YES

Problem:
 0(1(0(x1))) -> 0(2(1(0(x1))))
 0(1(0(x1))) -> 0(0(2(1(0(x1)))))
 0(1(0(x1))) -> 0(0(2(1(2(x1)))))
 0(1(0(x1))) -> 0(2(1(0(2(x1)))))
 0(1(0(x1))) -> 0(3(2(1(0(x1)))))
 0(1(0(x1))) -> 1(0(0(0(2(x1)))))
 0(1(0(x1))) -> 1(0(0(2(0(x1)))))
 0(1(0(x1))) -> 1(0(4(2(0(x1)))))
 0(1(0(x1))) -> 1(4(0(4(0(x1)))))
 0(1(0(x1))) -> 4(0(0(2(1(x1)))))
 0(1(0(x1))) -> 5(0(0(4(1(x1)))))
 0(1(0(x1))) -> 5(1(0(4(0(x1)))))
 0(1(0(x1))) -> 0(2(1(0(3(2(x1))))))
 0(1(0(x1))) -> 0(4(0(4(1(3(x1))))))
 0(1(0(x1))) -> 0(4(2(2(1(0(x1))))))
 0(1(0(x1))) -> 0(5(2(1(2(0(x1))))))
 0(1(0(x1))) -> 0(5(2(5(1(0(x1))))))
 0(1(0(x1))) -> 1(0(0(5(4(4(x1))))))
 0(1(0(x1))) -> 1(0(4(4(4(0(x1))))))
 0(1(0(x1))) -> 1(5(0(0(4(2(x1))))))
 0(1(0(x1))) -> 3(0(0(4(1(4(x1))))))
 0(1(0(x1))) -> 4(5(1(0(2(0(x1))))))
 0(1(0(x1))) -> 5(5(1(0(0(2(x1))))))
 0(0(1(0(x1)))) -> 1(0(0(2(0(x1)))))
 0(0(1(0(x1)))) -> 0(1(5(0(0(2(x1))))))
 0(1(0(3(x1)))) -> 1(0(3(3(0(2(x1))))))
 0(1(0(3(x1)))) -> 1(0(5(3(2(0(x1))))))
 0(1(1(0(x1)))) -> 0(4(4(1(1(0(x1))))))
 0(1(1(3(x1)))) -> 3(4(5(1(1(0(x1))))))
 0(1(2(0(x1)))) -> 1(1(0(2(0(x1)))))
 0(1(2(0(x1)))) -> 3(0(2(1(0(x1)))))
 0(1(2(0(x1)))) -> 4(1(0(0(2(x1)))))
 0(1(2(0(x1)))) -> 0(0(4(2(5(1(x1))))))
 0(1(2(0(x1)))) -> 1(1(2(0(4(0(x1))))))
 0(1(2(0(x1)))) -> 3(0(2(1(0(4(x1))))))
 0(1(3(0(x1)))) -> 1(0(3(0(2(x1)))))
 0(1(4(0(x1)))) -> 0(3(4(2(1(0(x1))))))
 0(1(5(0(x1)))) -> 0(5(1(4(0(x1)))))
 0(1(5(0(x1)))) -> 1(5(3(0(2(0(x1))))))
 0(3(1(0(x1)))) -> 1(2(3(0(5(0(x1))))))
 5(0(1(0(x1)))) -> 1(4(0(0(5(1(x1))))))
 5(0(1(0(x1)))) -> 2(1(0(0(4(5(x1))))))
 0(1(0(0(0(x1))))) -> 0(0(5(1(0(0(x1))))))
 0(1(2(4(0(x1))))) -> 0(0(5(4(2(1(x1))))))
 0(1(2(5(0(x1))))) -> 1(0(2(0(5(4(x1))))))
 0(1(4(0(0(x1))))) -> 0(0(0(4(1(0(x1))))))
 0(1(4(5(0(x1))))) -> 1(5(0(0(4(2(x1))))))
 0(3(0(1(0(x1))))) -> 0(3(0(0(2(1(x1))))))
 3(0(3(1(0(x1))))) -> 0(1(3(2(3(0(x1))))))
 5(0(1(2(0(x1))))) -> 0(0(5(2(1(0(x1))))))

