MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(a(x1)) -> a(b(c(x1)))
   b(x1) -> x1
   c(b(x1)) -> b(a(c(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [b](x0) = x0 + 24,
    
    [c](x0) = x0,
    
    [a](x0) = x0
   orientation:
    a(x1) = x1 >= x1 = x1
    
    a(a(x1)) = x1 >= x1 + 24 = a(b(c(x1)))
    
    b(x1) = x1 + 24 >= x1 = x1
    
    c(b(x1)) = x1 + 24 >= x1 + 24 = b(a(c(x1)))
   problem:
    strict:
     a(x1) -> x1
     a(a(x1)) -> a(b(c(x1)))
     c(b(x1)) -> b(a(c(x1)))
    weak:
     b(x1) -> x1
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [b](x0) = x0 + 2,
     
     [c](x0) = x0,
     
     [a](x0) = x0 + 1
    orientation:
     a(x1) = x1 + 1 >= x1 = x1
     
     a(a(x1)) = x1 + 2 >= x1 + 3 = a(b(c(x1)))
     
     c(b(x1)) = x1 + 2 >= x1 + 3 = b(a(c(x1)))
     
     b(x1) = x1 + 2 >= x1 = x1
    problem:
     strict:
      a(a(x1)) -> a(b(c(x1)))
      c(b(x1)) -> b(a(c(x1)))
     weak:
      a(x1) -> x1
      b(x1) -> x1
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [b](x0) = x0 + 2,
      
      [c](x0) = x0 + 8,
      
      [a](x0) = x0 + 17
     orientation:
      a(a(x1)) = x1 + 34 >= x1 + 27 = a(b(c(x1)))
      
      c(b(x1)) = x1 + 10 >= x1 + 27 = b(a(c(x1)))
      
      a(x1) = x1 + 17 >= x1 = x1
      
      b(x1) = x1 + 2 >= x1 = x1
     problem:
      strict:
       c(b(x1)) -> b(a(c(x1)))
      weak:
       a(a(x1)) -> a(b(c(x1)))
       a(x1) -> x1
       b(x1) -> x1
     Open