YES

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

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