Proof:
 DP Processor:
  DPs:
   0#(1(0(x1))) -> 0#(2(1(0(x1))))
   0#(1(0(x1))) -> 0#(0(2(1(0(x1)))))
   0#(1(0(x1))) -> 0#(2(1(2(x1))))
   0#(1(0(x1))) -> 0#(0(2(1(2(x1)))))
   0#(1(0(x1))) -> 0#(2(x1))
   0#(1(0(x1))) -> 0#(2(1(0(2(x1)))))
   0#(1(0(x1))) -> 3#(2(1(0(x1))))
   0#(1(0(x1))) -> 0#(3(2(1(0(x1)))))
   0#(1(0(x1))) -> 0#(0(2(x1)))
   0#(1(0(x1))) -> 0#(0(0(2(x1))))
   0#(1(0(x1))) -> 0#(2(0(x1)))
   0#(1(0(x1))) -> 0#(0(2(0(x1))))
   0#(1(0(x1))) -> 0#(4(2(0(x1))))
   0#(1(0(x1))) -> 0#(4(0(x1)))
   0#(1(0(x1))) -> 0#(2(1(x1)))
   0#(1(0(x1))) -> 0#(0(2(1(x1))))
   0#(1(0(x1))) -> 0#(4(1(x1)))
   0#(1(0(x1))) -> 0#(0(4(1(x1))))
   0#(1(0(x1))) -> 5#(0(0(4(1(x1)))))
   0#(1(0(x1))) -> 5#(1(0(4(0(x1)))))
   0#(1(0(x1))) -> 3#(2(x1))
   0#(1(0(x1))) -> 0#(3(2(x1)))
   0#(1(0(x1))) -> 0#(2(1(0(3(2(x1))))))
   0#(1(0(x1))) -> 3#(x1)
   0#(1(0(x1))) -> 0#(4(1(3(x1))))
   0#(1(0(x1))) -> 0#(4(0(4(1(3(x1))))))
   0#(1(0(x1))) -> 0#(4(2(2(1(0(x1))))))
   0#(1(0(x1))) -> 5#(2(1(2(0(x1)))))
   0#(1(0(x1))) -> 0#(5(2(1(2(0(x1))))))
   0#(1(0(x1))) -> 5#(1(0(x1)))
   0#(1(0(x1))) -> 5#(2(5(1(0(x1)))))
   0#(1(0(x1))) -> 0#(5(2(5(1(0(x1))))))
   0#(1(0(x1))) -> 5#(4(4(x1)))
   0#(1(0(x1))) -> 0#(5(4(4(x1))))
   0#(1(0(x1))) -> 0#(0(5(4(4(x1)))))
   0#(1(0(x1))) -> 0#(4(4(4(0(x1)))))
   0#(1(0(x1))) -> 0#(4(2(x1)))
   0#(1(0(x1))) -> 0#(0(4(2(x1))))
   0#(1(0(x1))) -> 5#(0(0(4(2(x1)))))
   0#(1(0(x1))) -> 0#(4(1(4(x1))))
   0#(1(0(x1))) -> 0#(0(4(1(4(x1)))))
   0#(1(0(x1))) -> 3#(0(0(4(1(4(x1))))))
   0#(1(0(x1))) -> 5#(1(0(2(0(x1)))))
   0#(1(0(x1))) -> 5#(1(0(0(2(x1)))))
   0#(1(0(x1))) -> 5#(5(1(0(0(2(x1))))))
   0#(0(1(0(x1)))) -> 0#(2(0(x1)))
   0#(0(1(0(x1)))) -> 0#(0(2(0(x1))))
   0#(0(1(0(x1)))) -> 0#(2(x1))
   0#(0(1(0(x1)))) -> 0#(0(2(x1)))
   0#(0(1(0(x1)))) -> 5#(0(0(2(x1))))
   0#(0(1(0(x1)))) -> 0#(1(5(0(0(2(x1))))))
   0#(1(0(3(x1)))) -> 0#(2(x1))
   0#(1(0(3(x1)))) -> 3#(0(2(x1)))
   0#(1(0(3(x1)))) -> 3#(3(0(2(x1))))
   0#(1(0(3(x1)))) -> 0#(3(3(0(2(x1)))))
   0#(1(0(3(x1)))) -> 0#(x1)
   0#(1(0(3(x1)))) -> 3#(2(0(x1)))
   0#(1(0(3(x1)))) -> 5#(3(2(0(x1))))
   0#(1(0(3(x1)))) -> 0#(5(3(2(0(x1)))))
   0#(1(1(0(x1)))) -> 0#(4(4(1(1(0(x1))))))
   0#(1(1(3(x1)))) -> 0#(x1)
   0#(1(1(3(x1)))) -> 5#(1(1(0(x1))))
   0#(1(1(3(x1)))) -> 3#(4(5(1(1(0(x1))))))
   0#(1(2(0(x1)))) -> 0#(2(0(x1)))
   0#(1(2(0(x1)))) -> 0#(2(1(0(x1))))
   0#(1(2(0(x1)))) -> 3#(0(2(1(0(x1)))))
   0#(1(2(0(x1)))) -> 0#(2(x1))
   0#(1(2(0(x1)))) -> 0#(0(2(x1)))
   0#(1(2(0(x1)))) -> 5#(1(x1))
   0#(1(2(0(x1)))) -> 0#(4(2(5(1(x1)))))
   0#(1(2(0(x1)))) -> 0#(0(4(2(5(1(x1))))))
   0#(1(2(0(x1)))) -> 0#(4(0(x1)))
   0#(1(2(0(x1)))) -> 0#(4(x1))
   0#(1(2(0(x1)))) -> 0#(2(1(0(4(x1)))))
   0#(1(2(0(x1)))) -> 3#(0(2(1(0(4(x1))))))
   0#(1(3(0(x1)))) -> 0#(2(x1))
   0#(1(3(0(x1)))) -> 3#(0(2(x1)))
   0#(1(3(0(x1)))) -> 0#(3(0(2(x1))))
   0#(1(4(0(x1)))) -> 3#(4(2(1(0(x1)))))
   0#(1(4(0(x1)))) -> 0#(3(4(2(1(0(x1))))))
   0#(1(5(0(x1)))) -> 5#(1(4(0(x1))))
   0#(1(5(0(x1)))) -> 0#(5(1(4(0(x1)))))
   0#(1(5(0(x1)))) -> 0#(2(0(x1)))
   0#(1(5(0(x1)))) -> 3#(0(2(0(x1))))
   0#(1(5(0(x1)))) -> 5#(3(0(2(0(x1)))))
   0#(3(1(0(x1)))) -> 5#(0(x1))
   0#(3(1(0(x1)))) -> 0#(5(0(x1)))
   0#(3(1(0(x1)))) -> 3#(0(5(0(x1))))
   5#(0(1(0(x1)))) -> 5#(1(x1))
   5#(0(1(0(x1)))) -> 0#(5(1(x1)))
