31.89/8.53	YES
31.89/8.54	
31.89/8.54	Problem:
31.89/8.54	 0(0(1(x1))) -> 0(1(2(0(x1))))
31.89/8.54	 0(0(1(x1))) -> 0(3(1(0(x1))))
31.89/8.54	 0(0(1(x1))) -> 1(0(4(0(x1))))
31.89/8.54	 0(0(1(x1))) -> 0(1(3(0(2(x1)))))
31.89/8.54	 0(0(1(x1))) -> 0(1(3(0(4(x1)))))
31.89/8.54	 0(0(1(x1))) -> 0(2(0(1(2(x1)))))
31.89/8.54	 0(0(1(x1))) -> 0(3(0(1(2(x1)))))
31.89/8.54	 0(0(1(x1))) -> 0(3(0(3(1(x1)))))
31.89/8.54	 0(0(1(x1))) -> 0(4(0(4(1(x1)))))
31.89/8.54	 0(0(1(x1))) -> 1(2(0(2(0(x1)))))
31.89/8.54	 0(0(1(x1))) -> 1(2(2(0(0(x1)))))
31.89/8.54	 0(0(1(x1))) -> 0(0(2(2(1(2(x1))))))
31.89/8.54	 0(0(1(x1))) -> 0(1(2(4(2(0(x1))))))
31.89/8.54	 0(0(1(x1))) -> 1(2(0(3(0(4(x1))))))
31.89/8.54	 0(1(1(x1))) -> 0(2(1(1(x1))))
31.89/8.54	 0(1(1(x1))) -> 0(3(1(1(x1))))
31.89/8.54	 0(1(1(x1))) -> 1(1(3(0(4(x1)))))
31.89/8.54	 0(1(1(x1))) -> 1(2(0(2(1(x1)))))
31.89/8.54	 0(1(1(x1))) -> 1(0(3(1(2(4(x1))))))
31.89/8.54	 0(1(1(x1))) -> 1(0(4(2(1(2(x1))))))
31.89/8.54	 0(1(1(x1))) -> 1(1(2(4(3(0(x1))))))
31.89/8.54	 0(1(1(x1))) -> 1(2(1(0(4(4(x1))))))
31.89/8.54	 0(1(1(x1))) -> 1(2(2(1(3(0(x1))))))
31.89/8.54	 0(5(1(x1))) -> 0(3(1(5(x1))))
31.89/8.54	 0(5(1(x1))) -> 0(4(5(1(x1))))
31.89/8.54	 0(5(1(x1))) -> 0(2(3(1(5(x1)))))
31.89/8.54	 0(5(1(x1))) -> 0(3(1(5(2(x1)))))
31.89/8.54	 0(5(1(x1))) -> 0(3(1(2(5(2(x1))))))
31.89/8.54	 5(0(1(x1))) -> 5(1(2(4(0(x1)))))
31.89/8.54	 5(0(1(x1))) -> 5(0(2(1(2(4(x1))))))
31.89/8.54	 5(0(1(x1))) -> 5(1(2(3(0(4(x1))))))
31.89/8.54	 0(0(1(5(x1)))) -> 0(4(1(0(5(x1)))))
31.89/8.54	 0(0(2(1(x1)))) -> 2(0(3(0(2(1(x1))))))
31.89/8.54	 0(0(2(1(x1)))) -> 2(3(0(2(0(1(x1))))))
31.89/8.54	 0(1(0(1(x1)))) -> 1(0(2(0(1(x1)))))
31.89/8.54	 0(1(1(1(x1)))) -> 1(1(3(1(0(x1)))))
31.89/8.54	 5(0(1(1(x1)))) -> 1(5(1(2(0(x1)))))
31.89/8.54	 5(3(0(1(x1)))) -> 5(1(2(3(0(x1)))))
31.89/8.54	 5(3(1(5(x1)))) -> 5(3(1(2(5(x1)))))
31.89/8.54	 5(3(2(1(x1)))) -> 1(2(3(5(2(x1)))))
31.89/8.54	 5(4(0(1(x1)))) -> 1(2(5(0(4(x1)))))
31.89/8.54	 0(0(5(1(5(x1))))) -> 1(2(5(5(0(0(x1))))))
31.89/8.54	 0(5(3(0(1(x1))))) -> 1(0(5(3(0(4(x1))))))
31.89/8.54	 0(5(3(4(1(x1))))) -> 1(0(3(5(4(5(x1))))))
31.89/8.54	 0(5(4(0(1(x1))))) -> 0(1(3(0(4(5(x1))))))
31.89/8.54	 5(4(2(1(1(x1))))) -> 5(4(1(2(1(2(x1))))))
31.89/8.54	
31.89/8.54	Proof:
31.89/8.54	 Matrix Interpretation Processor: dim=1
31.89/8.54	  
31.89/8.54	  interpretation:
31.89/8.54	   [5](x0) = x0,
31.89/8.54	   
31.89/8.54	   [4](x0) = x0,
31.89/8.54	   
31.89/8.54	   [3](x0) = x0,
