YES

Problem:
 strict:
  n(s(x1)) -> s(x1)
  o(s(x1)) -> s(x1)
  n(o(p(x1))) -> o(n(x1))
 weak:
  t(x1) -> t(c(n(x1)))
  p(s(x1)) -> s(x1)
  o(n(x1)) -> n(o(x1))
  p(n(x1)) -> m(p(x1))
  p(m(x1)) -> m(p(x1))
  o(m(x1)) -> n(o(x1))
  n(p(x1)) -> p(n(x1))
  c(p(x1)) -> p(c(x1))
  c(m(x1)) -> m(c(x1))
  c(n(x1)) -> n(c(x1))
  c(o(x1)) -> o(c(x1))
  c(o(x1)) -> o(x1)

Proof:
 String Reversal Processor:
  strict:
   s(n(x1)) -> s(x1)
   s(o(x1)) -> s(x1)
   p(o(n(x1))) -> n(o(x1))
  weak:
   t(x1) -> n(c(t(x1)))
   s(p(x1)) -> s(x1)
   n(o(x1)) -> o(n(x1))
   n(p(x1)) -> p(m(x1))
   m(p(x1)) -> p(m(x1))
   m(o(x1)) -> o(n(x1))
   p(n(x1)) -> n(p(x1))
   p(c(x1)) -> c(p(x1))
   m(c(x1)) -> c(m(x1))
   n(c(x1)) -> c(n(x1))
   o(c(x1)) -> c(o(x1))
   o(c(x1)) -> o(x1)
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [t](x0) = x0,
    
    [n](x0) = x0,
    
    [p](x0) = 4x0,
    
    [c](x0) = x0,
    
    [s](x0) = x0,
    
    [m](x0) = x0,
    
    [o](x0) = 8x0
   orientation:
    s(n(x1)) = x1 >= x1 = s(x1)
    
    s(o(x1)) = 8x1 >= x1 = s(x1)
    
    p(o(n(x1))) = 12x1 >= 8x1 = n(o(x1))
    
    t(x1) = x1 >= x1 = n(c(t(x1)))
    
    s(p(x1)) = 4x1 >= x1 = s(x1)
    
    n(o(x1)) = 8x1 >= 8x1 = o(n(x1))
    
    n(p(x1)) = 4x1 >= 4x1 = p(m(x1))
    
    m(p(x1)) = 4x1 >= 4x1 = p(m(x1))
    
    m(o(x1)) = 8x1 >= 8x1 = o(n(x1))
    
    p(n(x1)) = 4x1 >= 4x1 = n(p(x1))
    
    p(c(x1)) = 4x1 >= 4x1 = c(p(x1))
    
    m(c(x1)) = x1 >= x1 = c(m(x1))
    
    n(c(x1)) = x1 >= x1 = c(n(x1))
    
    o(c(x1)) = 8x1 >= 8x1 = c(o(x1))
    
    o(c(x1)) = 8x1 >= 8x1 = o(x1)
   problem:
    strict:
     s(n(x1)) -> s(x1)
    weak:
     t(x1) -> n(c(t(x1)))
     n(o(x1)) -> o(n(x1))
     n(p(x1)) -> p(m(x1))
     m(p(x1)) -> p(m(x1))
     m(o(x1)) -> o(n(x1))
     p(n(x1)) -> n(p(x1))
     p(c(x1)) -> c(p(x1))
     m(c(x1)) -> c(m(x1))
     n(c(x1)) -> c(n(x1))
     o(c(x1)) -> c(o(x1))
     o(c(x1)) -> o(x1)
   Matrix Interpretation Processor: dim=2
    
    interpretation:
               [2 0]     [1]
     [t](x0) = [2 2]x0 + [2],
     
                    [0]
     [n](x0) = x0 + [1],
     
               [2 0]  
     [p](x0) = [0 1]x0,
     
               [1 0]  
     [c](x0) = [0 0]x0,
     
               [2 1]     [2]
     [s](x0) = [0 0]x0 + [0],
     
                    [0]
     [m](x0) = x0 + [1],
     
               [2 0]     [0]
     [o](x0) = [0 0]x0 + [2]
    orientation:
                [2 1]     [3]    [2 1]     [2]        
     s(n(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = s(x1)
     
             [2 0]     [1]    [2 0]     [1]              
     t(x1) = [2 2]x1 + [2] >= [0 0]x1 + [1] = n(c(t(x1)))
     
                [2 0]     [0]    [2 0]     [0]           
     n(o(x1)) = [0 0]x1 + [3] >= [0 0]x1 + [2] = o(n(x1))
     
                [2 0]     [0]    [2 0]     [0]           
     n(p(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [1] = p(m(x1))
     
                [2 0]     [0]    [2 0]     [0]           
     m(p(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [1] = p(m(x1))
     
                [2 0]     [0]    [2 0]     [0]           
     m(o(x1)) = [0 0]x1 + [3] >= [0 0]x1 + [2] = o(n(x1))
     
                [2 0]     [0]    [2 0]     [0]           
     p(n(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [1] = n(p(x1))
     
                [2 0]      [2 0]             
     p(c(x1)) = [0 0]x1 >= [0 0]x1 = c(p(x1))
     
                [1 0]     [0]    [1 0]             
     m(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 = c(m(x1))
     
                [1 0]     [0]    [1 0]             
     n(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 = c(n(x1))
     
                [2 0]     [0]    [2 0]             
     o(c(x1)) = [0 0]x1 + [2] >= [0 0]x1 = c(o(x1))
     
                [2 0]     [0]    [2 0]     [0]        
     o(c(x1)) = [0 0]x1 + [2] >= [0 0]x1 + [2] = o(x1)
    problem:
     strict:
      
     weak:
      t(x1) -> n(c(t(x1)))
      n(o(x1)) -> o(n(x1))
      n(p(x1)) -> p(m(x1))
      m(p(x1)) -> p(m(x1))
      m(o(x1)) -> o(n(x1))
      p(n(x1)) -> n(p(x1))
      p(c(x1)) -> c(p(x1))
      m(c(x1)) -> c(m(x1))
      n(c(x1)) -> c(n(x1))
      o(c(x1)) -> c(o(x1))
      o(c(x1)) -> o(x1)
    Qed