MAYBE

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

Proof:
 RT Transformation Processor:
  strict:
   a(x1) -> x1
   a(x1) -> b(b(x1))
   a(b(x1)) -> a(c(a(c(x1))))
   c(c(x1)) -> x1
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [c](x0) = x0 + 5,
    
    [b](x0) = x0 + 9,
    
    [a](x0) = x0 + 7
   orientation:
    a(x1) = x1 + 7 >= x1 = x1
    
    a(x1) = x1 + 7 >= x1 + 18 = b(b(x1))
    
    a(b(x1)) = x1 + 16 >= x1 + 24 = a(c(a(c(x1))))
    
    c(c(x1)) = x1 + 10 >= x1 = x1
   problem:
    strict:
     a(x1) -> b(b(x1))
     a(b(x1)) -> a(c(a(c(x1))))
    weak:
     a(x1) -> x1
     c(c(x1)) -> x1
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [c](x0) = x0 + 1,
     
     [b](x0) = x0 + 27,
     
     [a](x0) = x0 + 4
    orientation:
     a(x1) = x1 + 4 >= x1 + 54 = b(b(x1))
     
     a(b(x1)) = x1 + 31 >= x1 + 10 = a(c(a(c(x1))))
     
     a(x1) = x1 + 4 >= x1 = x1
     
     c(c(x1)) = x1 + 2 >= x1 = x1
    problem:
     strict:
      a(x1) -> b(b(x1))
     weak:
      a(b(x1)) -> a(c(a(c(x1))))
      a(x1) -> x1
      c(c(x1)) -> x1
    Open