MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   b(c(a(x1))) -> a(b(x1))
   b(b(b(x1))) -> c(a(c(x1)))
   c(d(x1)) -> d(c(x1))
   c(d(b(x1))) -> d(c(c(x1)))
   d(c(x1)) -> b(b(b(x1)))
   c(b(x1)) -> d(a(x1))
   d(b(c(x1))) -> a(a(x1))
   d(a(x1)) -> b(x1)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [d](x0) = x0 + 6,
    
    [b](x0) = x0 + 2,
    
    [c](x0) = x0,
    
    [a](x0) = x0 + 1
   orientation:
    b(c(a(x1))) = x1 + 3 >= x1 + 3 = a(b(x1))
    
    b(b(b(x1))) = x1 + 6 >= x1 + 1 = c(a(c(x1)))
    
    c(d(x1)) = x1 + 6 >= x1 + 6 = d(c(x1))
    
    c(d(b(x1))) = x1 + 8 >= x1 + 6 = d(c(c(x1)))
    
    d(c(x1)) = x1 + 6 >= x1 + 6 = b(b(b(x1)))
    
    c(b(x1)) = x1 + 2 >= x1 + 7 = d(a(x1))
    
    d(b(c(x1))) = x1 + 8 >= x1 + 2 = a(a(x1))
    
    d(a(x1)) = x1 + 7 >= x1 + 2 = b(x1)
   problem:
    strict:
     b(c(a(x1))) -> a(b(x1))
     c(d(x1)) -> d(c(x1))
     d(c(x1)) -> b(b(b(x1)))
     c(b(x1)) -> d(a(x1))
    weak:
     b(b(b(x1))) -> c(a(c(x1)))
     c(d(b(x1))) -> d(c(c(x1)))
     d(b(c(x1))) -> a(a(x1))
     d(a(x1)) -> b(x1)
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [d](x0) = x0,
     
     [b](x0) = x0 + 3,
     
     [c](x0) = x0 + 3,
     
     [a](x0) = x0 + 3
    orientation:
     b(c(a(x1))) = x1 + 9 >= x1 + 6 = a(b(x1))
     
     c(d(x1)) = x1 + 3 >= x1 + 3 = d(c(x1))
     
     d(c(x1)) = x1 + 3 >= x1 + 9 = b(b(b(x1)))
     
     c(b(x1)) = x1 + 6 >= x1 + 3 = d(a(x1))
     
     b(b(b(x1))) = x1 + 9 >= x1 + 9 = c(a(c(x1)))
     
     c(d(b(x1))) = x1 + 6 >= x1 + 6 = d(c(c(x1)))
     
     d(b(c(x1))) = x1 + 6 >= x1 + 6 = a(a(x1))
     
     d(a(x1)) = x1 + 3 >= x1 + 3 = b(x1)
    problem:
     strict:
      c(d(x1)) -> d(c(x1))
      d(c(x1)) -> b(b(b(x1)))
     weak:
      b(c(a(x1))) -> a(b(x1))
      c(b(x1)) -> d(a(x1))
      b(b(b(x1))) -> c(a(c(x1)))
      c(d(b(x1))) -> d(c(c(x1)))
      d(b(c(x1))) -> a(a(x1))
      d(a(x1)) -> b(x1)
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
                [5 3]  
      [d](x0) = [7 0]x0,
      
                [2  -&]  
      [b](x0) = [5  -&]x0,
      
                [3  -&]  
      [c](x0) = [5  -&]x0,
      
                [0  -&]  
      [a](x0) = [0  -&]x0
     orientation:
                 [8  6 ]      [8  -&]             
      c(d(x1)) = [10 8 ]x1 >= [10 -&]x1 = d(c(x1))
      
                 [8  -&]      [6  -&]                
      d(c(x1)) = [10 -&]x1 >= [9  -&]x1 = b(b(b(x1)))
      
                    [5  -&]      [2  -&]             
      b(c(a(x1))) = [8  -&]x1 >= [2  -&]x1 = a(b(x1))
      
                 [5  -&]      [5  -&]             
      c(b(x1)) = [7  -&]x1 >= [7  -&]x1 = d(a(x1))
      
                    [6  -&]      [6  -&]                
      b(b(b(x1))) = [9  -&]x1 >= [8  -&]x1 = c(a(c(x1)))
      
                    [11 -&]      [11 -&]                
      c(d(b(x1))) = [13 -&]x1 >= [13 -&]x1 = d(c(c(x1)))
      
                    [11 -&]      [0  -&]             
      d(b(c(x1))) = [12 -&]x1 >= [0  -&]x1 = a(a(x1))
      
                 [5  -&]      [2  -&]          
      d(a(x1)) = [7  -&]x1 >= [5  -&]x1 = b(x1)
     problem:
      strict:
       c(d(x1)) -> d(c(x1))
      weak:
       d(c(x1)) -> b(b(b(x1)))
       b(c(a(x1))) -> a(b(x1))
       c(b(x1)) -> d(a(x1))
       b(b(b(x1))) -> c(a(c(x1)))
       c(d(b(x1))) -> d(c(c(x1)))
       d(b(c(x1))) -> a(a(x1))
       d(a(x1)) -> b(x1)
     Open