3.73/3.72	YES
3.73/3.72	
3.73/3.72	DP problem for innermost termination.
3.73/3.72	P =
3.73/3.72	  init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
3.73/3.72	  f5#(I0, I1, I2) -> f5#(I0 - 1, I3, I4) [0 <= I0 - 1]
3.73/3.72	  f1#(I5, I6, I7) -> f5#(I8, I9, I10) [-1 <= y2 - 1 /\ 1 <= I6 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ y1 - 1 = I8]
3.73/3.72	  f4#(I11, I12, I13) -> f3#(I14, I15, I16) [-1 <= I13 - 1 /\ 0 <= I12 - 1 /\ I15 <= I13 - 1 /\ I15 <= I12 - 1 /\ I11 - 2 * I17 = 1 /\ I14 <= I11 /\ 0 <= I15 - 1 /\ 0 <= I11 - 2 * I17 /\ I11 - 2 * I17 <= 1 /\ I11 - 2 * I14 <= 1 /\ 0 <= I11 - 2 * I14 /\ I15 = I16]
3.73/3.72	  f3#(I18, I19, I20) -> f4#(I18, I19, I20) [-1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I21 <= I20 - 1 /\ I21 <= I19 - 1 /\ I18 - 2 * I22 = 1 /\ 0 <= I21 - 1 /\ y3 <= I18]
3.73/3.72	  f4#(I23, I24, I25) -> f3#(I26, I27, I28) [-1 <= I25 - 1 /\ 0 <= I24 - 1 /\ I28 <= I25 - 1 /\ I29 <= I24 - 1 /\ I23 - 2 * I30 = 1 /\ I26 <= I23 /\ -1 <= I29 - 1 /\ 0 <= I28 - 1 /\ I27 <= I29 /\ 0 <= I23 - 2 * I30 /\ I23 - 2 * I30 <= 1 /\ I23 - 2 * I26 <= 1 /\ 0 <= I23 - 2 * I26]
3.73/3.72	  f3#(I31, I32, I33) -> f4#(I31, I32, I33) [-1 <= I33 - 1 /\ 0 <= I32 - 1 /\ I34 <= I33 - 1 /\ I35 <= I32 - 1 /\ I31 - 2 * I36 = 1 /\ y4 <= I31 /\ -1 <= I35 - 1 /\ y5 <= I35 /\ 0 <= I34 - 1]
3.73/3.72	  f4#(I37, I38, I39) -> f3#(I40, I41, I42) [-1 <= I43 - 1 /\ 0 <= I38 - 1 /\ I43 <= I42 - 1 /\ -1 <= I39 - 1 /\ I43 <= I39 - 1 /\ I43 <= I44 - 1 /\ I41 <= I38 - 1 /\ I43 <= I41 - 1 /\ I43 <= I45 - 1 /\ I37 - 2 * I46 = 0 /\ I40 <= I37 /\ 0 <= I37 - 2 * I46 /\ I37 - 2 * I46 <= 1 /\ I37 - 2 * I40 <= 1 /\ 0 <= I37 - 2 * I40]
3.73/3.72	  f3#(I47, I48, I49) -> f4#(I47, I48, I49) [-1 <= I50 - 1 /\ 0 <= I48 - 1 /\ I50 <= I51 - 1 /\ -1 <= I49 - 1 /\ I50 <= I49 - 1 /\ I50 <= I52 - 1 /\ I53 <= I48 - 1 /\ I50 <= I53 - 1 /\ I50 <= I54 - 1 /\ y6 <= I47 /\ I47 - 2 * y7 = 0]
3.73/3.72	  f2#(I55, I56, I57) -> f3#(I55, I56, I56) [0 <= I56 - 1]
3.73/3.72	  f1#(I58, I59, I60) -> f2#(I61, I62, I63) [-1 <= I64 - 1 /\ 1 <= I59 - 1 /\ I62 <= 0 /\ -1 <= I61 - 1 /\ 0 <= I58 - 1]
3.73/3.72	  f1#(I65, I66, I67) -> f2#(I68, I69, I70) [-1 <= I71 - 1 /\ 1 <= I66 - 1 /\ -1 <= I68 - 1 /\ I69 <= I72 - 1 /\ -1 <= I72 - 1 /\ 0 <= I65 - 1]
3.73/3.72	R = 
3.73/3.72	  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
3.73/3.72	  f5(I0, I1, I2) -> f5(I0 - 1, I3, I4) [0 <= I0 - 1]
3.73/3.72	  f1(I5, I6, I7) -> f5(I8, I9, I10) [-1 <= y2 - 1 /\ 1 <= I6 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ y1 - 1 = I8]
3.73/3.72	  f4(I11, I12, I13) -> f3(I14, I15, I16) [-1 <= I13 - 1 /\ 0 <= I12 - 1 /\ I15 <= I13 - 1 /\ I15 <= I12 - 1 /\ I11 - 2 * I17 = 1 /\ I14 <= I11 /\ 0 <= I15 - 1 /\ 0 <= I11 - 2 * I17 /\ I11 - 2 * I17 <= 1 /\ I11 - 2 * I14 <= 1 /\ 0 <= I11 - 2 * I14 /\ I15 = I16]
3.73/3.72	  f3(I18, I19, I20) -> f4(I18, I19, I20) [-1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I21 <= I20 - 1 /\ I21 <= I19 - 1 /\ I18 - 2 * I22 = 1 /\ 0 <= I21 - 1 /\ y3 <= I18]
