3.64/3.63	MAYBE
3.64/3.63	
3.64/3.63	DP problem for innermost termination.
3.64/3.63	P =
3.64/3.63	  init#(x1, x2) -> f1#(rnd1, rnd2) 
3.64/3.63	  f3#(I0, I1) -> f2#(3 * I0 + 1, I2) [I0 - 2 * y1 = 1 /\ 1 <= I0 - 1 /\ 0 <= 3 * I0 - 1 /\ I0 - 2 * y1 <= 1 /\ 0 <= I0 - 2 * y1]
3.64/3.63	  f2#(I3, I4) -> f3#(I3, I5) [I3 - 2 * I6 = 1 /\ 0 <= 3 * I3 - 1 /\ 1 <= I3 - 1]
3.64/3.63	  f3#(I7, I8) -> f2#(I9, I10) [I7 - 2 * I11 = 0 /\ 1 <= I7 - 1 /\ I9 <= I7 - 1 /\ 0 <= I7 - 2 * I11 /\ I7 - 2 * I11 <= 1 /\ I7 - 2 * I9 <= 1 /\ 0 <= I7 - 2 * I9]
3.64/3.63	  f2#(I12, I13) -> f3#(I12, I14) [I12 - 2 * I15 = 0 /\ y2 <= I12 - 1 /\ 1 <= I12 - 1]
3.64/3.63	  f1#(I16, I17) -> f2#(I18, I19) [0 <= I16 - 1 /\ -1 <= I18 - 1 /\ -1 <= I17 - 1]
3.64/3.63	R = 
3.64/3.63	  init(x1, x2) -> f1(rnd1, rnd2) 
3.64/3.63	  f3(I0, I1) -> f2(3 * I0 + 1, I2) [I0 - 2 * y1 = 1 /\ 1 <= I0 - 1 /\ 0 <= 3 * I0 - 1 /\ I0 - 2 * y1 <= 1 /\ 0 <= I0 - 2 * y1]
3.64/3.63	  f2(I3, I4) -> f3(I3, I5) [I3 - 2 * I6 = 1 /\ 0 <= 3 * I3 - 1 /\ 1 <= I3 - 1]
3.64/3.63	  f3(I7, I8) -> f2(I9, I10) [I7 - 2 * I11 = 0 /\ 1 <= I7 - 1 /\ I9 <= I7 - 1 /\ 0 <= I7 - 2 * I11 /\ I7 - 2 * I11 <= 1 /\ I7 - 2 * I9 <= 1 /\ 0 <= I7 - 2 * I9]
3.64/3.63	  f2(I12, I13) -> f3(I12, I14) [I12 - 2 * I15 = 0 /\ y2 <= I12 - 1 /\ 1 <= I12 - 1]
3.64/3.63	  f1(I16, I17) -> f2(I18, I19) [0 <= I16 - 1 /\ -1 <= I18 - 1 /\ -1 <= I17 - 1]
3.64/3.63	
3.64/3.63	The dependency graph for this problem is:
3.64/3.63	  0 -> 5
3.64/3.63	  1 -> 4
3.64/3.63	  2 -> 1
3.64/3.63	  3 -> 2, 4
3.64/3.63	  4 -> 3
3.64/3.63	  5 -> 2, 4
3.64/3.63	Where:
3.64/3.63	  0) init#(x1, x2) -> f1#(rnd1, rnd2) 
3.64/3.63	  1) f3#(I0, I1) -> f2#(3 * I0 + 1, I2) [I0 - 2 * y1 = 1 /\ 1 <= I0 - 1 /\ 0 <= 3 * I0 - 1 /\ I0 - 2 * y1 <= 1 /\ 0 <= I0 - 2 * y1]
3.64/3.63	  2) f2#(I3, I4) -> f3#(I3, I5) [I3 - 2 * I6 = 1 /\ 0 <= 3 * I3 - 1 /\ 1 <= I3 - 1]
3.64/3.63	  3) f3#(I7, I8) -> f2#(I9, I10) [I7 - 2 * I11 = 0 /\ 1 <= I7 - 1 /\ I9 <= I7 - 1 /\ 0 <= I7 - 2 * I11 /\ I7 - 2 * I11 <= 1 /\ I7 - 2 * I9 <= 1 /\ 0 <= I7 - 2 * I9]
3.64/3.63	  4) f2#(I12, I13) -> f3#(I12, I14) [I12 - 2 * I15 = 0 /\ y2 <= I12 - 1 /\ 1 <= I12 - 1]
3.64/3.63	  5) f1#(I16, I17) -> f2#(I18, I19) [0 <= I16 - 1 /\ -1 <= I18 - 1 /\ -1 <= I17 - 1]
3.64/3.63	
3.64/3.63	We have the following SCCs.
3.64/3.63	  { 1, 2, 3, 4 }
3.64/3.63	
3.64/3.63	DP problem for innermost termination.
3.64/3.63	P =
3.64/3.63	  f3#(I0, I1) -> f2#(3 * I0 + 1, I2) [I0 - 2 * y1 = 1 /\ 1 <= I0 - 1 /\ 0 <= 3 * I0 - 1 /\ I0 - 2 * y1 <= 1 /\ 0 <= I0 - 2 * y1]
3.64/3.63	  f2#(I3, I4) -> f3#(I3, I5) [I3 - 2 * I6 = 1 /\ 0 <= 3 * I3 - 1 /\ 1 <= I3 - 1]
3.64/3.63	  f3#(I7, I8) -> f2#(I9, I10) [I7 - 2 * I11 = 0 /\ 1 <= I7 - 1 /\ I9 <= I7 - 1 /\ 0 <= I7 - 2 * I11 /\ I7 - 2 * I11 <= 1 /\ I7 - 2 * I9 <= 1 /\ 0 <= I7 - 2 * I9]
3.64/3.63	  f2#(I12, I13) -> f3#(I12, I14) [I12 - 2 * I15 = 0 /\ y2 <= I12 - 1 /\ 1 <= I12 - 1]
3.64/3.63	R = 
3.64/3.63	  init(x1, x2) -> f1(rnd1, rnd2) 
3.64/3.63	  f3(I0, I1) -> f2(3 * I0 + 1, I2) [I0 - 2 * y1 = 1 /\ 1 <= I0 - 1 /\ 0 <= 3 * I0 - 1 /\ I0 - 2 * y1 <= 1 /\ 0 <= I0 - 2 * y1]
3.64/3.63	  f2(I3, I4) -> f3(I3, I5) [I3 - 2 * I6 = 1 /\ 0 <= 3 * I3 - 1 /\ 1 <= I3 - 1]
3.64/3.63	  f3(I7, I8) -> f2(I9, I10) [I7 - 2 * I11 = 0 /\ 1 <= I7 - 1 /\ I9 <= I7 - 1 /\ 0 <= I7 - 2 * I11 /\ I7 - 2 * I11 <= 1 /\ I7 - 2 * I9 <= 1 /\ 0 <= I7 - 2 * I9]
3.64/3.63	  f2(I12, I13) -> f3(I12, I14) [I12 - 2 * I15 = 0 /\ y2 <= I12 - 1 /\ 1 <= I12 - 1]
3.64/3.63	  f1(I16, I17) -> f2(I18, I19) [0 <= I16 - 1 /\ -1 <= I18 - 1 /\ -1 <= I17 - 1]
3.64/3.63	
3.64/3.63	EOF