14.71/4.11	YES
14.71/4.12	
14.71/4.12	Problem:
14.71/4.12	 twoto(0(x1)) -> p(p(s(s(s(p(p(p(s(s(s(0(p(p(s(s(x1))))))))))))))))
14.71/4.12	 twoto(s(x1)) ->
14.71/4.12	 p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))
14.71/4.12	 twice(0(x1)) -> p(s(p(s(0(s(p(s(s(s(s(p(s(x1)))))))))))))
14.71/4.12	 twice(s(x1)) -> s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(x1)))))))))))))))))))
14.71/4.12	 p(p(s(x1))) -> p(x1)
14.71/4.12	 p(s(x1)) -> x1
14.71/4.12	 p(0(x1)) -> 0(s(s(s(s(p(s(x1)))))))
14.71/4.12	 0(x1) -> x1
14.71/4.12	
14.71/4.12	Proof:
14.71/4.12	 Matrix Interpretation Processor: dim=1
14.71/4.12	  
14.71/4.12	  interpretation:
14.71/4.12	   [twice](x0) = x0,
14.71/4.12	   
14.71/4.12	   [p](x0) = x0,
14.71/4.12	   
14.71/4.12	   [s](x0) = x0,
14.71/4.12	   
14.71/4.12	   [twoto](x0) = 4x0,
14.71/4.12	   
14.71/4.12	   [0](x0) = 4x0 + 2
14.71/4.12	  orientation:
14.71/4.12	   twoto(0(x1)) = 16x1 + 8 >= 4x1 + 2 = p(p(s(s(s(p(p(p(s(s(s(0(p(p(s(s(x1))))))))))))))))
14.71/4.12	   
14.71/4.12	   twoto(s(x1)) = 4x1 >= 4x1 = p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))
14.71/4.12	   
14.71/4.12	   twice(0(x1)) = 4x1 + 2 >= 4x1 + 2 = p(s(p(s(0(s(p(s(s(s(s(p(s(x1)))))))))))))
14.71/4.12	   
14.71/4.12	   twice(s(x1)) = x1 >= x1 = s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(x1)))))))))))))))))))
14.71/4.12	   
14.71/4.12	   p(p(s(x1))) = x1 >= x1 = p(x1)
14.71/4.12	   
14.71/4.12	   p(s(x1)) = x1 >= x1 = x1
14.71/4.12	   
14.71/4.12	   p(0(x1)) = 4x1 + 2 >= 4x1 + 2 = 0(s(s(s(s(p(s(x1)))))))
14.71/4.12	   
14.71/4.12	   0(x1) = 4x1 + 2 >= x1 = x1
14.71/4.12	  problem:
14.71/4.12	   twoto(s(x1)) ->
14.71/4.12	   p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))
14.71/4.12	   twice(0(x1)) -> p(s(p(s(0(s(p(s(s(s(s(p(s(x1)))))))))))))
14.71/4.12	   twice(s(x1)) -> s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(x1)))))))))))))))))))
14.71/4.12	   p(p(s(x1))) -> p(x1)
14.71/4.12	   p(s(x1)) -> x1
14.71/4.12	   p(0(x1)) -> 0(s(s(s(s(p(s(x1)))))))
14.71/4.12	  Bounds Processor:
14.71/4.12	   bound: 1
14.71/4.12	   enrichment: match
14.71/4.12	   automaton:
14.71/4.12	    final states: {54,2,53,38,28,1}
14.71/4.12	    transitions:
14.71/4.12	     p1(55) -> 56*
14.71/4.12	     p1(87) -> 88*
14.71/4.12	     p1(77) -> 78*
14.71/4.12	     p1(79) -> 80*
14.71/4.12	     p1(69) -> 70*
14.71/4.12	     p1(71) -> 72*
14.71/4.12	     p1(61) -> 62*
14.71/4.12	     p1(63) -> 64*
14.71/4.12	     p1(85) -> 86*
14.71/4.12	     f50() -> 2*
14.71/4.12	     p0(50) -> 51*
