0.00/0.36	YES
0.00/0.36	
0.00/0.36	DP problem for innermost termination.
0.00/0.36	P =
0.00/0.36	  init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
0.00/0.36	  f2#(I0, I1, I2) -> f2#(I0 - 1, I1 - 1, I2) [I2 <= I0 - 1 /\ I2 <= I1 - 1]
0.00/0.36	  f1#(I3, I4, I5) -> f2#(I6, I7, I8) [0 <= I3 - 1 /\ -1 <= I6 - 1 /\ -1 <= I8 - 1 /\ -1 <= I4 - 1 /\ -1 <= I7 - 1]
0.00/0.36	R = 
0.00/0.36	  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
0.00/0.36	  f2(I0, I1, I2) -> f2(I0 - 1, I1 - 1, I2) [I2 <= I0 - 1 /\ I2 <= I1 - 1]
0.00/0.36	  f1(I3, I4, I5) -> f2(I6, I7, I8) [0 <= I3 - 1 /\ -1 <= I6 - 1 /\ -1 <= I8 - 1 /\ -1 <= I4 - 1 /\ -1 <= I7 - 1]
0.00/0.36	
0.00/0.36	The dependency graph for this problem is:
0.00/0.36	  0 -> 2
0.00/0.36	  1 -> 1
0.00/0.36	  2 -> 1
0.00/0.36	Where:
0.00/0.36	  0) init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
0.00/0.36	  1) f2#(I0, I1, I2) -> f2#(I0 - 1, I1 - 1, I2) [I2 <= I0 - 1 /\ I2 <= I1 - 1]
0.00/0.36	  2) f1#(I3, I4, I5) -> f2#(I6, I7, I8) [0 <= I3 - 1 /\ -1 <= I6 - 1 /\ -1 <= I8 - 1 /\ -1 <= I4 - 1 /\ -1 <= I7 - 1]
0.00/0.36	
0.00/0.36	We have the following SCCs.
0.00/0.36	  { 1 }
0.00/0.36	
0.00/0.36	DP problem for innermost termination.
0.00/0.36	P =
0.00/0.36	  f2#(I0, I1, I2) -> f2#(I0 - 1, I1 - 1, I2) [I2 <= I0 - 1 /\ I2 <= I1 - 1]
0.00/0.36	R = 
0.00/0.36	  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
0.00/0.36	  f2(I0, I1, I2) -> f2(I0 - 1, I1 - 1, I2) [I2 <= I0 - 1 /\ I2 <= I1 - 1]
0.00/0.36	  f1(I3, I4, I5) -> f2(I6, I7, I8) [0 <= I3 - 1 /\ -1 <= I6 - 1 /\ -1 <= I8 - 1 /\ -1 <= I4 - 1 /\ -1 <= I7 - 1]
0.00/0.36	
0.00/0.36	We use the reverse value criterion with the projection function NU:
0.00/0.36	  NU[f2#(z1,z2,z3)] = z1 - 1 + -1 * z3
0.00/0.36	
0.00/0.36	This gives the following inequalities:
0.00/0.36	  I2 <= I0 - 1 /\ I2 <= I1 - 1  ==>  I0 - 1 + -1 * I2 > I0 - 1 - 1 + -1 * I2  with  I0 - 1 + -1 * I2 >= 0
0.00/0.36	
0.00/0.36	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
0.00/3.34	EOF