MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(x1) -> b(x1)
   a(b(x1)) -> b(c(x1))
   c(c(x1)) -> a(c(a(x1)))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0 + 5,
    
    [b](x0) = x0 + 19,
    
    [a](x0) = x0 + 4
   orientation:
    a(x1) = x1 + 4 >= x1 = x1
    
    a(x1) = x1 + 4 >= x1 + 19 = b(x1)
    
    a(b(x1)) = x1 + 23 >= x1 + 24 = b(c(x1))
    
    c(c(x1)) = x1 + 10 >= x1 + 13 = a(c(a(x1)))
   problem:
    strict:
     a(x1) -> b(x1)
     a(b(x1)) -> b(c(x1))
     c(c(x1)) -> a(c(a(x1)))
    weak:
     a(x1) -> x1
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 9,
     
     [b](x0) = x0 + 24,
     
     [a](x0) = x0 + 1
    orientation:
     a(x1) = x1 + 1 >= x1 + 24 = b(x1)
     
     a(b(x1)) = x1 + 25 >= x1 + 33 = b(c(x1))
     
     c(c(x1)) = x1 + 18 >= x1 + 11 = a(c(a(x1)))
     
     a(x1) = x1 + 1 >= x1 = x1
    problem:
     strict:
      a(x1) -> b(x1)
      a(b(x1)) -> b(c(x1))
     weak:
      c(c(x1)) -> a(c(a(x1)))
      a(x1) -> x1
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [c](x0) = x0 + 11,
      
      [b](x0) = x0,
      
      [a](x0) = x0 + 5
     orientation:
      a(x1) = x1 + 5 >= x1 = b(x1)
      
      a(b(x1)) = x1 + 5 >= x1 + 11 = b(c(x1))
      
      c(c(x1)) = x1 + 22 >= x1 + 21 = a(c(a(x1)))
      
      a(x1) = x1 + 5 >= x1 = x1
     problem:
      strict:
       a(b(x1)) -> b(c(x1))
      weak:
       a(x1) -> b(x1)
       c(c(x1)) -> a(c(a(x1)))
       a(x1) -> x1
     Open