1.61/1.68	MAYBE
1.61/1.68	
1.61/1.68	DP problem for innermost termination.
1.61/1.68	P =
1.61/1.68	  init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
1.61/1.68	  f3#(I0, I1, I2, I3) -> f3#(I0 + 1, I1 + 1, I2 - 1, I0 + 1 + I1 + 1 + 3 * I2 - 3) [I0 <= I1 /\ I1 <= I2 /\ -1 <= I3 - 1]
1.61/1.68	  f3#(I4, I5, I6, I7) -> f3#(I4 + 1, I5 - 2, I6, I4 + 1 + I5 - 2 + 3 * I6) [I4 <= I5 /\ -1 <= I7 - 1 /\ I6 <= I5 - 1]
1.61/1.68	  f3#(I8, I9, I10, I11) -> f3#(I8 - 1, I9, I10, I8 - 1 + I9 + 3 * I10) [I9 <= I8 - 1 /\ -1 <= I11 - 1]
1.61/1.68	  f2#(I12, I13, I14, I15) -> f3#(I13, I16, I17, I18) [0 <= I12 - 1 /\ -1 <= I13 - 1 /\ 0 <= I13 - 5 * y1 /\ I13 - 5 * y1 <= 4 /\ 0 <= I13 - 4 * y2 /\ I13 - 4 * y2 <= 3 /\ 0 <= I13 - 5 * y3 /\ I13 - 5 * y3 <= 4 /\ I13 - 4 * y4 <= 3 /\ 0 <= I13 - 4 * y4 /\ I13 - 5 * y1 = I16 /\ I13 - 4 * y2 = I17 /\ I13 + I13 - 5 * y3 + 3 * I13 - 12 * y4 = I18]
1.61/1.68	  f1#(I19, I20, I21, I22) -> f2#(I19, I20, I23, I24) [-1 <= I20 - 1 /\ 0 <= I19 - 1]
1.61/1.68	R = 
1.61/1.68	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
1.61/1.68	  f3(I0, I1, I2, I3) -> f3(I0 + 1, I1 + 1, I2 - 1, I0 + 1 + I1 + 1 + 3 * I2 - 3) [I0 <= I1 /\ I1 <= I2 /\ -1 <= I3 - 1]
1.61/1.68	  f3(I4, I5, I6, I7) -> f3(I4 + 1, I5 - 2, I6, I4 + 1 + I5 - 2 + 3 * I6) [I4 <= I5 /\ -1 <= I7 - 1 /\ I6 <= I5 - 1]
1.61/1.68	  f3(I8, I9, I10, I11) -> f3(I8 - 1, I9, I10, I8 - 1 + I9 + 3 * I10) [I9 <= I8 - 1 /\ -1 <= I11 - 1]
1.61/1.68	  f2(I12, I13, I14, I15) -> f3(I13, I16, I17, I18) [0 <= I12 - 1 /\ -1 <= I13 - 1 /\ 0 <= I13 - 5 * y1 /\ I13 - 5 * y1 <= 4 /\ 0 <= I13 - 4 * y2 /\ I13 - 4 * y2 <= 3 /\ 0 <= I13 - 5 * y3 /\ I13 - 5 * y3 <= 4 /\ I13 - 4 * y4 <= 3 /\ 0 <= I13 - 4 * y4 /\ I13 - 5 * y1 = I16 /\ I13 - 4 * y2 = I17 /\ I13 + I13 - 5 * y3 + 3 * I13 - 12 * y4 = I18]
1.61/1.68	  f1(I19, I20, I21, I22) -> f2(I19, I20, I23, I24) [-1 <= I20 - 1 /\ 0 <= I19 - 1]
1.61/1.68	
1.61/1.68	The dependency graph for this problem is:
1.61/1.68	  0 -> 5
1.61/1.68	  1 -> 1, 2
1.61/1.68	  2 -> 1, 2, 3
1.61/1.68	  3 -> 1, 2, 3
1.61/1.68	  4 -> 1, 2, 3
1.61/1.68	  5 -> 4
1.61/1.68	Where:
1.61/1.68	  0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