   5#(0(1(0(x1)))) -> 0#(0(5(1(x1))))
   5#(0(1(0(x1)))) -> 5#(x1)
   5#(0(1(0(x1)))) -> 0#(4(5(x1)))
   5#(0(1(0(x1)))) -> 0#(0(4(5(x1))))
   0#(1(0(0(0(x1))))) -> 5#(1(0(0(x1))))
   0#(1(0(0(0(x1))))) -> 0#(5(1(0(0(x1)))))
   0#(1(0(0(0(x1))))) -> 0#(0(5(1(0(0(x1))))))
   0#(1(2(4(0(x1))))) -> 5#(4(2(1(x1))))
   0#(1(2(4(0(x1))))) -> 0#(5(4(2(1(x1)))))
   0#(1(2(4(0(x1))))) -> 0#(0(5(4(2(1(x1))))))
   0#(1(2(5(0(x1))))) -> 5#(4(x1))
   0#(1(2(5(0(x1))))) -> 0#(5(4(x1)))
   0#(1(2(5(0(x1))))) -> 0#(2(0(5(4(x1)))))
   0#(1(4(0(0(x1))))) -> 0#(4(1(0(x1))))
   0#(1(4(0(0(x1))))) -> 0#(0(4(1(0(x1)))))
   0#(1(4(0(0(x1))))) -> 0#(0(0(4(1(0(x1))))))
   0#(1(4(5(0(x1))))) -> 0#(4(2(x1)))
   0#(1(4(5(0(x1))))) -> 0#(0(4(2(x1))))
   0#(1(4(5(0(x1))))) -> 5#(0(0(4(2(x1)))))
   0#(3(0(1(0(x1))))) -> 0#(2(1(x1)))
   0#(3(0(1(0(x1))))) -> 0#(0(2(1(x1))))
   0#(3(0(1(0(x1))))) -> 3#(0(0(2(1(x1)))))
   0#(3(0(1(0(x1))))) -> 0#(3(0(0(2(1(x1))))))
   3#(0(3(1(0(x1))))) -> 3#(0(x1))
   3#(0(3(1(0(x1))))) -> 3#(2(3(0(x1))))
   3#(0(3(1(0(x1))))) -> 0#(1(3(2(3(0(x1))))))
   5#(0(1(2(0(x1))))) -> 5#(2(1(0(x1))))
   5#(0(1(2(0(x1))))) -> 0#(5(2(1(0(x1)))))
   5#(0(1(2(0(x1))))) -> 0#(0(5(2(1(0(x1))))))
  TRS:
   0(1(0(x1))) -> 0(2(1(0(x1))))
   0(1(0(x1))) -> 0(0(2(1(0(x1)))))
   0(1(0(x1))) -> 0(0(2(1(2(x1)))))
   0(1(0(x1))) -> 0(2(1(0(2(x1)))))
   0(1(0(x1))) -> 0(3(2(1(0(x1)))))
   0(1(0(x1))) -> 1(0(0(0(2(x1)))))
   0(1(0(x1))) -> 1(0(0(2(0(x1)))))
   0(1(0(x1))) -> 1(0(4(2(0(x1)))))
   0(1(0(x1))) -> 1(4(0(4(0(x1)))))
   0(1(0(x1))) -> 4(0(0(2(1(x1)))))
   0(1(0(x1))) -> 5(0(0(4(1(x1)))))
   0(1(0(x1))) -> 5(1(0(4(0(x1)))))
   0(1(0(x1))) -> 0(2(1(0(3(2(x1))))))
   0(1(0(x1))) -> 0(4(0(4(1(3(x1))))))
   0(1(0(x1))) -> 0(4(2(2(1(0(x1))))))
   0(1(0(x1))) -> 0(5(2(1(2(0(x1))))))
   0(1(0(x1))) -> 0(5(2(5(1(0(x1))))))
   0(1(0(x1))) -> 1(0(0(5(4(4(x1))))))
   0(1(0(x1))) -> 1(0(4(4(4(0(x1))))))
   0(1(0(x1))) -> 1(5(0(0(4(2(x1))))))
   0(1(0(x1))) -> 3(0(0(4(1(4(x1))))))
   0(1(0(x1))) -> 4(5(1(0(2(0(x1))))))
   0(1(0(x1))) -> 5(5(1(0(0(2(x1))))))
   0(0(1(0(x1)))) -> 1(0(0(2(0(x1)))))
   0(0(1(0(x1)))) -> 0(1(5(0(0(2(x1))))))
   0(1(0(3(x1)))) -> 1(0(3(3(0(2(x1))))))
   0(1(0(3(x1)))) -> 1(0(5(3(2(0(x1))))))
   0(1(1(0(x1)))) -> 0(4(4(1(1(0(x1))))))
   0(1(1(3(x1)))) -> 3(4(5(1(1(0(x1))))))
   0(1(2(0(x1)))) -> 1(1(0(2(0(x1)))))
   0(1(2(0(x1)))) -> 3(0(2(1(0(x1)))))
   0(1(2(0(x1)))) -> 4(1(0(0(2(x1)))))
   0(1(2(0(x1)))) -> 0(0(4(2(5(1(x1))))))
   0(1(2(0(x1)))) -> 1(1(2(0(4(0(x1))))))
   0(1(2(0(x1)))) -> 3(0(2(1(0(4(x1))))))
   0(1(3(0(x1)))) -> 1(0(3(0(2(x1)))))
   0(1(4(0(x1)))) -> 0(3(4(2(1(0(x1))))))
   0(1(5(0(x1)))) -> 0(5(1(4(0(x1)))))
   0(1(5(0(x1)))) -> 1(5(3(0(2(0(x1))))))
   0(3(1(0(x1)))) -> 1(2(3(0(5(0(x1))))))
   5(0(1(0(x1)))) -> 1(4(0(0(5(1(x1))))))
   5(0(1(0(x1)))) -> 2(1(0(0(4(5(x1))))))
   0(1(0(0(0(x1))))) -> 0(0(5(1(0(0(x1))))))
   0(1(2(4(0(x1))))) -> 0(0(5(4(2(1(x1))))))
   0(1(2(5(0(x1))))) -> 1(0(2(0(5(4(x1))))))
   0(1(4(0(0(x1))))) -> 0(0(0(4(1(0(x1))))))
   0(1(4(5(0(x1))))) -> 1(5(0(0(4(2(x1))))))
   0(3(0(1(0(x1))))) -> 0(3(0(0(2(1(x1))))))
   3(0(3(1(0(x1))))) -> 0(1(3(2(3(0(x1))))))
   5(0(1(2(0(x1))))) -> 0(0(5(2(1(0(x1))))))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
    [5#](x0) = [1 0 0]x0,
    
