0]  ,
     
               [1 0 1]     [0]
     [n](x0) = [0 1 0]x0 + [1]
               [0 0 0]     [0],
     
               [1 0 1]     [0]
     [t](x0) = [1 1 0]x0 + [1]
               [0 0 0]     [0],
     
               [1 0 0]  
     [f](x0) = [0 1 0]x0
               [0 0 0]  
    orientation:
                [1 0 1]     [0]    [1 0 1]     [0]              
     f(t(x1)) = [1 1 0]x1 + [1] >= [0 0 0]x1 + [1] = n(c(t(x1)))
                [0 0 0]     [0]    [0 0 0]     [0]              
     
                [1 0 1]     [0]    [1 0 0]     [0]           
     f(n(x1)) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = n(f(x1))
                [0 0 0]     [0]    [0 0 0]     [0]           
     
                [1 0 0]     [0]    [1 0 0]     [0]           
     f(o(x1)) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = o(f(x1))
                [0 0 0]     [0]    [0 0 0]     [0]           
     
                [1 1 1]     [1]    [1 1 0]             
     s(n(x1)) = [1 1 1]x1 + [1] >= [1 1 0]x1 = s(f(x1))
                [0 0 0]     [0]    [0 0 0]             
     
                [1 0 1]      [1 0 0]             
     f(c(x1)) = [0 0 0]x1 >= [0 0 0]x1 = c(f(x1))
                [0 0 0]      [0 0 0]             
     
                [1 0 1]     [0]    [1 0 1]             
     n(c(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 = c(n(x1))
                [0 0 0]     [0]    [0 0 0]             
     
                [1 0 1]     [0]    [1 0 0]             
     o(c(x1)) = [1 0 1]x1 + [1] >= [0 0 0]x1 = c(o(x1))
                [0 0 0]     [0]    [0 0 0]             
     
                [1 0 1]     [0]    [1 0 0]     [0]        
     o(c(x1)) = [1 0 1]x1 + [1] >= [1 0 0]x1 + [1] = o(x1)
                [0 0 0]     [0]    [0 0 0]     [0]        
    problem:
     f(t(x1)) -> n(c(t(x1)))
     f(n(x1)) -> n(f(x1))
     f(o(x1)) -> o(f(x1))
     f(c(x1)) -> c(f(x1))
     n(c(x1)) -> c(n(x1))
     o(c(x1)) -> c(o(x1))
     o(c(x1)) -> o(x1)
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [o](x0) = 14x0,
      
      [c](x0) = 1x0,
      
      [n](x0) = 10x0,
      
      [t](x0) = 5x0,
      
      [f](x0) = 11x0
     orientation:
      f(t(x1)) = 16x1 >= 16x1 = n(c(t(x1)))
      
      f(n(x1)) = 21x1 >= 21x1 = n(f(x1))
      
      f(o(x1)) = 25x1 >= 25x1 = o(f(x1))
      
      f(c(x1)) = 12x1 >= 12x1 = c(f(x1))
      
      n(c(x1)) = 11x1 >= 11x1 = c(n(x1))
      
      o(c(x1)) = 15x1 >= 15x1 = c(o(x1))
      
      o(c(x1)) = 15x1 >= 14x1 = o(x1)
     problem:
      f(t(x1)) -> n(c(t(x1)))
      f(n(x1)) -> n(f(x1))
      f(o(x1)) -> o(f(x1))
      f(c(x1)) -> c(f(x1))
      n(c(x1)) -> c(n(x1))
      o(c(x1)) -> c(o(x1))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [o](x0) = 8x0,
       
       [c](x0) = x0,
       
       [n](x0) = x0,
       
       [t](x0) = 14x0,
       
       [f](x0) = 2x0
      orientation:
       f(t(x1)) = 16x1 >= 14x1 = n(c(t(x1)))
       
       f(n(x1)) = 2x1 >= 2x1 = n(f(x1))
       
       f(o(x1)) = 10x1 >= 10x1 = o(f(x1))
       
       f(c(x1)) = 2x1 >= 2x1 = c(f(x1))
       
       n(c(x1)) = x1 >= x1 = c(n(x1))
       
       o(c(x1)) = 8x1 >= 8x1 = c(o(x1))
      problem:
       f(n(x1)) -> n(f(x1))
       f(o(x1)) -> o(f(x1))
       f(c(x1)) -> c(f(x1))
       n(c(x1)) -> c(n(x1))
       o(c(x1)) -> c(o(x1))
      KBO Processor:
       weight function:
        w0 = 1
        w(o) = w(c) = w(n) = w(f) = 1
       precedence:
        f > o ~ n > c
       problem:
        
       Qed