14.71/4.12	     p0(35) -> 36*
14.71/4.12	     p0(15) -> 16*
14.71/4.12	     p0(10) -> 11*
14.71/4.12	     p0(5) -> 6*
14.71/4.12	     p0(37) -> 28*
14.71/4.12	     p0(27) -> 1*
14.71/4.12	     p0(22) -> 23*
14.71/4.12	     p0(12) -> 13*
14.71/4.12	     p0(2) -> 53*
14.71/4.12	     p0(49) -> 50*
14.71/4.12	     p0(39) -> 40*
14.71/4.12	     p0(51) -> 52*
14.71/4.12	     p0(41) -> 42*
14.71/4.12	     p0(31) -> 32*
14.71/4.12	     p0(26) -> 27*
14.71/4.12	     p0(21) -> 22*
14.71/4.12	     p0(16) -> 17*
14.71/4.12	     p0(11) -> 12*
14.71/4.12	     p0(48) -> 49*
14.71/4.12	     p0(23) -> 24*
14.71/4.12	     p0(3) -> 4*
14.71/4.12	     s0(45) -> 46*
14.71/4.12	     s0(40) -> 41*
14.71/4.12	     s0(30) -> 31*
14.71/4.12	     s0(25) -> 26*
14.71/4.12	     s0(20) -> 21*
14.71/4.12	     s0(5) -> 29*
14.71/4.12	     s0(52) -> 38*
14.71/4.12	     s0(47) -> 48*
14.71/4.12	     s0(32) -> 33*
14.71/4.12	     s0(7) -> 8*
14.71/4.12	     s0(2) -> 3*
14.71/4.12	     s0(44) -> 45*
14.71/4.12	     s0(34) -> 35*
14.71/4.12	     s0(29) -> 30*
14.71/4.12	     s0(24) -> 25*
14.71/4.12	     s0(19) -> 20*
14.71/4.12	     s0(14) -> 15*
14.71/4.12	     s0(9) -> 10*
14.71/4.12	     s0(4) -> 5*
14.71/4.12	     s0(46) -> 47*
14.71/4.12	     s0(36) -> 37*
14.71/4.12	     s0(6) -> 39*
14.71/4.12	     s0(43) -> 44*
14.71/4.12	     s0(18) -> 19*
14.71/4.12	     s0(13) -> 14*
14.71/4.12	     s0(8) -> 9*
14.71/4.12	     twice0(42) -> 43*
14.71/4.12	     twice0(17) -> 18*
14.71/4.12	     twoto0(6) -> 7*
14.71/4.12	     00(31) -> 54*
14.71/4.12	     00(33) -> 34*
14.71/4.12	     1 -> 7,78,13,17
14.71/4.12	     2 -> 53,4
14.71/4.12	     4 -> 6*
14.71/4.12	     6 -> 40*
14.71/4.12	     7 -> 78*
14.71/4.12	     8 -> 64,12,77
14.71/4.12	     9 -> 11,63
14.71/4.12	     13 -> 62*
14.71/4.12	     14 -> 16,61
14.71/4.12	     18 -> 80,24,72
14.71/4.12	     19 -> 56,23,79
14.71/4.12	     20 -> 22,55
14.71/4.12	     24 -> 72,1
14.71/4.12	     25 -> 27,71
14.71/4.12	     28 -> 43*
14.71/4.12	     30 -> 32*
14.71/4.12	     34 -> 53,36
14.71/4.12	     36 -> 28*
14.71/4.12	     38 -> 43*
14.71/4.12	     40 -> 42*
14.71/4.12	     44 -> 88*
14.71/4.12	     45 -> 86,87
14.71/4.12	     46 -> 70,85
14.71/4.12	     47 -> 49,69
14.71/4.12	     56 -> 23*
14.71/4.12	     62 -> 17*
14.71/4.12	     64 -> 12*
14.71/4.12	     70 -> 50*
14.71/4.12	     72 -> 1*
14.71/4.12	     78 -> 13*
14.71/4.12	     80 -> 24*
14.71/4.12	     86 -> 51*
14.71/4.12	     88 -> 52*
14.71/4.12	   problem:
14.71/4.12	    
14.71/4.12	   Qed
14.71/4.13	EOF