    [3#](x0) = [1 0 0]x0,
    
    [0#](x0) = [1 1 0]x0,
    
              [0 0 1]  
    [5](x0) = [1 0 0]x0
              [0 0 0]  ,
    
              [0]
    [4](x0) = [0]
              [0],
    
              [1 1 0]  
    [3](x0) = [0 1 1]x0
              [0 1 0]  ,
    
              [0]
    [2](x0) = [0]
              [0],
    
              [0 0 0]     [0]
    [1](x0) = [0 0 1]x0 + [1]
              [1 0 0]     [0],
    
              [0 1 1]  
    [0](x0) = [0 1 0]x0
              [1 0 0]  
   orientation:
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(2(1(0(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(0(2(1(0(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(2(1(2(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(0(2(1(2(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(2(x1))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(2(1(0(2(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 3#(2(1(0(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(3(2(1(0(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(0(2(x1)))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(0(0(2(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(2(0(x1)))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(0(2(0(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(4(2(0(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(4(0(x1)))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(2(1(x1)))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(0(2(1(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(4(1(x1)))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(0(4(1(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5#(0(0(4(1(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5#(1(0(4(0(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 3#(2(x1))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(3(2(x1)))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(2(1(0(3(2(x1))))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [1 0 0]x1 = 3#(x1)
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(4(1(3(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(4(0(4(1(3(x1))))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(4(2(2(1(0(x1))))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5#(2(1(2(0(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(5(2(1(2(0(x1))))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5#(1(0(x1)))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5#(2(5(1(0(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(5(2(5(1(0(x1))))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5#(4(4(x1)))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(5(4(4(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(0(5(4(4(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(4(4(4(0(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(4(2(x1)))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(0(4(2(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5#(0(0(4(2(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(4(1(4(x1))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0#(0(4(1(4(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 3#(0(0(4(1(4(x1))))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5#(1(0(2(0(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5#(1(0(0(2(x1)))))
    
    0#(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5#(5(1(0(0(2(x1))))))
    
    0#(0(1(0(x1)))) = [2 1 1]x1 + [2] >= [0] = 0#(2(0(x1)))
    
    0#(0(1(0(x1)))) = [2 1 1]x1 + [2] >= [0] = 0#(0(2(0(x1))))
    
    0#(0(1(0(x1)))) = [2 1 1]x1 + [2] >= [0] = 0#(2(x1))
    
    0#(0(1(0(x1)))) = [2 1 1]x1 + [2] >= [0] = 0#(0(2(x1)))
    
    0#(0(1(0(x1)))) = [2 1 1]x1 + [2] >= [0] = 5#(0(0(2(x1))))
    
    0#(0(1(0(x1)))) = [2 1 1]x1 + [2] >= [1] = 0#(1(5(0(0(2(x1))))))
    
    0#(1(0(3(x1)))) = [1 1 0]x1 + [1] >= [0] = 0#(2(x1))
    
    0#(1(0(3(x1)))) = [1 1 0]x1 + [1] >= [0] = 3#(0(2(x1)))
    