31.89/8.54	   
31.89/8.54	   [2](x0) = x0,
31.89/8.54	   
31.89/8.54	   [0](x0) = 2x0,
31.89/8.54	   
31.89/8.54	   [1](x0) = 2x0 + 2
31.89/8.54	  orientation:
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 4 = 0(1(2(0(x1))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 4 = 0(3(1(0(x1))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 2 = 1(0(4(0(x1))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 4 = 0(1(3(0(2(x1)))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 4 = 0(1(3(0(4(x1)))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 8 = 0(2(0(1(2(x1)))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 8 = 0(3(0(1(2(x1)))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 8 = 0(3(0(3(1(x1)))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 8 = 0(4(0(4(1(x1)))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 2 = 1(2(0(2(0(x1)))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 2 = 1(2(2(0(0(x1)))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 8 = 0(0(2(2(1(2(x1))))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 4 = 0(1(2(4(2(0(x1))))))
31.89/8.54	   
31.89/8.54	   0(0(1(x1))) = 8x1 + 8 >= 8x1 + 2 = 1(2(0(3(0(4(x1))))))
31.89/8.54	   
31.89/8.54	   0(1(1(x1))) = 8x1 + 12 >= 8x1 + 12 = 0(2(1(1(x1))))
31.89/8.54	   
31.89/8.54	   0(1(1(x1))) = 8x1 + 12 >= 8x1 + 12 = 0(3(1(1(x1))))
31.89/8.54	   
31.89/8.54	   0(1(1(x1))) = 8x1 + 12 >= 8x1 + 6 = 1(1(3(0(4(x1)))))
31.89/8.54	   
31.89/8.54	   0(1(1(x1))) = 8x1 + 12 >= 8x1 + 10 = 1(2(0(2(1(x1)))))
31.89/8.54	   
31.89/8.54	   0(1(1(x1))) = 8x1 + 12 >= 8x1 + 10 = 1(0(3(1(2(4(x1))))))
31.89/8.54	   
31.89/8.54	   0(1(1(x1))) = 8x1 + 12 >= 8x1 + 10 = 1(0(4(2(1(2(x1))))))
31.89/8.54	   
31.89/8.54	   0(1(1(x1))) = 8x1 + 12 >= 8x1 + 6 = 1(1(2(4(3(0(x1))))))
31.89/8.54	   
31.89/8.54	   0(1(1(x1))) = 8x1 + 12 >= 8x1 + 6 = 1(2(1(0(4(4(x1))))))
31.89/8.54	   
31.89/8.54	   0(1(1(x1))) = 8x1 + 12 >= 8x1 + 6 = 1(2(2(1(3(0(x1))))))
31.89/8.54	   
31.89/8.54	   0(5(1(x1))) = 4x1 + 4 >= 4x1 + 4 = 0(3(1(5(x1))))
31.89/8.54	   
31.89/8.54	   0(5(1(x1))) = 4x1 + 4 >= 4x1 + 4 = 0(4(5(1(x1))))
31.89/8.54	   
31.89/8.54	   0(5(1(x1))) = 4x1 + 4 >= 4x1 + 4 = 0(2(3(1(5(x1)))))
31.89/8.54	   
31.89/8.54	   0(5(1(x1))) = 4x1 + 4 >= 4x1 + 4 = 0(3(1(5(2(x1)))))
31.89/8.54	   
31.89/8.54	   0(5(1(x1))) = 4x1 + 4 >= 4x1 + 4 = 0(3(1(2(5(2(x1))))))
31.89/8.54	   
31.89/8.54	   5(0(1(x1))) = 4x1 + 4 >= 4x1 + 2 = 5(1(2(4(0(x1)))))
