YES

Problem:
 p(0(x1)) -> s(s(0(s(s(p(x1))))))
 p(s(0(x1))) -> 0(x1)
 p(s(s(x1))) -> s(p(s(x1)))
 f(s(x1)) -> g(q(i(x1)))
 g(x1) -> f(p(p(x1)))
 q(i(x1)) -> q(s(x1))
 q(s(x1)) -> s(s(x1))
 i(x1) -> s(x1)

Proof:
 Matrix Interpretation Processor: dim=4
  
  interpretation:
             [1 0 0 0]  
             [0 1 1 0]  
   [i](x0) = [0 0 0 0]x0
             [1 0 0 0]  ,
   
             [1 0 0 1]     [0]
             [1 0 0 0]     [1]
   [p](x0) = [1 0 0 0]x0 + [1]
             [0 1 0 0]     [0],
   
             [1 0 0 0]     [0]
             [0 0 0 0]     [0]
   [f](x0) = [0 0 0 0]x0 + [1]
             [1 0 0 0]     [0],
   
             [1 0 0 0]  
             [0 0 0 0]  
   [q](x0) = [0 0 0 1]x0
             [0 0 0 0]  ,
   
             [1 0 0 1]     [0]
             [0 0 0 0]     [0]
   [0](x0) = [0 0 0 0]x0 + [1]
             [0 0 0 0]     [1],
   
             [1 1 0 1]     [0]
             [0 0 0 0]     [0]
   [g](x0) = [0 0 0 1]x0 + [1]
             [1 1 0 1]     [0],
   
             [1 0 0 0]  
             [0 0 1 0]  
   [s](x0) = [0 0 0 0]x0
             [0 0 0 0]  
  orientation:
              [1 0 0 1]     [1]    [1 0 0 1]                         
              [1 0 0 1]     [1]    [0 0 0 0]                         
   p(0(x1)) = [1 0 0 1]x1 + [1] >= [0 0 0 0]x1 = s(s(0(s(s(p(x1))))))
              [0 0 0 0]     [0]    [0 0 0 0]                         
   
                 [1 0 0 1]     [0]    [1 0 0 1]     [0]        
                 [1 0 0 1]     [1]    [0 0 0 0]     [0]        
   p(s(0(x1))) = [1 0 0 1]x1 + [1] >= [0 0 0 0]x1 + [1] = 0(x1)
                 [0 0 0 0]     [1]    [0 0 0 0]     [1]        
   
                 [1 0 0 0]     [0]    [1 0 0 0]     [0]              
                 [1 0 0 0]     [1]    [1 0 0 0]     [1]              
   p(s(s(x1))) = [1 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [0] = s(p(s(x1)))
                 [0 0 0 0]     [0]    [0 0 0 0]     [0]              
   
              [1 0 0 0]     [0]    [1 0 0 0]     [0]              
              [0 0 0 0]     [0]    [0 0 0 0]     [0]              
   f(s(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = g(q(i(x1)))
              [1 0 0 0]     [0]    [1 0 0 0]     [0]              
   
           [1 1 0 1]     [0]    [1 1 0 1]     [0]              
           [0 0 0 0]     [0]    [0 0 0 0]     [0]              
   g(x1) = [0 0 0 1]x1 + [1] >= [0 0 0 0]x1 + [1] = f(p(p(x1)))
           [1 1 0 1]     [0]    [1 1 0 1]     [0]              
   
              [1 0 0 0]      [1 0 0 0]             
              [0 0 0 0]      [0 0 0 0]             
   q(i(x1)) = [1 0 0 0]x1 >= [0 0 0 0]x1 = q(s(x1))
              [0 0 0 0]      [0 0 0 0]             
   
              [1 0 0 0]      [1 0 0 0]             
              [0 0 0 0]      [0 0 0 0]             
   q(s(x1)) = [0 0 0 0]x1 >= [0 0 0 0]x1 = s(s(x1))
              [0 0 0 0]      [0 0 0 0]             
   
           [1 0 0 0]      [1 0 0 0]          
           [0 1 1 0]      [0 0 1 0]          
   i(x1) = [0 0 0 0]x1 >= [0 0 0 0]x1 = s(x1)
           [1 0 0 0]      [0 0 0 0]          
  problem:
   p(s(0(x1))) -> 0(x1)
   p(s(s(x1))) -> s(p(s(x1)))
   f(s(x1)) -> g(q(i(x1)))
   g(x1) -> f(p(p(x1)))
   q(i(x1)) -> q(s(x1))
   q(s(x1)) -> s(s(x1))
   i(x1) -> s(x1)
  Matrix Interpretation Processor: dim=4
   
   interpretation:
              [1 0 0 1]     [0]
              [0 1 0 1]     [1]
    [i](x0) = [1 0 0 1]x0 + [0]
              [0 1 0 0]     [0],
    