    0#(1(0(3(x1)))) = [1 1 0]x1 + [1] >= [0] = 3#(3(0(2(x1))))
    
    0#(1(0(3(x1)))) = [1 1 0]x1 + [1] >= [0] = 0#(3(3(0(2(x1)))))
    
    0#(1(0(3(x1)))) = [1 1 0]x1 + [1] >= [1 1 0]x1 = 0#(x1)
    
    0#(1(0(3(x1)))) = [1 1 0]x1 + [1] >= [0] = 3#(2(0(x1)))
    
    0#(1(0(3(x1)))) = [1 1 0]x1 + [1] >= [0] = 5#(3(2(0(x1))))
    
    0#(1(0(3(x1)))) = [1 1 0]x1 + [1] >= [0] = 0#(5(3(2(0(x1)))))
    
    0#(1(1(0(x1)))) = [0 1 1]x1 + [1] >= [0] = 0#(4(4(1(1(0(x1))))))
    
    0#(1(1(3(x1)))) = [1 1 0]x1 + [1] >= [1 1 0]x1 = 0#(x1)
    
    0#(1(1(3(x1)))) = [1 1 0]x1 + [1] >= [0] = 5#(1(1(0(x1))))
    
    0#(1(1(3(x1)))) = [1 1 0]x1 + [1] >= [0] = 3#(4(5(1(1(0(x1))))))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 0#(2(0(x1)))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 0#(2(1(0(x1))))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 3#(0(2(1(0(x1)))))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 0#(2(x1))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 0#(0(2(x1)))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 5#(1(x1))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 0#(4(2(5(1(x1)))))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 0#(0(4(2(5(1(x1))))))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 0#(4(0(x1)))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 0#(4(x1))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 0#(2(1(0(4(x1)))))
    
    0#(1(2(0(x1)))) = [1] >= [0] = 3#(0(2(1(0(4(x1))))))
    
    0#(1(3(0(x1)))) = [0 1 0]x1 + [1] >= [0] = 0#(2(x1))
    
    0#(1(3(0(x1)))) = [0 1 0]x1 + [1] >= [0] = 3#(0(2(x1)))
    
    0#(1(3(0(x1)))) = [0 1 0]x1 + [1] >= [0] = 0#(3(0(2(x1))))
    
    0#(1(4(0(x1)))) = [1] >= [0] = 3#(4(2(1(0(x1)))))
    
    0#(1(4(0(x1)))) = [1] >= [0] = 0#(3(4(2(1(0(x1))))))
    
    0#(1(5(0(x1)))) = [1] >= [0] = 5#(1(4(0(x1))))
    
    0#(1(5(0(x1)))) = [1] >= [0] = 0#(5(1(4(0(x1)))))
    
    0#(1(5(0(x1)))) = [1] >= [0] = 0#(2(0(x1)))
    
    0#(1(5(0(x1)))) = [1] >= [0] = 3#(0(2(0(x1))))
    
    0#(1(5(0(x1)))) = [1] >= [0] = 5#(3(0(2(0(x1)))))
    
    0#(3(1(0(x1)))) = [2 1 1]x1 + [2] >= [0 1 1]x1 = 5#(0(x1))
    
    0#(3(1(0(x1)))) = [2 1 1]x1 + [2] >= [1 1 1]x1 = 0#(5(0(x1)))
    
    0#(3(1(0(x1)))) = [2 1 1]x1 + [2] >= [0 1 1]x1 = 3#(0(5(0(x1))))
    
    5#(0(1(0(x1)))) = [1 1 1]x1 + [1] >= [0] = 5#(1(x1))
    
    5#(0(1(0(x1)))) = [1 1 1]x1 + [1] >= [1 0 0]x1 = 0#(5(1(x1)))
    
    5#(0(1(0(x1)))) = [1 1 1]x1 + [1] >= [0] = 0#(0(5(1(x1))))
    
    5#(0(1(0(x1)))) = [1 1 1]x1 + [1] >= [1 0 0]x1 = 5#(x1)
    
    5#(0(1(0(x1)))) = [1 1 1]x1 + [1] >= [0] = 0#(4(5(x1)))
    
    5#(0(1(0(x1)))) = [1 1 1]x1 + [1] >= [0] = 0#(0(4(5(x1))))
    
    0#(1(0(0(0(x1))))) = [1 1 0]x1 + [1] >= [0] = 5#(1(0(0(x1))))
    
    0#(1(0(0(0(x1))))) = [1 1 0]x1 + [1] >= [1 1 0]x1 = 0#(5(1(0(0(x1)))))
    
    0#(1(0(0(0(x1))))) = [1 1 0]x1 + [1] >= [0] = 0#(0(5(1(0(0(x1))))))
    
    0#(1(2(4(0(x1))))) = [1] >= [0] = 5#(4(2(1(x1))))
    
    0#(1(2(4(0(x1))))) = [1] >= [0] = 0#(5(4(2(1(x1)))))
    
    0#(1(2(4(0(x1))))) = [1] >= [0] = 0#(0(5(4(2(1(x1))))))
    
    0#(1(2(5(0(x1))))) = [1] >= [0] = 5#(4(x1))
    
    0#(1(2(5(0(x1))))) = [1] >= [0] = 0#(5(4(x1)))
    