31.89/8.54	   
31.89/8.54	   5(0(1(x1))) = 4x1 + 4 >= 4x1 + 4 = 5(0(2(1(2(4(x1))))))
31.89/8.54	   
31.89/8.54	   5(0(1(x1))) = 4x1 + 4 >= 4x1 + 2 = 5(1(2(3(0(4(x1))))))
31.89/8.54	   
31.89/8.54	   0(0(1(5(x1)))) = 8x1 + 8 >= 8x1 + 4 = 0(4(1(0(5(x1)))))
31.89/8.54	   
31.89/8.54	   0(0(2(1(x1)))) = 8x1 + 8 >= 8x1 + 8 = 2(0(3(0(2(1(x1))))))
31.89/8.54	   
31.89/8.54	   0(0(2(1(x1)))) = 8x1 + 8 >= 8x1 + 8 = 2(3(0(2(0(1(x1))))))
31.89/8.54	   
31.89/8.54	   0(1(0(1(x1)))) = 16x1 + 20 >= 16x1 + 18 = 1(0(2(0(1(x1)))))
31.89/8.54	   
31.89/8.54	   0(1(1(1(x1)))) = 16x1 + 28 >= 16x1 + 14 = 1(1(3(1(0(x1)))))
31.89/8.54	   
31.89/8.54	   5(0(1(1(x1)))) = 8x1 + 12 >= 8x1 + 6 = 1(5(1(2(0(x1)))))
31.89/8.55	   
31.89/8.55	   5(3(0(1(x1)))) = 4x1 + 4 >= 4x1 + 2 = 5(1(2(3(0(x1)))))
31.89/8.55	   
31.89/8.55	   5(3(1(5(x1)))) = 2x1 + 2 >= 2x1 + 2 = 5(3(1(2(5(x1)))))
31.89/8.55	   
31.89/8.55	   5(3(2(1(x1)))) = 2x1 + 2 >= 2x1 + 2 = 1(2(3(5(2(x1)))))
31.89/8.55	   
31.89/8.55	   5(4(0(1(x1)))) = 4x1 + 4 >= 4x1 + 2 = 1(2(5(0(4(x1)))))
31.89/8.55	   
31.89/8.55	   0(0(5(1(5(x1))))) = 8x1 + 8 >= 8x1 + 2 = 1(2(5(5(0(0(x1))))))
31.89/8.55	   
31.89/8.55	   0(5(3(0(1(x1))))) = 8x1 + 8 >= 8x1 + 2 = 1(0(5(3(0(4(x1))))))
31.89/8.55	   
31.89/8.55	   0(5(3(4(1(x1))))) = 4x1 + 4 >= 4x1 + 2 = 1(0(3(5(4(5(x1))))))
31.89/8.55	   
31.89/8.55	   0(5(4(0(1(x1))))) = 8x1 + 8 >= 8x1 + 4 = 0(1(3(0(4(5(x1))))))
31.89/8.55	   
31.89/8.55	   5(4(2(1(1(x1))))) = 4x1 + 6 >= 4x1 + 6 = 5(4(1(2(1(2(x1))))))
31.89/8.55	  problem:
31.89/8.55	   0(0(1(x1))) -> 0(2(0(1(2(x1)))))
31.89/8.55	   0(0(1(x1))) -> 0(3(0(1(2(x1)))))
31.89/8.55	   0(0(1(x1))) -> 0(3(0(3(1(x1)))))
31.89/8.55	   0(0(1(x1))) -> 0(4(0(4(1(x1)))))
31.89/8.55	   0(0(1(x1))) -> 0(0(2(2(1(2(x1))))))
31.89/8.55	   0(1(1(x1))) -> 0(2(1(1(x1))))
31.89/8.55	   0(1(1(x1))) -> 0(3(1(1(x1))))
31.89/8.55	   0(5(1(x1))) -> 0(3(1(5(x1))))
31.89/8.55	   0(5(1(x1))) -> 0(4(5(1(x1))))
31.89/8.55	   0(5(1(x1))) -> 0(2(3(1(5(x1)))))
31.89/8.55	   0(5(1(x1))) -> 0(3(1(5(2(x1)))))
31.89/8.55	   0(5(1(x1))) -> 0(3(1(2(5(2(x1))))))
31.89/8.55	   5(0(1(x1))) -> 5(0(2(1(2(4(x1))))))
31.89/8.55	   0(0(2(1(x1)))) -> 2(0(3(0(2(1(x1))))))
31.89/8.55	   0(0(2(1(x1)))) -> 2(3(0(2(0(1(x1))))))
31.89/8.55	   5(3(1(5(x1)))) -> 5(3(1(2(5(x1)))))
31.89/8.55	   5(3(2(1(x1)))) -> 1(2(3(5(2(x1)))))
31.89/8.55	   5(4(2(1(1(x1))))) -> 5(4(1(2(1(2(x1))))))
31.89/8.55	  Bounds Processor:
31.89/8.55	   bound: 0