1.61/1.68	  1) f3#(I0, I1, I2, I3) -> f3#(I0 + 1, I1 + 1, I2 - 1, I0 + 1 + I1 + 1 + 3 * I2 - 3) [I0 <= I1 /\ I1 <= I2 /\ -1 <= I3 - 1]
1.61/1.68	  2) f3#(I4, I5, I6, I7) -> f3#(I4 + 1, I5 - 2, I6, I4 + 1 + I5 - 2 + 3 * I6) [I4 <= I5 /\ -1 <= I7 - 1 /\ I6 <= I5 - 1]
1.61/1.68	  3) f3#(I8, I9, I10, I11) -> f3#(I8 - 1, I9, I10, I8 - 1 + I9 + 3 * I10) [I9 <= I8 - 1 /\ -1 <= I11 - 1]
1.61/1.68	  4) f2#(I12, I13, I14, I15) -> f3#(I13, I16, I17, I18) [0 <= I12 - 1 /\ -1 <= I13 - 1 /\ 0 <= I13 - 5 * y1 /\ I13 - 5 * y1 <= 4 /\ 0 <= I13 - 4 * y2 /\ I13 - 4 * y2 <= 3 /\ 0 <= I13 - 5 * y3 /\ I13 - 5 * y3 <= 4 /\ I13 - 4 * y4 <= 3 /\ 0 <= I13 - 4 * y4 /\ I13 - 5 * y1 = I16 /\ I13 - 4 * y2 = I17 /\ I13 + I13 - 5 * y3 + 3 * I13 - 12 * y4 = I18]
1.61/1.68	  5) f1#(I19, I20, I21, I22) -> f2#(I19, I20, I23, I24) [-1 <= I20 - 1 /\ 0 <= I19 - 1]
1.61/1.68	
1.61/1.68	We have the following SCCs.
1.61/1.68	  { 1, 2, 3 }
1.61/1.68	
1.61/1.68	DP problem for innermost termination.
1.61/1.68	P =
1.61/1.68	  f3#(I0, I1, I2, I3) -> f3#(I0 + 1, I1 + 1, I2 - 1, I0 + 1 + I1 + 1 + 3 * I2 - 3) [I0 <= I1 /\ I1 <= I2 /\ -1 <= I3 - 1]
1.61/1.68	  f3#(I4, I5, I6, I7) -> f3#(I4 + 1, I5 - 2, I6, I4 + 1 + I5 - 2 + 3 * I6) [I4 <= I5 /\ -1 <= I7 - 1 /\ I6 <= I5 - 1]
1.61/1.68	  f3#(I8, I9, I10, I11) -> f3#(I8 - 1, I9, I10, I8 - 1 + I9 + 3 * I10) [I9 <= I8 - 1 /\ -1 <= I11 - 1]
1.61/1.68	R = 
1.61/1.68	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
1.61/1.68	  f3(I0, I1, I2, I3) -> f3(I0 + 1, I1 + 1, I2 - 1, I0 + 1 + I1 + 1 + 3 * I2 - 3) [I0 <= I1 /\ I1 <= I2 /\ -1 <= I3 - 1]
1.61/1.68	  f3(I4, I5, I6, I7) -> f3(I4 + 1, I5 - 2, I6, I4 + 1 + I5 - 2 + 3 * I6) [I4 <= I5 /\ -1 <= I7 - 1 /\ I6 <= I5 - 1]
1.61/1.68	  f3(I8, I9, I10, I11) -> f3(I8 - 1, I9, I10, I8 - 1 + I9 + 3 * I10) [I9 <= I8 - 1 /\ -1 <= I11 - 1]
1.61/1.68	  f2(I12, I13, I14, I15) -> f3(I13, I16, I17, I18) [0 <= I12 - 1 /\ -1 <= I13 - 1 /\ 0 <= I13 - 5 * y1 /\ I13 - 5 * y1 <= 4 /\ 0 <= I13 - 4 * y2 /\ I13 - 4 * y2 <= 3 /\ 0 <= I13 - 5 * y3 /\ I13 - 5 * y3 <= 4 /\ I13 - 4 * y4 <= 3 /\ 0 <= I13 - 4 * y4 /\ I13 - 5 * y1 = I16 /\ I13 - 4 * y2 = I17 /\ I13 + I13 - 5 * y3 + 3 * I13 - 12 * y4 = I18]
1.61/1.68	  f1(I19, I20, I21, I22) -> f2(I19, I20, I23, I24) [-1 <= I20 - 1 /\ 0 <= I19 - 1]
1.61/1.68	
1.61/4.66	EOF