    0#(1(2(5(0(x1))))) = [1] >= [0] = 0#(2(0(5(4(x1)))))
    
    0#(1(4(0(0(x1))))) = [1] >= [0] = 0#(4(1(0(x1))))
    
    0#(1(4(0(0(x1))))) = [1] >= [0] = 0#(0(4(1(0(x1)))))
    
    0#(1(4(0(0(x1))))) = [1] >= [0] = 0#(0(0(4(1(0(x1))))))
    
    0#(1(4(5(0(x1))))) = [1] >= [0] = 0#(4(2(x1)))
    
    0#(1(4(5(0(x1))))) = [1] >= [0] = 0#(0(4(2(x1))))
    
    0#(1(4(5(0(x1))))) = [1] >= [0] = 5#(0(0(4(2(x1)))))
    
    0#(3(0(1(0(x1))))) = [3 1 1]x1 + [3] >= [0] = 0#(2(1(x1)))
    
    0#(3(0(1(0(x1))))) = [3 1 1]x1 + [3] >= [0] = 0#(0(2(1(x1))))
    
    0#(3(0(1(0(x1))))) = [3 1 1]x1 + [3] >= [0] = 3#(0(0(2(1(x1)))))
    
    0#(3(0(1(0(x1))))) = [3 1 1]x1 + [3] >= [0] = 0#(3(0(0(2(1(x1))))))
    
    3#(0(3(1(0(x1))))) = [2 1 1]x1 + [2] >= [0 1 1]x1 = 3#(0(x1))
    
    3#(0(3(1(0(x1))))) = [2 1 1]x1 + [2] >= [0] = 3#(2(3(0(x1))))
    
    3#(0(3(1(0(x1))))) = [2 1 1]x1 + [2] >= [1] = 0#(1(3(2(3(0(x1))))))
    
    5#(0(1(2(0(x1))))) = [1] >= [0] = 5#(2(1(0(x1))))
    
    5#(0(1(2(0(x1))))) = [1] >= [0] = 0#(5(2(1(0(x1)))))
    
    5#(0(1(2(0(x1))))) = [1] >= [0] = 0#(0(5(2(1(0(x1))))))
    
                  [1 1 1]     [1]    [0]                 
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0(2(1(0(x1))))
                  [0 0 0]     [0]    [0]                 
    
                  [1 1 1]     [1]    [0]                    
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0(0(2(1(0(x1)))))
                  [0 0 0]     [0]    [0]                    
    
                  [1 1 1]     [1]    [0]                    
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0(0(2(1(2(x1)))))
                  [0 0 0]     [0]    [0]                    
    
                  [1 1 1]     [1]    [0]                    
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0(2(1(0(2(x1)))))
                  [0 0 0]     [0]    [0]                    
    
                  [1 1 1]     [1]    [0]                    
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0(3(2(1(0(x1)))))
                  [0 0 0]     [0]    [0]                    
    
                  [1 1 1]     [1]    [0]                    
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [1] = 1(0(0(0(2(x1)))))
                  [0 0 0]     [0]    [0]                    
    
                  [1 1 1]     [1]    [0]                    
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [1] = 1(0(0(2(0(x1)))))
                  [0 0 0]     [0]    [0]                    
    
                  [1 1 1]     [1]    [0]                    
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [1] = 1(0(4(2(0(x1)))))
                  [0 0 0]     [0]    [0]                    
    
                  [1 1 1]     [1]    [0]                    
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [1] = 1(4(0(4(0(x1)))))
                  [0 0 0]     [0]    [0]                    
    
                  [1 1 1]     [1]    [0]                    
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 4(0(0(2(1(x1)))))
                  [0 0 0]     [0]    [0]                    
    
                  [1 1 1]     [1]    [0]                    
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5(0(0(4(1(x1)))))
                  [0 0 0]     [0]    [0]                    
    
                  [1 1 1]     [1]    [0]                    
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5(1(0(4(0(x1)))))
                  [0 0 0]     [0]    [0]                    
    
                  [1 1 1]     [1]    [0]                       
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0(2(1(0(3(2(x1))))))
                  [0 0 0]     [0]    [0]                       
    
                  [1 1 1]     [1]    [0]                       
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0(4(0(4(1(3(x1))))))
                  [0 0 0]     [0]    [0]                       
    
                  [1 1 1]     [1]    [0]                       
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0(4(2(2(1(0(x1))))))
                  [0 0 0]     [0]    [0]                       
    
                  [1 1 1]     [1]    [0]                       
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0(5(2(1(2(0(x1))))))
                  [0 0 0]     [0]    [0]                       
    
                  [1 1 1]     [1]    [0]                       
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 0(5(2(5(1(0(x1))))))
                  [0 0 0]     [0]    [0]                       
    
                  [1 1 1]     [1]    [0]                       
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [1] = 1(0(0(5(4(4(x1))))))
                  [0 0 0]     [0]    [0]                       
    
                  [1 1 1]     [1]    [0]                       
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [1] = 1(0(4(4(4(0(x1))))))
                  [0 0 0]     [0]    [0]                       
    
                  [1 1 1]     [1]    [0]                       
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [1] = 1(5(0(0(4(2(x1))))))
                  [0 0 0]     [0]    [0]                       
    
