MAYBE

Problem:
 a(b(x1)) -> c(b(x1))
 c(c(x1)) -> d(b(x1))
 d(x1) -> c(e(x1))
 b(b(x1)) -> f(x1)
 c(b(x1)) -> g(x1)
 e(x1) -> f(x1)
 e(x1) -> b(b(x1))
 f(g(x1)) -> a(c(x1))
 g(f(x1)) -> e(x1)
 a(x1) -> b(c(x1))

Proof:
 RT Transformation Processor:
  strict:
   a(b(x1)) -> c(b(x1))
   c(c(x1)) -> d(b(x1))
   d(x1) -> c(e(x1))
   b(b(x1)) -> f(x1)
   c(b(x1)) -> g(x1)
   e(x1) -> f(x1)
   e(x1) -> b(b(x1))
   f(g(x1)) -> a(c(x1))
   g(f(x1)) -> e(x1)
   a(x1) -> b(c(x1))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [g](x0) = x0 + 1,
    
    [f](x0) = x0,
    
    [e](x0) = x0 + 16,
    
    [d](x0) = x0,
    
    [c](x0) = x0 + 18,
    
    [a](x0) = x0 + 23,
    
    [b](x0) = x0
   orientation:
    a(b(x1)) = x1 + 23 >= x1 + 18 = c(b(x1))
    
    c(c(x1)) = x1 + 36 >= x1 = d(b(x1))
    
    d(x1) = x1 >= x1 + 34 = c(e(x1))
    
    b(b(x1)) = x1 >= x1 = f(x1)
    
    c(b(x1)) = x1 + 18 >= x1 + 1 = g(x1)
    
    e(x1) = x1 + 16 >= x1 = f(x1)
    
    e(x1) = x1 + 16 >= x1 = b(b(x1))
    
    f(g(x1)) = x1 + 1 >= x1 + 41 = a(c(x1))
    
    g(f(x1)) = x1 + 1 >= x1 + 16 = e(x1)
    
    a(x1) = x1 + 23 >= x1 + 18 = b(c(x1))
   problem:
    strict:
     d(x1) -> c(e(x1))
     b(b(x1)) -> f(x1)
     f(g(x1)) -> a(c(x1))
     g(f(x1)) -> e(x1)
    weak:
     a(b(x1)) -> c(b(x1))
     c(c(x1)) -> d(b(x1))
     c(b(x1)) -> g(x1)
     e(x1) -> f(x1)
     e(x1) -> b(b(x1))
     a(x1) -> b(c(x1))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [g](x0) = x0 + 13,
     
     [f](x0) = x0 + 9,
     
     [e](x0) = x0 + 14,
     
     [d](x0) = x0 + 4,
     
     [c](x0) = x0 + 9,
     
     [a](x0) = x0 + 24,
     
     [b](x0) = x0 + 4
    orientation:
     d(x1) = x1 + 4 >= x1 + 23 = c(e(x1))
     
     b(b(x1)) = x1 + 8 >= x1 + 9 = f(x1)
     
     f(g(x1)) = x1 + 22 >= x1 + 33 = a(c(x1))
     
     g(f(x1)) = x1 + 22 >= x1 + 14 = e(x1)
     
     a(b(x1)) = x1 + 28 >= x1 + 13 = c(b(x1))
     
     c(c(x1)) = x1 + 18 >= x1 + 8 = d(b(x1))
     
     c(b(x1)) = x1 + 13 >= x1 + 13 = g(x1)
     
     e(x1) = x1 + 14 >= x1 + 9 = f(x1)
     
     e(x1) = x1 + 14 >= x1 + 8 = b(b(x1))
     
     a(x1) = x1 + 24 >= x1 + 13 = b(c(x1))
    problem:
     strict:
      d(x1) -> c(e(x1))
      b(b(x1)) -> f(x1)
      f(g(x1)) -> a(c(x1))
     weak:
      g(f(x1)) -> e(x1)
      a(b(x1)) -> c(b(x1))
      c(c(x1)) -> d(b(x1))
      c(b(x1)) -> g(x1)
      e(x1) -> f(x1)
      e(x1) -> b(b(x1))
      a(x1) -> b(c(x1))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [g](x0) = x0,
      
      [f](x0) = x0 + 12,
      
      [e](x0) = x0 + 12,
      
      [d](x0) = x0,
      
      [c](x0) = x0,
      
      [a](x0) = x0,
      
      [b](x0) = x0
     orientation:
      d(x1) = x1 >= x1 + 12 = c(e(x1))
      
      b(b(x1)) = x1 >= x1 + 12 = f(x1)
      
      f(g(x1)) = x1 + 12 >= x1 = a(c(x1))
      
      g(f(x1)) = x1 + 12 >= x1 + 12 = e(x1)
      
      a(b(x1)) = x1 >= x1 = c(b(x1))
      
      c(c(x1)) = x1 >= x1 = d(b(x1))
      
      c(b(x1)) = x1 >= x1 = g(x1)
      
      e(x1) = x1 + 12 >= x1 + 12 = f(x1)
      
      e(x1) = x1 + 12 >= x1 = b(b(x1))
      
      a(x1) = x1 >= x1 = b(c(x1))
     problem:
      strict:
       d(x1) -> c(e(x1))
       b(b(x1)) -> f(x1)
      weak:
       f(g(x1)) -> a(c(x1))
       g(f(x1)) -> e(x1)
       a(b(x1)) -> c(b(x1))
       c(c(x1)) -> d(b(x1))
       c(b(x1)) -> g(x1)
       e(x1) -> f(x1)
       e(x1) -> b(b(x1))
       a(x1) -> b(c(x1))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [g](x0) = x0 + 7,
       
       [f](x0) = x0 + 7,
       
       [e](x0) = x0 + 14,
       
       [d](x0) = x0 + 2,
       
       [c](x0) = x0 + 3,
       
       [a](x0) = x0 + 10,
       
       [b](x0) = x0 + 4
      orientation:
       d(x1) = x1 + 2 >= x1 + 17 = c(e(x1))
       
       b(b(x1)) = x1 + 8 >= x1 + 7 = f(x1)
       
       f(g(x1)) = x1 + 14 >= x1 + 13 = a(c(x1))
       
       g(f(x1)) = x1 + 14 >= x1 + 14 = e(x1)
       
       a(b(x1)) = x1 + 14 >= x1 + 7 = c(b(x1))
       
       c(c(x1)) = x1 + 6 >= x1 + 6 = d(b(x1))
       
       c(b(x1)) = x1 + 7 >= x1 + 7 = g(x1)
       
       e(x1) = x1 + 14 >= x1 + 7 = f(x1)
       
       e(x1) = x1 + 14 >= x1 + 8 = b(b(x1))
       
       a(x1) = x1 + 10 >= x1 + 7 = b(c(x1))
      problem:
       strict:
        d(x1) -> c(e(x1))
       weak:
        b(b(x1)) -> f(x1)
        f(g(x1)) -> a(c(x1))
        g(f(x1)) -> e(x1)
        a(b(x1)) -> c(b(x1))
        c(c(x1)) -> d(b(x1))
        c(b(x1)) -> g(x1)
        e(x1) -> f(x1)
        e(x1) -> b(b(x1))
        a(x1) -> b(c(x1))
      Open