              [1 0 0 0]  
              [0 0 0 1]  
    [p](x0) = [0 0 0 1]x0
              [0 0 1 0]  ,
    
              [1 1 0 0]     [0]
              [1 1 0 0]     [1]
    [f](x0) = [0 0 0 0]x0 + [0]
              [0 1 0 0]     [1],
    
              [1 0 0 0]     [0]
              [0 1 0 1]     [1]
    [q](x0) = [0 0 0 1]x0 + [0]
              [0 1 1 0]     [0],
    
              [1 1 0 1]  
              [1 1 0 0]  
    [0](x0) = [0 0 0 0]x0
              [0 0 0 0]  ,
    
              [1 0 1 0]     [1]
              [1 0 1 0]     [1]
    [g](x0) = [0 0 0 0]x0 + [0]
              [0 0 1 0]     [1],
    
              [1 0 0 0]     [0]
              [0 1 0 1]     [1]
    [s](x0) = [0 0 0 1]x0 + [0]
              [0 1 0 0]     [0]
   orientation:
                  [1 1 0 1]      [1 1 0 1]          
                  [1 1 0 0]      [1 1 0 0]          
    p(s(0(x1))) = [1 1 0 0]x1 >= [0 0 0 0]x1 = 0(x1)
                  [0 0 0 0]      [0 0 0 0]          
    
                  [1 0 0 0]     [0]    [1 0 0 0]     [0]              
                  [0 1 0 1]     [1]    [0 1 0 1]     [1]              
    p(s(s(x1))) = [0 1 0 1]x1 + [1] >= [0 0 0 1]x1 + [0] = s(p(s(x1)))
                  [0 1 0 0]     [0]    [0 1 0 0]     [0]              
    
               [1 1 0 1]     [1]    [1 1 0 1]     [1]              
               [1 1 0 1]     [2]    [1 1 0 1]     [1]              
    f(s(x1)) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = g(q(i(x1)))
               [0 1 0 1]     [2]    [0 1 0 0]     [1]              
    
            [1 0 1 0]     [1]    [1 0 1 0]     [0]              
            [1 0 1 0]     [1]    [1 0 1 0]     [1]              
    g(x1) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = f(p(p(x1)))
            [0 0 1 0]     [1]    [0 0 1 0]     [1]              
    
               [1 0 0 1]     [0]    [1 0 0 0]     [0]           
               [0 2 0 1]     [2]    [0 2 0 1]     [2]           
    q(i(x1)) = [0 1 0 0]x1 + [0] >= [0 1 0 0]x1 + [0] = q(s(x1))
               [1 1 0 2]     [1]    [0 1 0 2]     [1]           
    
               [1 0 0 0]     [0]    [1 0 0 0]     [0]           
               [0 2 0 1]     [2]    [0 2 0 1]     [2]           
    q(s(x1)) = [0 1 0 0]x1 + [0] >= [0 1 0 0]x1 + [0] = s(s(x1))
               [0 1 0 2]     [1]    [0 1 0 1]     [1]           
    
            [1 0 0 1]     [0]    [1 0 0 0]     [0]        
            [0 1 0 1]     [1]    [0 1 0 1]     [1]        
    i(x1) = [1 0 0 1]x1 + [0] >= [0 0 0 1]x1 + [0] = s(x1)
            [0 1 0 0]     [0]    [0 1 0 0]     [0]        
   problem:
    p(s(0(x1))) -> 0(x1)
    p(s(s(x1))) -> s(p(s(x1)))
    f(s(x1)) -> g(q(i(x1)))
    q(i(x1)) -> q(s(x1))
    q(s(x1)) -> s(s(x1))
    i(x1) -> s(x1)
   String Reversal Processor:
    0(s(p(x1))) -> 0(x1)
    s(s(p(x1))) -> s(p(s(x1)))
    s(f(x1)) -> i(q(g(x1)))
    i(q(x1)) -> s(q(x1))
    s(q(x1)) -> s(s(x1))
    i(x1) -> s(x1)
    WPO Processor:
     algebra: Sum
     weight function:
      w0 = 0
      w(f) = 5
      w(i) = 4
      w(q) = w(s) = w(p) = 2
      w(0) = 1
      w(g) = 0
     status function:
      st(g) = st(q) = st(i) = st(f) = st(s) = st(p) = st(0) = [0]
     precedence:
      q > s > g ~ i ~ f ~ p ~ 0
     problem:
      
     Qed