31.89/8.55	   enrichment: match
31.89/8.55	   automaton:
31.89/8.55	    final states: {67,64,60,55,50,44,40,36,34,31,27,25,22,18,14,9,7,1}
31.89/8.55	    transitions:
31.89/8.55	     f60() -> 2*
31.89/8.55	     00(35) -> 34*
31.89/8.55	     00(30) -> 27*
31.89/8.55	     00(20) -> 21*
31.89/8.55	     00(15) -> 16*
31.89/8.55	     00(10) -> 56*
31.89/8.55	     00(57) -> 58*
31.89/8.55	     00(17) -> 14*
31.89/8.55	     00(39) -> 36*
31.89/8.55	     00(24) -> 22*
31.89/8.55	     00(4) -> 5*
31.89/8.55	     00(51) -> 52*
31.89/8.55	     00(26) -> 25*
31.89/8.55	     00(21) -> 18*
31.89/8.55	     00(11) -> 12*
31.89/8.55	     00(6) -> 1*
31.89/8.55	     00(53) -> 54*
31.89/8.55	     00(48) -> 49*
31.89/8.55	     00(43) -> 40*
31.89/8.55	     00(33) -> 31*
31.89/8.55	     00(13) -> 9*
31.89/8.55	     00(8) -> 7*
31.89/8.55	     20(65) -> 66*
31.89/8.55	     20(45) -> 46*
31.89/8.55	     20(30) -> 35*
31.89/8.55	     20(10) -> 51*
31.89/8.55	     20(5) -> 6*
31.89/8.55	     20(47) -> 48*
31.89/8.55	     20(37) -> 41*
31.89/8.55	     20(2) -> 3*
31.89/8.55	     20(59) -> 55*
31.89/8.55	     20(54) -> 50*
31.89/8.55	     20(19) -> 20*
31.89/8.55	     20(4) -> 19*
31.89/8.55	     20(56) -> 57*
31.89/8.55	     20(28) -> 61*
31.89/8.55	     20(23) -> 24*
31.89/8.55	     10(10) -> 23*
31.89/8.55	     10(37) -> 38*
31.89/8.55	     10(2) -> 10*
31.89/8.55	     10(19) -> 68*
31.89/8.55	     10(66) -> 64*
31.89/8.55	     10(61) -> 62*
31.89/8.55	     10(46) -> 47*
31.89/8.55	     10(41) -> 42*
31.89/8.55	     10(28) -> 29*
31.89/8.55	     10(3) -> 4*
31.89/8.55	     30(10) -> 11*
31.89/8.55	     30(5) -> 8*
31.89/8.55	     30(62) -> 63*
31.89/8.55	     30(52) -> 53*
31.89/8.55	     30(42) -> 43*
31.89/8.55	     30(37) -> 65*
31.89/8.55	     30(12) -> 13*
31.89/8.55	     30(29) -> 30*
31.89/8.55	     30(58) -> 59*
31.89/8.55	     30(38) -> 39*
31.89/8.55	     30(23) -> 26*
31.89/8.55	     40(10) -> 15*
31.89/8.55	     40(32) -> 33*
31.89/8.55	     40(2) -> 45*
31.89/8.55	     40(16) -> 17*
31.89/8.55	     40(68) -> 69*
31.89/8.55	     50(10) -> 32*
31.89/8.55	     50(2) -> 28*
31.89/8.55	     50(69) -> 67*
31.89/8.55	     50(49) -> 44*
31.89/8.55	     50(63) -> 60*
31.89/8.55	     50(3) -> 37*
31.89/8.55	     22 -> 56*
31.89/8.55	     25 -> 56*
31.89/8.55	     44 -> 28*
31.89/8.55	     60 -> 28*
31.89/8.55	     64 -> 28*
31.89/8.55	     67 -> 28*
31.89/8.55	   problem:
31.89/8.55	    
31.89/8.55	   Qed
31.89/8.55	EOF