MAYBE

Problem:
 f(x1) -> n(c(n(a(x1))))
 c(f(x1)) -> f(n(a(c(x1))))
 n(a(x1)) -> c(x1)
 c(c(x1)) -> c(x1)
 n(s(x1)) -> f(s(s(x1)))
 n(f(x1)) -> f(n(x1))

Proof:
 RT Transformation Processor:
  strict:
   f(x1) -> n(c(n(a(x1))))
   c(f(x1)) -> f(n(a(c(x1))))
   n(a(x1)) -> c(x1)
   c(c(x1)) -> c(x1)
   n(s(x1)) -> f(s(s(x1)))
   n(f(x1)) -> f(n(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [s](x0) = x0 + 16,
    
    [c](x0) = x0 + 24,
    
    [n](x0) = x0 + 1,
    
    [a](x0) = x0 + 17,
    
    [f](x0) = x0 + 20
   orientation:
    f(x1) = x1 + 20 >= x1 + 43 = n(c(n(a(x1))))
    
    c(f(x1)) = x1 + 44 >= x1 + 62 = f(n(a(c(x1))))
    
    n(a(x1)) = x1 + 18 >= x1 + 24 = c(x1)
    
    c(c(x1)) = x1 + 48 >= x1 + 24 = c(x1)
    
    n(s(x1)) = x1 + 17 >= x1 + 52 = f(s(s(x1)))
    
    n(f(x1)) = x1 + 21 >= x1 + 21 = f(n(x1))
   problem:
    strict:
     f(x1) -> n(c(n(a(x1))))
     c(f(x1)) -> f(n(a(c(x1))))
     n(a(x1)) -> c(x1)
     n(s(x1)) -> f(s(s(x1)))
     n(f(x1)) -> f(n(x1))
    weak:
     c(c(x1)) -> c(x1)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [s](x0) = x0,
     
     [c](x0) = x0,
     
     [n](x0) = x0,
     
     [a](x0) = x0 + 12,
     
     [f](x0) = x0
    orientation:
     f(x1) = x1 >= x1 + 12 = n(c(n(a(x1))))
     
     c(f(x1)) = x1 >= x1 + 12 = f(n(a(c(x1))))
     
     n(a(x1)) = x1 + 12 >= x1 = c(x1)
     
     n(s(x1)) = x1 >= x1 = f(s(s(x1)))
     
     n(f(x1)) = x1 >= x1 = f(n(x1))
     
     c(c(x1)) = x1 >= x1 = c(x1)
    problem:
     strict:
      f(x1) -> n(c(n(a(x1))))
      c(f(x1)) -> f(n(a(c(x1))))
      n(s(x1)) -> f(s(s(x1)))
      n(f(x1)) -> f(n(x1))
     weak:
      n(a(x1)) -> c(x1)
      c(c(x1)) -> c(x1)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [s](x0) = x0,
      
      [c](x0) = x0,
      
      [n](x0) = x0,
      
      [a](x0) = x0,
      
      [f](x0) = x0 + 1
     orientation:
      f(x1) = x1 + 1 >= x1 = n(c(n(a(x1))))
      
      c(f(x1)) = x1 + 1 >= x1 + 1 = f(n(a(c(x1))))
      
      n(s(x1)) = x1 >= x1 + 1 = f(s(s(x1)))
      
      n(f(x1)) = x1 + 1 >= x1 + 1 = f(n(x1))
      
      n(a(x1)) = x1 >= x1 = c(x1)
      
      c(c(x1)) = x1 >= x1 = c(x1)
     problem:
      strict:
       c(f(x1)) -> f(n(a(c(x1))))
       n(s(x1)) -> f(s(s(x1)))
       n(f(x1)) -> f(n(x1))
      weak:
       f(x1) -> n(c(n(a(x1))))
       n(a(x1)) -> c(x1)
       c(c(x1)) -> c(x1)
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
                 [0 0]  
       [s](x0) = [0 0]x0,
       
                 [0  0 ]  
       [c](x0) = [-& -&]x0,
       
                 [0  5 ]  
       [n](x0) = [-& 5 ]x0,
       
                 [0  0 ]  
       [a](x0) = [-& -&]x0,
       
                 [0  0 ]  
       [f](x0) = [-& 4 ]x0
      orientation:
                  [0  4 ]      [0  0 ]                   
       c(f(x1)) = [-& -&]x1 >= [-& -&]x1 = f(n(a(c(x1))))
       
                  [5 5]      [0 0]                
       n(s(x1)) = [5 5]x1 >= [4 4]x1 = f(s(s(x1)))
       
                  [0  9 ]      [0  5 ]             
       n(f(x1)) = [-& 9 ]x1 >= [-& 9 ]x1 = f(n(x1))
       
               [0  0 ]      [0  0 ]                   
       f(x1) = [-& 4 ]x1 >= [-& -&]x1 = n(c(n(a(x1))))
       
                  [0  0 ]      [0  0 ]          
       n(a(x1)) = [-& -&]x1 >= [-& -&]x1 = c(x1)
       
                  [0  0 ]      [0  0 ]          
       c(c(x1)) = [-& -&]x1 >= [-& -&]x1 = c(x1)
      problem:
       strict:
        c(f(x1)) -> f(n(a(c(x1))))
        n(f(x1)) -> f(n(x1))
       weak:
        n(s(x1)) -> f(s(s(x1)))
        f(x1) -> n(c(n(a(x1))))
        n(a(x1)) -> c(x1)
        c(c(x1)) -> c(x1)
      Open