1.08/1.13	MAYBE
1.08/1.13	
1.08/1.13	DP problem for innermost termination.
1.08/1.13	P =
1.08/1.13	  init#(x1, x2) -> f3#(rnd1, rnd2) 
1.08/1.13	  f5#(I0, I1) -> f5#(I2, I3) [-1 <= I2 - 1 /\ 0 <= I0 - 1 /\ I2 + 1 <= I0]
1.08/1.13	  f2#(I4, I5) -> f5#(I6, I7) [0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I6 + 2 <= I5 /\ 0 <= I4 - 1 /\ 2 <= I5 - 1 /\ 0 <= I6 - 1]
1.08/1.13	  f4#(I8, I9) -> f4#(I8 - 1, I9 + 1) [0 <= I9 - 1 /\ 0 <= I8 - 1]
1.08/1.13	  f3#(I10, I11) -> f4#(I12, 1) [0 <= I10 - 1 /\ -1 <= I12 - 1 /\ -1 <= I11 - 1]
1.08/1.13	  f2#(I13, I14) -> f2#(I15, I16) [0 <= I17 - 1 /\ 0 <= I18 - 1 /\ I15 <= I13 /\ I15 + 2 <= I14 /\ 0 <= I13 - 1 /\ 2 <= I14 - 1 /\ 0 <= I15 - 1 /\ -1 <= I16 - 1]
1.08/1.13	  f2#(I19, I20) -> f2#(I21, I22) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ 1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I22 + 2 <= I20 /\ I22 + 1 <= I19 /\ I21 + 1 <= I20 /\ I21 <= I19]
1.08/1.13	  f3#(I23, I24) -> f2#(I25, I26) [-1 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I23 - 1 /\ I25 <= I23]
1.08/1.13	  f1#(I27, I28) -> f2#(I29, I30) [-1 <= I30 - 1 /\ 0 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I27 - 1 /\ I30 <= I28 /\ I29 - 1 <= I28 /\ I29 <= I27]
1.08/1.13	R = 
1.08/1.13	  init(x1, x2) -> f3(rnd1, rnd2) 
1.08/1.13	  f5(I0, I1) -> f5(I2, I3) [-1 <= I2 - 1 /\ 0 <= I0 - 1 /\ I2 + 1 <= I0]
1.08/1.13	  f2(I4, I5) -> f5(I6, I7) [0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I6 + 2 <= I5 /\ 0 <= I4 - 1 /\ 2 <= I5 - 1 /\ 0 <= I6 - 1]
1.08/1.13	  f4(I8, I9) -> f4(I8 - 1, I9 + 1) [0 <= I9 - 1 /\ 0 <= I8 - 1]
1.08/1.13	  f3(I10, I11) -> f4(I12, 1) [0 <= I10 - 1 /\ -1 <= I12 - 1 /\ -1 <= I11 - 1]
1.08/1.13	  f2(I13, I14) -> f2(I15, I16) [0 <= I17 - 1 /\ 0 <= I18 - 1 /\ I15 <= I13 /\ I15 + 2 <= I14 /\ 0 <= I13 - 1 /\ 2 <= I14 - 1 /\ 0 <= I15 - 1 /\ -1 <= I16 - 1]
1.08/1.13	  f2(I19, I20) -> f2(I21, I22) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ 1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I22 + 2 <= I20 /\ I22 + 1 <= I19 /\ I21 + 1 <= I20 /\ I21 <= I19]
1.08/1.13	  f3(I23, I24) -> f2(I25, I26) [-1 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I23 - 1 /\ I25 <= I23]
1.08/1.13	  f1(I27, I28) -> f2(I29, I30) [-1 <= I30 - 1 /\ 0 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I27 - 1 /\ I30 <= I28 /\ I29 - 1 <= I28 /\ I29 <= I27]
1.08/1.13	
1.08/1.13	The dependency graph for this problem is:
1.08/1.13	  0 -> 4, 7
1.08/1.13	  1 -> 1
1.08/1.13	  2 -> 1
1.08/1.13	  3 -> 3
1.08/1.13	  4 -> 3
1.08/1.13	  5 -> 2, 5, 6
1.08/1.13	  6 -> 2, 5, 6
1.08/1.13	  7 -> 2, 5, 6
1.08/1.13	  8 -> 2, 5, 6
1.08/1.13	Where:
1.08/1.13	  0) init#(x1, x2) -> f3#(rnd1, rnd2) 
1.08/1.13	  1) f5#(I0, I1) -> f5#(I2, I3) [-1 <= I2 - 1 /\ 0 <= I0 - 1 /\ I2 + 1 <= I0]
1.08/1.13	  2) f2#(I4, I5) -> f5#(I6, I7) [0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I6 + 2 <= I5 /\ 0 <= I4 - 1 /\ 2 <= I5 - 1 /\ 0 <= I6 - 1]
1.08/1.13	  3) f4#(I8, I9) -> f4#(I8 - 1, I9 + 1) [0 <= I9 - 1 /\ 0 <= I8 - 1]
1.08/1.13	  4) f3#(I10, I11) -> f4#(I12, 1) [0 <= I10 - 1 /\ -1 <= I12 - 1 /\ -1 <= I11 - 1]
1.08/1.13	  5) f2#(I13, I14) -> f2#(I15, I16) [0 <= I17 - 1 /\ 0 <= I18 - 1 /\ I15 <= I13 /\ I15 + 2 <= I14 /\ 0 <= I13 - 1 /\ 2 <= I14 - 1 /\ 0 <= I15 - 1 /\ -1 <= I16 - 1]
1.08/1.13	  6) f2#(I19, I20) -> f2#(I21, I22) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ 1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I22 + 2 <= I20 /\ I22 + 1 <= I19 /\ I21 + 1 <= I20 /\ I21 <= I19]
1.08/1.13	  7) f3#(I23, I24) -> f2#(I25, I26) [-1 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I23 - 1 /\ I25 <= I23]
1.08/1.13	  8) f1#(I27, I28) -> f2#(I29, I30) [-1 <= I30 - 1 /\ 0 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I27 - 1 /\ I30 <= I28 /\ I29 - 1 <= I28 /\ I29 <= I27]
1.08/1.13	
1.08/1.13	We have the following SCCs.