                  [1 1 1]     [1]    [0]                       
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 3(0(0(4(1(4(x1))))))
                  [0 0 0]     [0]    [0]                       
    
                  [1 1 1]     [1]    [0]                       
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 4(5(1(0(2(0(x1))))))
                  [0 0 0]     [0]    [0]                       
    
                  [1 1 1]     [1]    [0]                       
    0(1(0(x1))) = [1 0 0]x1 + [1] >= [0] = 5(5(1(0(0(2(x1))))))
                  [0 0 0]     [0]    [0]                       
    
                     [1 0 0]     [1]    [0]                    
    0(0(1(0(x1)))) = [1 0 0]x1 + [1] >= [1] = 1(0(0(2(0(x1)))))
                     [1 1 1]     [1]    [0]                    
    
                     [1 0 0]     [1]    [1]                       
    0(0(1(0(x1)))) = [1 0 0]x1 + [1] >= [1] = 0(1(5(0(0(2(x1))))))
                     [1 1 1]     [1]    [0]                       
    
                     [1 3 1]     [1]    [0]                       
    0(1(0(3(x1)))) = [1 1 0]x1 + [1] >= [1] = 1(0(3(3(0(2(x1))))))
                     [0 0 0]     [0]    [0]                       
    
                     [1 3 1]     [1]    [0]                       
    0(1(0(3(x1)))) = [1 1 0]x1 + [1] >= [1] = 1(0(5(3(2(0(x1))))))
                     [0 0 0]     [0]    [0]                       
    
                     [0 1 1]     [1]    [0]                       
    0(1(1(0(x1)))) = [0 1 1]x1 + [1] >= [0] = 0(4(4(1(1(0(x1))))))
                     [0 0 0]     [0]    [0]                       
    
                     [1 1 0]     [1]    [0]                       
    0(1(1(3(x1)))) = [1 1 0]x1 + [1] >= [0] = 3(4(5(1(1(0(x1))))))
                     [0 0 0]     [0]    [0]                       
    
                     [1]    [0]                    
    0(1(2(0(x1)))) = [1] >= [1] = 1(1(0(2(0(x1)))))
                     [0]    [0]                    
    
                     [1]    [0]                    
    0(1(2(0(x1)))) = [1] >= [0] = 3(0(2(1(0(x1)))))
                     [0]    [0]                    
    
                     [1]    [0]                    
    0(1(2(0(x1)))) = [1] >= [0] = 4(1(0(0(2(x1)))))
                     [0]    [0]                    
    
                     [1]    [0]                       
    0(1(2(0(x1)))) = [1] >= [0] = 0(0(4(2(5(1(x1))))))
                     [0]    [0]                       
    
                     [1]    [0]                       
    0(1(2(0(x1)))) = [1] >= [1] = 1(1(2(0(4(0(x1))))))
                     [0]    [0]                       
    
                     [1]    [0]                       
    0(1(2(0(x1)))) = [1] >= [0] = 3(0(2(1(0(4(x1))))))
                     [0]    [0]                       
    
                     [0 3 1]     [1]    [0]                    
    0(1(3(0(x1)))) = [0 1 0]x1 + [1] >= [1] = 1(0(3(0(2(x1)))))
                     [0 0 0]     [0]    [0]                    
    
                     [1]    [0]                       
    0(1(4(0(x1)))) = [1] >= [0] = 0(3(4(2(1(0(x1))))))
                     [0]    [0]                       
    
                     [1 0 0]     [1]    [0]                    
    0(1(5(0(x1)))) = [0 0 0]x1 + [1] >= [0] = 0(5(1(4(0(x1)))))
                     [0 0 0]     [0]    [0]                    
    
                     [1 0 0]     [1]    [0]                       
    0(1(5(0(x1)))) = [0 0 0]x1 + [1] >= [1] = 1(5(3(0(2(0(x1))))))
                     [0 0 0]     [0]    [0]                       
    
                     [2 1 1]     [2]    [0]                       
    0(3(1(0(x1)))) = [1 1 1]x1 + [1] >= [1] = 1(2(3(0(5(0(x1))))))
                     [1 0 0]     [1]    [0]                       
    
                     [0 0 0]     [0]    [0]                       
    5(0(1(0(x1)))) = [1 1 1]x1 + [1] >= [1] = 1(4(0(0(5(1(x1))))))
                     [0 0 0]     [0]    [0]                       
    
                     [0 0 0]     [0]    [0]                       
    5(0(1(0(x1)))) = [1 1 1]x1 + [1] >= [0] = 2(1(0(0(4(5(x1))))))
                     [0 0 0]     [0]    [0]                       
    
                        [1 3 1]     [1]    [1 1 0]                         
    0(1(0(0(0(x1))))) = [1 1 0]x1 + [1] >= [0 0 0]x1 = 0(0(5(1(0(0(x1))))))
                        [0 0 0]     [0]    [0 0 0]                         
    
                        [1]    [0]                       
    0(1(2(4(0(x1))))) = [1] >= [0] = 0(0(5(4(2(1(x1))))))
                        [0]    [0]                       
    
                        [1]    [0]                       
    0(1(2(5(0(x1))))) = [1] >= [1] = 1(0(2(0(5(4(x1))))))
                        [0]    [0]                       
    
