MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(a(b(x1))) -> b(a(b(x1)))
   b(a(x1)) -> a(b(b(x1)))
   b(c(a(x1))) -> c(c(a(a(b(x1)))))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0,
    
    [a](x0) = x0 + 19,
    
    [b](x0) = x0
   orientation:
    a(a(b(x1))) = x1 + 38 >= x1 + 19 = b(a(b(x1)))
    
    b(a(x1)) = x1 + 19 >= x1 + 19 = a(b(b(x1)))
    
    b(c(a(x1))) = x1 + 19 >= x1 + 38 = c(c(a(a(b(x1)))))
   problem:
    strict:
     b(a(x1)) -> a(b(b(x1)))
     b(c(a(x1))) -> c(c(a(a(b(x1)))))
    weak:
     a(a(b(x1))) -> b(a(b(x1)))
   Arctic Interpretation Processor:
    dimension: 3
    interpretation:
               [0  -& -&]  
     [c](x0) = [-& -& -&]x0
               [0  2  -&]  ,
     
               [0  -& 0 ]  
     [a](x0) = [2  -& 2 ]x0
               [3  -& 3 ]  ,
     
               [0  -& 0 ]  
     [b](x0) = [1  3  0 ]x0
               [0  -& 0 ]  
    orientation:
                [3  -& 3 ]      [0  -& 0 ]                
     b(a(x1)) = [5  -& 5 ]x1 >= [2  -& 2 ]x1 = a(b(b(x1)))
                [3  -& 3 ]      [3  -& 3 ]                
     
                   [4  -& 4 ]      [3  -& 3 ]                      
     b(c(a(x1))) = [4  -& 4 ]x1 >= [-& -& -&]x1 = c(c(a(a(b(x1)))))
                   [4  -& 4 ]      [3  -& 3 ]                      
     
                   [3  -& 3 ]      [3  -& 3 ]                
     a(a(b(x1))) = [5  -& 5 ]x1 >= [5  -& 5 ]x1 = b(a(b(x1)))
                   [6  -& 6 ]      [3  -& 3 ]                
    problem:
     strict:
      b(a(x1)) -> a(b(b(x1)))
     weak:
      b(c(a(x1))) -> c(c(a(a(b(x1)))))
      a(a(b(x1))) -> b(a(b(x1)))
    Open