YES

Problem:
 r(e(x1)) -> w(r(x1))
 i(t(x1)) -> e(r(x1))
 e(w(x1)) -> r(i(x1))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
 e(r(x1)) -> e(w(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))

Proof:
 DP Processor:
  DPs:
   r#(e(x1)) -> r#(x1)
   r#(e(x1)) -> w#(r(x1))
   i#(t(x1)) -> r#(x1)
   i#(t(x1)) -> e#(r(x1))
   e#(w(x1)) -> i#(x1)
   e#(w(x1)) -> r#(i(x1))
   t#(e(x1)) -> r#(e(x1))
   w#(r(x1)) -> t#(x1)
   w#(r(x1)) -> i#(t(x1))
   e#(r(x1)) -> w#(x1)
   e#(r(x1)) -> e#(w(x1))
   r#(i(t(e(r(x1))))) -> e#(x1)
   r#(i(t(e(r(x1))))) -> t#(e(x1))
   r#(i(t(e(r(x1))))) -> i#(t(e(x1)))
   r#(i(t(e(r(x1))))) -> r#(i(t(e(x1))))
   r#(i(t(e(r(x1))))) -> w#(r(i(t(e(x1)))))
   r#(i(t(e(r(x1))))) -> e#(w(r(i(t(e(x1))))))
  TRS:
   r(e(x1)) -> w(r(x1))
   i(t(x1)) -> e(r(x1))
   e(w(x1)) -> r(i(x1))
   t(e(x1)) -> r(e(x1))
   w(r(x1)) -> i(t(x1))
   e(r(x1)) -> e(w(x1))
   r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [t#](x0) = 3x0 + 13/2,
    
    [e#](x0) = 3/2x0 + 7/2,
    
    [i#](x0) = x0 + 1,
    
    [w#](x0) = 2x0 + 4,
    
    [r#](x0) = 3x0 + 9/2,
    
    [i](x0) = 1/2x0,
    
    [t](x0) = 3x0 + 5,
    
    [w](x0) = x0 + 1,
    
    [r](x0) = 3/2x0 + 3/2,
    
    [e](x0) = x0 + 1
   orientation:
    r#(e(x1)) = 3x1 + 15/2 >= 3x1 + 9/2 = r#(x1)
    
    r#(e(x1)) = 3x1 + 15/2 >= 3x1 + 7 = w#(r(x1))
    
    i#(t(x1)) = 3x1 + 6 >= 3x1 + 9/2 = r#(x1)
    
    i#(t(x1)) = 3x1 + 6 >= 9/4x1 + 23/4 = e#(r(x1))
    
    e#(w(x1)) = 3/2x1 + 5 >= x1 + 1 = i#(x1)
    
    e#(w(x1)) = 3/2x1 + 5 >= 3/2x1 + 9/2 = r#(i(x1))
    
    t#(e(x1)) = 3x1 + 19/2 >= 3x1 + 15/2 = r#(e(x1))
    
    w#(r(x1)) = 3x1 + 7 >= 3x1 + 13/2 = t#(x1)
    
    w#(r(x1)) = 3x1 + 7 >= 3x1 + 6 = i#(t(x1))
    
    e#(r(x1)) = 9/4x1 + 23/4 >= 2x1 + 4 = w#(x1)
    
    e#(r(x1)) = 9/4x1 + 23/4 >= 3/2x1 + 5 = e#(w(x1))
    
    r#(i(t(e(r(x1))))) = 27/4x1 + 93/4 >= 3/2x1 + 7/2 = e#(x1)
    
    r#(i(t(e(r(x1))))) = 27/4x1 + 93/4 >= 3x1 + 19/2 = t#(e(x1))
    
    r#(i(t(e(r(x1))))) = 27/4x1 + 93/4 >= 3x1 + 9 = i#(t(e(x1)))
    
    r#(i(t(e(r(x1))))) = 27/4x1 + 93/4 >= 9/2x1 + 33/2 = r#(i(t(e(x1))))
    
    r#(i(t(e(r(x1))))) = 27/4x1 + 93/4 >= 9/2x1 + 19 = w#(r(i(t(e(x1)))))
    
    r#(i(t(e(r(x1))))) = 27/4x1 + 93/4 >= 27/8x1 + 65/4 = e#(w(r(i(t(e(x1))))))
    
    r(e(x1)) = 3/2x1 + 3 >= 3/2x1 + 5/2 = w(r(x1))
    
    i(t(x1)) = 3/2x1 + 5/2 >= 3/2x1 + 5/2 = e(r(x1))
    
    e(w(x1)) = x1 + 2 >= 3/4x1 + 3/2 = r(i(x1))
    
    t(e(x1)) = 3x1 + 8 >= 3/2x1 + 3 = r(e(x1))
    
    w(r(x1)) = 3/2x1 + 5/2 >= 3/2x1 + 5/2 = i(t(x1))
    
    e(r(x1)) = 3/2x1 + 5/2 >= x1 + 2 = e(w(x1))
    
    r(i(t(e(r(x1))))) = 27/8x1 + 87/8 >= 9/4x1 + 19/2 = e(w(r(i(t(e(x1))))))
   problem:
    DPs:
     
    TRS:
     r(e(x1)) -> w(r(x1))
     i(t(x1)) -> e(r(x1))
     e(w(x1)) -> r(i(x1))
     t(e(x1)) -> r(e(x1))
     w(r(x1)) -> i(t(x1))
     e(r(x1)) -> e(w(x1))
     r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
   Qed