MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(b(x1)) -> b(c(a(x1)))
   c(x1) -> b(x1)
   c(c(x1)) -> a(c(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0,
    
    [b](x0) = x0,
    
    [a](x0) = x0 + 4
   orientation:
    a(x1) = x1 + 4 >= x1 = x1
    
    a(b(x1)) = x1 + 4 >= x1 + 4 = b(c(a(x1)))
    
    c(x1) = x1 >= x1 = b(x1)
    
    c(c(x1)) = x1 >= x1 + 4 = a(c(x1))
   problem:
    strict:
     a(b(x1)) -> b(c(a(x1)))
     c(x1) -> b(x1)
     c(c(x1)) -> a(c(x1))
    weak:
     a(x1) -> x1
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 3,
     
     [b](x0) = x0 + 28,
     
     [a](x0) = x0 + 2
    orientation:
     a(b(x1)) = x1 + 30 >= x1 + 33 = b(c(a(x1)))
     
     c(x1) = x1 + 3 >= x1 + 28 = b(x1)
     
     c(c(x1)) = x1 + 6 >= x1 + 5 = a(c(x1))
     
     a(x1) = x1 + 2 >= x1 = x1
    problem:
     strict:
      a(b(x1)) -> b(c(a(x1)))
      c(x1) -> b(x1)
     weak:
      c(c(x1)) -> a(c(x1))
      a(x1) -> x1
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [c](x0) = x0 + 1,
      
      [b](x0) = x0,
      
      [a](x0) = x0 + 1
     orientation:
      a(b(x1)) = x1 + 1 >= x1 + 2 = b(c(a(x1)))
      
      c(x1) = x1 + 1 >= x1 = b(x1)
      
      c(c(x1)) = x1 + 2 >= x1 + 2 = a(c(x1))
      
      a(x1) = x1 + 1 >= x1 = x1
     problem:
      strict:
       a(b(x1)) -> b(c(a(x1)))
      weak:
       c(x1) -> b(x1)
       c(c(x1)) -> a(c(x1))
       a(x1) -> x1
     Open