MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(c(a(x1))) -> c(a(c(x1)))
   a(a(b(x1))) -> a(d(b(x1)))
   a(b(x1)) -> b(a(a(x1)))
   d(d(x1)) -> a(d(b(x1)))
   b(b(x1)) -> b(c(x1))
   a(d(c(x1))) -> c(a(x1))
   b(c(x1)) -> a(a(a(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [d](x0) = x0 + 29,
    
    [b](x0) = x0 + 11,
    
    [c](x0) = x0 + 4,
    
    [a](x0) = x0 + 17
   orientation:
    a(c(a(x1))) = x1 + 38 >= x1 + 25 = c(a(c(x1)))
    
    a(a(b(x1))) = x1 + 45 >= x1 + 57 = a(d(b(x1)))
    
    a(b(x1)) = x1 + 28 >= x1 + 45 = b(a(a(x1)))
    
    d(d(x1)) = x1 + 58 >= x1 + 57 = a(d(b(x1)))
    
    b(b(x1)) = x1 + 22 >= x1 + 15 = b(c(x1))
    
    a(d(c(x1))) = x1 + 50 >= x1 + 21 = c(a(x1))
    
    b(c(x1)) = x1 + 15 >= x1 + 51 = a(a(a(x1)))
   problem:
    strict:
     a(a(b(x1))) -> a(d(b(x1)))
     a(b(x1)) -> b(a(a(x1)))
     b(c(x1)) -> a(a(a(x1)))
    weak:
     a(c(a(x1))) -> c(a(c(x1)))
     d(d(x1)) -> a(d(b(x1)))
     b(b(x1)) -> b(c(x1))
     a(d(c(x1))) -> c(a(x1))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [d](x0) = x0 + 24,
     
     [b](x0) = x0 + 16,
     
     [c](x0) = x0,
     
     [a](x0) = x0 + 2
    orientation:
     a(a(b(x1))) = x1 + 20 >= x1 + 42 = a(d(b(x1)))
     
     a(b(x1)) = x1 + 18 >= x1 + 20 = b(a(a(x1)))
     
     b(c(x1)) = x1 + 16 >= x1 + 6 = a(a(a(x1)))
     
     a(c(a(x1))) = x1 + 4 >= x1 + 2 = c(a(c(x1)))
     
     d(d(x1)) = x1 + 48 >= x1 + 42 = a(d(b(x1)))
     
     b(b(x1)) = x1 + 32 >= x1 + 16 = b(c(x1))
     
     a(d(c(x1))) = x1 + 26 >= x1 + 2 = c(a(x1))
    problem:
     strict:
      a(a(b(x1))) -> a(d(b(x1)))
      a(b(x1)) -> b(a(a(x1)))
     weak:
      b(c(x1)) -> a(a(a(x1)))
      a(c(a(x1))) -> c(a(c(x1)))
      d(d(x1)) -> a(d(b(x1)))
      b(b(x1)) -> b(c(x1))
      a(d(c(x1))) -> c(a(x1))
    Arctic Interpretation Processor:
     dimension: 3
     interpretation:
                [0  -& 0 ]  
      [d](x0) = [-& -& 0 ]x0
                [0  0  1 ]  ,
      
                [0 0 0]  
      [b](x0) = [1 1 1]x0
                [0 0 0]  ,
      
                [0  0  -&]  
      [c](x0) = [0  0  -&]x0
                [0  0  -&]  ,
      
                [0  0  -&]  
      [a](x0) = [0  0  -&]x0
                [0  0  -&]  
     orientation:
                    [1 1 1]      [0 0 0]                
      a(a(b(x1))) = [1 1 1]x1 >= [0 0 0]x1 = a(d(b(x1)))
                    [1 1 1]      [0 0 0]                
      
                 [1 1 1]      [0  0  -&]                
      a(b(x1)) = [1 1 1]x1 >= [1  1  -&]x1 = b(a(a(x1)))
                 [1 1 1]      [0  0  -&]                
      
                 [0  0  -&]      [0  0  -&]                
      b(c(x1)) = [1  1  -&]x1 >= [0  0  -&]x1 = a(a(a(x1)))
                 [0  0  -&]      [0  0  -&]                
      
                    [0  0  -&]      [0  0  -&]                
      a(c(a(x1))) = [0  0  -&]x1 >= [0  0  -&]x1 = c(a(c(x1)))
                    [0  0  -&]      [0  0  -&]                
      
                 [0 0 1]      [0 0 0]                
      d(d(x1)) = [0 0 1]x1 >= [0 0 0]x1 = a(d(b(x1)))
                 [1 1 2]      [0 0 0]                
      
                 [1 1 1]      [0  0  -&]             
      b(b(x1)) = [2 2 2]x1 >= [1  1  -&]x1 = b(c(x1))
                 [1 1 1]      [0  0  -&]             
      
                    [0  0  -&]      [0  0  -&]             
      a(d(c(x1))) = [0  0  -&]x1 >= [0  0  -&]x1 = c(a(x1))
                    [0  0  -&]      [0  0  -&]             
     problem:
      strict:
       a(b(x1)) -> b(a(a(x1)))
      weak:
       a(a(b(x1))) -> a(d(b(x1)))
       b(c(x1)) -> a(a(a(x1)))
       a(c(a(x1))) -> c(a(c(x1)))
       d(d(x1)) -> a(d(b(x1)))
       b(b(x1)) -> b(c(x1))
       a(d(c(x1))) -> c(a(x1))
     Open