1.08/1.13	  { 3 }
1.08/1.13	  { 5, 6 }
1.08/1.13	  { 1 }
1.08/1.13	
1.08/1.13	DP problem for innermost termination.
1.08/1.13	P =
1.08/1.13	  f5#(I0, I1) -> f5#(I2, I3) [-1 <= I2 - 1 /\ 0 <= I0 - 1 /\ I2 + 1 <= I0]
1.08/1.13	R = 
1.08/1.13	  init(x1, x2) -> f3(rnd1, rnd2) 
1.08/1.13	  f5(I0, I1) -> f5(I2, I3) [-1 <= I2 - 1 /\ 0 <= I0 - 1 /\ I2 + 1 <= I0]
1.08/1.13	  f2(I4, I5) -> f5(I6, I7) [0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I6 + 2 <= I5 /\ 0 <= I4 - 1 /\ 2 <= I5 - 1 /\ 0 <= I6 - 1]
1.08/1.13	  f4(I8, I9) -> f4(I8 - 1, I9 + 1) [0 <= I9 - 1 /\ 0 <= I8 - 1]
1.08/1.13	  f3(I10, I11) -> f4(I12, 1) [0 <= I10 - 1 /\ -1 <= I12 - 1 /\ -1 <= I11 - 1]
1.08/1.13	  f2(I13, I14) -> f2(I15, I16) [0 <= I17 - 1 /\ 0 <= I18 - 1 /\ I15 <= I13 /\ I15 + 2 <= I14 /\ 0 <= I13 - 1 /\ 2 <= I14 - 1 /\ 0 <= I15 - 1 /\ -1 <= I16 - 1]
1.08/1.13	  f2(I19, I20) -> f2(I21, I22) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ 1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I22 + 2 <= I20 /\ I22 + 1 <= I19 /\ I21 + 1 <= I20 /\ I21 <= I19]
1.08/1.13	  f3(I23, I24) -> f2(I25, I26) [-1 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I23 - 1 /\ I25 <= I23]
1.08/1.13	  f1(I27, I28) -> f2(I29, I30) [-1 <= I30 - 1 /\ 0 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I27 - 1 /\ I30 <= I28 /\ I29 - 1 <= I28 /\ I29 <= I27]
1.08/1.13	
1.08/1.13	We use the basic value criterion with the projection function NU:
1.08/1.13	  NU[f5#(z1,z2)] = z1
1.08/1.13	
1.08/1.13	This gives the following inequalities:
1.08/1.13	  -1 <= I2 - 1 /\ 0 <= I0 - 1 /\ I2 + 1 <= I0  ==>  I0 >! I2
1.08/1.13	
1.08/1.13	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
1.08/1.13	
1.08/1.13	DP problem for innermost termination.
1.08/1.13	P =
1.08/1.13	  f2#(I13, I14) -> f2#(I15, I16) [0 <= I17 - 1 /\ 0 <= I18 - 1 /\ I15 <= I13 /\ I15 + 2 <= I14 /\ 0 <= I13 - 1 /\ 2 <= I14 - 1 /\ 0 <= I15 - 1 /\ -1 <= I16 - 1]
1.08/1.13	  f2#(I19, I20) -> f2#(I21, I22) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ 1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I22 + 2 <= I20 /\ I22 + 1 <= I19 /\ I21 + 1 <= I20 /\ I21 <= I19]
1.08/1.13	R = 
1.08/1.13	  init(x1, x2) -> f3(rnd1, rnd2) 
1.08/1.13	  f5(I0, I1) -> f5(I2, I3) [-1 <= I2 - 1 /\ 0 <= I0 - 1 /\ I2 + 1 <= I0]
1.08/1.13	  f2(I4, I5) -> f5(I6, I7) [0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I6 + 2 <= I5 /\ 0 <= I4 - 1 /\ 2 <= I5 - 1 /\ 0 <= I6 - 1]
1.08/1.13	  f4(I8, I9) -> f4(I8 - 1, I9 + 1) [0 <= I9 - 1 /\ 0 <= I8 - 1]
1.08/1.13	  f3(I10, I11) -> f4(I12, 1) [0 <= I10 - 1 /\ -1 <= I12 - 1 /\ -1 <= I11 - 1]
1.08/1.13	  f2(I13, I14) -> f2(I15, I16) [0 <= I17 - 1 /\ 0 <= I18 - 1 /\ I15 <= I13 /\ I15 + 2 <= I14 /\ 0 <= I13 - 1 /\ 2 <= I14 - 1 /\ 0 <= I15 - 1 /\ -1 <= I16 - 1]
1.08/1.13	  f2(I19, I20) -> f2(I21, I22) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ 1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I22 + 2 <= I20 /\ I22 + 1 <= I19 /\ I21 + 1 <= I20 /\ I21 <= I19]
1.08/1.13	  f3(I23, I24) -> f2(I25, I26) [-1 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I23 - 1 /\ I25 <= I23]
1.08/1.13	  f1(I27, I28) -> f2(I29, I30) [-1 <= I30 - 1 /\ 0 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I27 - 1 /\ I30 <= I28 /\ I29 - 1 <= I28 /\ I29 <= I27]
1.08/1.13	
1.08/1.13	EOF