0.00/0.17	YES
0.00/0.17	
0.00/0.17	DP problem for innermost termination.
0.00/0.17	P =
0.00/0.17	  init#(x1) -> f1#(rnd1) 
0.00/0.17	  f2#(I0) -> f2#(I1) [-1 <= I1 - 1 /\ 0 <= I0 - 1 /\ I1 + 1 <= I0]
0.00/0.17	  f1#(I2) -> f2#(I3) [3 <= I3 - 1]
0.00/0.17	R = 
0.00/0.17	  init(x1) -> f1(rnd1) 
0.00/0.17	  f2(I0) -> f2(I1) [-1 <= I1 - 1 /\ 0 <= I0 - 1 /\ I1 + 1 <= I0]
0.00/0.17	  f1(I2) -> f2(I3) [3 <= I3 - 1]
0.00/0.17	
0.00/0.17	The dependency graph for this problem is:
0.00/0.17	  0 -> 2
0.00/0.17	  1 -> 1
0.00/0.17	  2 -> 1
0.00/0.17	Where:
0.00/0.17	  0) init#(x1) -> f1#(rnd1) 
0.00/0.17	  1) f2#(I0) -> f2#(I1) [-1 <= I1 - 1 /\ 0 <= I0 - 1 /\ I1 + 1 <= I0]
0.00/0.17	  2) f1#(I2) -> f2#(I3) [3 <= I3 - 1]
0.00/0.17	
0.00/0.17	We have the following SCCs.
0.00/0.17	  { 1 }
0.00/0.17	
0.00/0.17	DP problem for innermost termination.
0.00/0.17	P =
0.00/0.17	  f2#(I0) -> f2#(I1) [-1 <= I1 - 1 /\ 0 <= I0 - 1 /\ I1 + 1 <= I0]
0.00/0.17	R = 
0.00/0.17	  init(x1) -> f1(rnd1) 
0.00/0.17	  f2(I0) -> f2(I1) [-1 <= I1 - 1 /\ 0 <= I0 - 1 /\ I1 + 1 <= I0]
0.00/0.17	  f1(I2) -> f2(I3) [3 <= I3 - 1]
0.00/0.17	
0.00/0.17	We use the basic value criterion with the projection function NU:
0.00/0.17	  NU[f2#(z1)] = z1
0.00/0.17	
0.00/0.17	This gives the following inequalities:
0.00/0.17	  -1 <= I1 - 1 /\ 0 <= I0 - 1 /\ I1 + 1 <= I0  ==>  I0 >! I1
0.00/0.17	
0.00/0.17	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
0.00/3.16	EOF