                        [1]    [0]                       
    0(1(4(0(0(x1))))) = [1] >= [0] = 0(0(0(4(1(0(x1))))))
                        [0]    [0]                       
    
                        [1]    [0]                       
    0(1(4(5(0(x1))))) = [1] >= [1] = 1(5(0(0(4(2(x1))))))
                        [0]    [0]                       
    
                        [2 0 0]     [2]    [0]                       
    0(3(0(1(0(x1))))) = [1 0 0]x1 + [1] >= [0] = 0(3(0(0(2(1(x1))))))
                        [2 1 1]     [2]    [0]                       
    
                        [3 2 2]     [3]    [1]                       
    3(0(3(1(0(x1))))) = [2 1 1]x1 + [2] >= [1] = 0(1(3(2(3(0(x1))))))
                        [1 1 1]     [1]    [0]                       
    
                        [0]    [0]                       
    5(0(1(2(0(x1))))) = [1] >= [0] = 0(0(5(2(1(0(x1))))))
                        [0]    [0]                       
   problem:
    DPs:
     
    TRS:
     0(1(0(x1))) -> 0(2(1(0(x1))))
     0(1(0(x1))) -> 0(0(2(1(0(x1)))))
     0(1(0(x1))) -> 0(0(2(1(2(x1)))))
     0(1(0(x1))) -> 0(2(1(0(2(x1)))))
     0(1(0(x1))) -> 0(3(2(1(0(x1)))))
     0(1(0(x1))) -> 1(0(0(0(2(x1)))))
     0(1(0(x1))) -> 1(0(0(2(0(x1)))))
     0(1(0(x1))) -> 1(0(4(2(0(x1)))))
     0(1(0(x1))) -> 1(4(0(4(0(x1)))))
     0(1(0(x1))) -> 4(0(0(2(1(x1)))))
     0(1(0(x1))) -> 5(0(0(4(1(x1)))))
     0(1(0(x1))) -> 5(1(0(4(0(x1)))))
     0(1(0(x1))) -> 0(2(1(0(3(2(x1))))))
     0(1(0(x1))) -> 0(4(0(4(1(3(x1))))))
     0(1(0(x1))) -> 0(4(2(2(1(0(x1))))))
     0(1(0(x1))) -> 0(5(2(1(2(0(x1))))))
     0(1(0(x1))) -> 0(5(2(5(1(0(x1))))))
     0(1(0(x1))) -> 1(0(0(5(4(4(x1))))))
     0(1(0(x1))) -> 1(0(4(4(4(0(x1))))))
     0(1(0(x1))) -> 1(5(0(0(4(2(x1))))))
     0(1(0(x1))) -> 3(0(0(4(1(4(x1))))))
     0(1(0(x1))) -> 4(5(1(0(2(0(x1))))))
     0(1(0(x1))) -> 5(5(1(0(0(2(x1))))))
     0(0(1(0(x1)))) -> 1(0(0(2(0(x1)))))
     0(0(1(0(x1)))) -> 0(1(5(0(0(2(x1))))))
     0(1(0(3(x1)))) -> 1(0(3(3(0(2(x1))))))
     0(1(0(3(x1)))) -> 1(0(5(3(2(0(x1))))))
     0(1(1(0(x1)))) -> 0(4(4(1(1(0(x1))))))
     0(1(1(3(x1)))) -> 3(4(5(1(1(0(x1))))))
     0(1(2(0(x1)))) -> 1(1(0(2(0(x1)))))
     0(1(2(0(x1)))) -> 3(0(2(1(0(x1)))))
     0(1(2(0(x1)))) -> 4(1(0(0(2(x1)))))
     0(1(2(0(x1)))) -> 0(0(4(2(5(1(x1))))))
     0(1(2(0(x1)))) -> 1(1(2(0(4(0(x1))))))
     0(1(2(0(x1)))) -> 3(0(2(1(0(4(x1))))))
     0(1(3(0(x1)))) -> 1(0(3(0(2(x1)))))
     0(1(4(0(x1)))) -> 0(3(4(2(1(0(x1))))))
     0(1(5(0(x1)))) -> 0(5(1(4(0(x1)))))
     0(1(5(0(x1)))) -> 1(5(3(0(2(0(x1))))))
     0(3(1(0(x1)))) -> 1(2(3(0(5(0(x1))))))
     5(0(1(0(x1)))) -> 1(4(0(0(5(1(x1))))))
     5(0(1(0(x1)))) -> 2(1(0(0(4(5(x1))))))
     0(1(0(0(0(x1))))) -> 0(0(5(1(0(0(x1))))))
     0(1(2(4(0(x1))))) -> 0(0(5(4(2(1(x1))))))
     0(1(2(5(0(x1))))) -> 1(0(2(0(5(4(x1))))))
     0(1(4(0(0(x1))))) -> 0(0(0(4(1(0(x1))))))
     0(1(4(5(0(x1))))) -> 1(5(0(0(4(2(x1))))))
     0(3(0(1(0(x1))))) -> 0(3(0(0(2(1(x1))))))
     3(0(3(1(0(x1))))) -> 0(1(3(2(3(0(x1))))))
     5(0(1(2(0(x1))))) -> 0(0(5(2(1(0(x1))))))
   Qed