MAYBE

Problem:
 a(c(x1)) -> c(b(c(c(a(x1)))))
 b(b(b(x1))) -> c(b(x1))
 d(d(x1)) -> d(b(d(b(d(x1)))))
 a(a(x1)) -> a(d(a(x1)))
 a(b(x1)) -> c(c(a(x1)))
 c(c(x1)) -> c(b(c(b(c(x1)))))
 c(c(c(x1))) -> c(b(b(x1)))

Proof:
 RT Transformation Processor:
  strict:
   a(c(x1)) -> c(b(c(c(a(x1)))))
   b(b(b(x1))) -> c(b(x1))
   d(d(x1)) -> d(b(d(b(d(x1)))))
   a(a(x1)) -> a(d(a(x1)))
   a(b(x1)) -> c(c(a(x1)))
   c(c(x1)) -> c(b(c(b(c(x1)))))
   c(c(c(x1))) -> c(b(b(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [d](x0) = x0,
    
    [b](x0) = x0,
    
    [a](x0) = x0 + 27,
    
    [c](x0) = x0 + 5
   orientation:
    a(c(x1)) = x1 + 32 >= x1 + 42 = c(b(c(c(a(x1)))))
    
    b(b(b(x1))) = x1 >= x1 + 5 = c(b(x1))
    
    d(d(x1)) = x1 >= x1 = d(b(d(b(d(x1)))))
    
    a(a(x1)) = x1 + 54 >= x1 + 54 = a(d(a(x1)))
    
    a(b(x1)) = x1 + 27 >= x1 + 37 = c(c(a(x1)))
    
    c(c(x1)) = x1 + 10 >= x1 + 15 = c(b(c(b(c(x1)))))
    
    c(c(c(x1))) = x1 + 15 >= x1 + 5 = c(b(b(x1)))
   problem:
    strict:
     a(c(x1)) -> c(b(c(c(a(x1)))))
     b(b(b(x1))) -> c(b(x1))
     d(d(x1)) -> d(b(d(b(d(x1)))))
     a(a(x1)) -> a(d(a(x1)))
     a(b(x1)) -> c(c(a(x1)))
     c(c(x1)) -> c(b(c(b(c(x1)))))
    weak:
     c(c(c(x1))) -> c(b(b(x1)))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [d](x0) = x0 + 2,
     
     [b](x0) = x0 + 8,
     
     [a](x0) = x0 + 3,
     
     [c](x0) = x0 + 8
    orientation:
     a(c(x1)) = x1 + 11 >= x1 + 35 = c(b(c(c(a(x1)))))
     
     b(b(b(x1))) = x1 + 24 >= x1 + 16 = c(b(x1))
     
     d(d(x1)) = x1 + 4 >= x1 + 22 = d(b(d(b(d(x1)))))
     
     a(a(x1)) = x1 + 6 >= x1 + 8 = a(d(a(x1)))
     
     a(b(x1)) = x1 + 11 >= x1 + 19 = c(c(a(x1)))
     
     c(c(x1)) = x1 + 16 >= x1 + 40 = c(b(c(b(c(x1)))))
     
     c(c(c(x1))) = x1 + 24 >= x1 + 24 = c(b(b(x1)))
    problem:
     strict:
      a(c(x1)) -> c(b(c(c(a(x1)))))
      d(d(x1)) -> d(b(d(b(d(x1)))))
      a(a(x1)) -> a(d(a(x1)))
      a(b(x1)) -> c(c(a(x1)))
      c(c(x1)) -> c(b(c(b(c(x1)))))
     weak:
      b(b(b(x1))) -> c(b(x1))
      c(c(c(x1))) -> c(b(b(x1)))
    Matrix Interpretation Processor:
     dimension: 2
     interpretation:
                [1  12]     [0]
      [d](x0) = [0  1 ]x0 + [1],
      
                [1 4]  
      [b](x0) = [0 0]x0,
      
                [1 0]  
      [a](x0) = [0 0]x0,
      
                [1 9]  
      [c](x0) = [0 0]x0
     orientation:
                 [1 9]      [1 0]                      
      a(c(x1)) = [0 0]x1 >= [0 0]x1 = c(b(c(c(a(x1)))))
      
                 [1  24]     [12]    [1  16]     [8]                    
      d(d(x1)) = [0  1 ]x1 + [2 ] >= [0  0 ]x1 + [1] = d(b(d(b(d(x1)))))
      
                 [1 0]      [1 0]                
      a(a(x1)) = [0 0]x1 >= [0 0]x1 = a(d(a(x1)))
      
                 [1 4]      [1 0]                
      a(b(x1)) = [0 0]x1 >= [0 0]x1 = c(c(a(x1)))
      
                 [1 9]      [1 9]                      
      c(c(x1)) = [0 0]x1 >= [0 0]x1 = c(b(c(b(c(x1)))))
      
                    [1 4]      [1 4]             
      b(b(b(x1))) = [0 0]x1 >= [0 0]x1 = c(b(x1))
      
                    [1 9]      [1 4]                
      c(c(c(x1))) = [0 0]x1 >= [0 0]x1 = c(b(b(x1)))
     problem:
      strict:
       a(c(x1)) -> c(b(c(c(a(x1)))))
       a(a(x1)) -> a(d(a(x1)))
       a(b(x1)) -> c(c(a(x1)))
       c(c(x1)) -> c(b(c(b(c(x1)))))
      weak:
       d(d(x1)) -> d(b(d(b(d(x1)))))
       b(b(b(x1))) -> c(b(x1))
       c(c(c(x1))) -> c(b(b(x1)))
     Matrix Interpretation Processor:
      dimension: 2
      interpretation:
                 [1 1]  
       [d](x0) = [0 0]x0,
       
                   
       [b](x0) = x0,
       
                 [1 2]     [1]
       [a](x0) = [0 0]x0 + [4],
       
                   
       [c](x0) = x0
      orientation:
                  [1 2]     [1]    [1 2]     [1]                    
       a(c(x1)) = [0 0]x1 + [4] >= [0 0]x1 + [4] = c(b(c(c(a(x1)))))
       
                  [1 2]     [10]    [1 2]     [6]              
       a(a(x1)) = [0 0]x1 + [4 ] >= [0 0]x1 + [4] = a(d(a(x1)))
       
                  [1 2]     [1]    [1 2]     [1]              
       a(b(x1)) = [0 0]x1 + [4] >= [0 0]x1 + [4] = c(c(a(x1)))
       
                                              
       c(c(x1)) = x1 >= x1 = c(b(c(b(c(x1)))))
       
                  [1 1]      [1 1]                      
       d(d(x1)) = [0 0]x1 >= [0 0]x1 = d(b(d(b(d(x1)))))
       
                                        
       b(b(b(x1))) = x1 >= x1 = c(b(x1))
       
                                           
       c(c(c(x1))) = x1 >= x1 = c(b(b(x1)))
      problem:
       strict:
        a(c(x1)) -> c(b(c(c(a(x1)))))
        a(b(x1)) -> c(c(a(x1)))
        c(c(x1)) -> c(b(c(b(c(x1)))))
       weak:
        a(a(x1)) -> a(d(a(x1)))
        d(d(x1)) -> d(b(d(b(d(x1)))))
        b(b(b(x1))) -> c(b(x1))
        c(c(c(x1))) -> c(b(b(x1)))
      Open