3.73/3.72	  f4(I23, I24, I25) -> f3(I26, I27, I28) [-1 <= I25 - 1 /\ 0 <= I24 - 1 /\ I28 <= I25 - 1 /\ I29 <= I24 - 1 /\ I23 - 2 * I30 = 1 /\ I26 <= I23 /\ -1 <= I29 - 1 /\ 0 <= I28 - 1 /\ I27 <= I29 /\ 0 <= I23 - 2 * I30 /\ I23 - 2 * I30 <= 1 /\ I23 - 2 * I26 <= 1 /\ 0 <= I23 - 2 * I26]
3.73/3.72	  f3(I31, I32, I33) -> f4(I31, I32, I33) [-1 <= I33 - 1 /\ 0 <= I32 - 1 /\ I34 <= I33 - 1 /\ I35 <= I32 - 1 /\ I31 - 2 * I36 = 1 /\ y4 <= I31 /\ -1 <= I35 - 1 /\ y5 <= I35 /\ 0 <= I34 - 1]
3.73/3.72	  f4(I37, I38, I39) -> f3(I40, I41, I42) [-1 <= I43 - 1 /\ 0 <= I38 - 1 /\ I43 <= I42 - 1 /\ -1 <= I39 - 1 /\ I43 <= I39 - 1 /\ I43 <= I44 - 1 /\ I41 <= I38 - 1 /\ I43 <= I41 - 1 /\ I43 <= I45 - 1 /\ I37 - 2 * I46 = 0 /\ I40 <= I37 /\ 0 <= I37 - 2 * I46 /\ I37 - 2 * I46 <= 1 /\ I37 - 2 * I40 <= 1 /\ 0 <= I37 - 2 * I40]
3.73/3.72	  f3(I47, I48, I49) -> f4(I47, I48, I49) [-1 <= I50 - 1 /\ 0 <= I48 - 1 /\ I50 <= I51 - 1 /\ -1 <= I49 - 1 /\ I50 <= I49 - 1 /\ I50 <= I52 - 1 /\ I53 <= I48 - 1 /\ I50 <= I53 - 1 /\ I50 <= I54 - 1 /\ y6 <= I47 /\ I47 - 2 * y7 = 0]
3.73/3.72	  f2(I55, I56, I57) -> f3(I55, I56, I56) [0 <= I56 - 1]
3.73/3.72	  f1(I58, I59, I60) -> f2(I61, I62, I63) [-1 <= I64 - 1 /\ 1 <= I59 - 1 /\ I62 <= 0 /\ -1 <= I61 - 1 /\ 0 <= I58 - 1]
3.73/3.72	  f1(I65, I66, I67) -> f2(I68, I69, I70) [-1 <= I71 - 1 /\ 1 <= I66 - 1 /\ -1 <= I68 - 1 /\ I69 <= I72 - 1 /\ -1 <= I72 - 1 /\ 0 <= I65 - 1]
3.73/3.72	
3.73/3.72	The dependency graph for this problem is:
3.73/3.72	  0 -> 2, 10, 11
3.73/3.72	  1 -> 1
3.73/3.72	  2 -> 1
3.73/3.72	  3 -> 4, 6, 8
3.73/3.72	  4 -> 3, 5
3.73/3.72	  5 -> 4, 6, 8
3.73/3.72	  6 -> 3, 5
3.73/3.72	  7 -> 4, 6, 8
3.73/3.72	  8 -> 7
3.73/3.72	  9 -> 4, 6, 8
3.73/3.72	  10 -> 
3.73/3.72	  11 -> 9
3.73/3.72	Where:
3.73/3.72	  0) init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 
3.73/3.72	  1) f5#(I0, I1, I2) -> f5#(I0 - 1, I3, I4) [0 <= I0 - 1]
3.73/3.72	  2) f1#(I5, I6, I7) -> f5#(I8, I9, I10) [-1 <= y2 - 1 /\ 1 <= I6 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ y1 - 1 = I8]
3.73/3.72	  3) f4#(I11, I12, I13) -> f3#(I14, I15, I16) [-1 <= I13 - 1 /\ 0 <= I12 - 1 /\ I15 <= I13 - 1 /\ I15 <= I12 - 1 /\ I11 - 2 * I17 = 1 /\ I14 <= I11 /\ 0 <= I15 - 1 /\ 0 <= I11 - 2 * I17 /\ I11 - 2 * I17 <= 1 /\ I11 - 2 * I14 <= 1 /\ 0 <= I11 - 2 * I14 /\ I15 = I16]
3.73/3.72	  4) f3#(I18, I19, I20) -> f4#(I18, I19, I20) [-1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I21 <= I20 - 1 /\ I21 <= I19 - 1 /\ I18 - 2 * I22 = 1 /\ 0 <= I21 - 1 /\ y3 <= I18]
3.73/3.72	  5) f4#(I23, I24, I25) -> f3#(I26, I27, I28) [-1 <= I25 - 1 /\ 0 <= I24 - 1 /\ I28 <= I25 - 1 /\ I29 <= I24 - 1 /\ I23 - 2 * I30 = 1 /\ I26 <= I23 /\ -1 <= I29 - 1 /\ 0 <= I28 - 1 /\ I27 <= I29 /\ 0 <= I23 - 2 * I30 /\ I23 - 2 * I30 <= 1 /\ I23 - 2 * I26 <= 1 /\ 0 <= I23 - 2 * I26]
3.73/3.72	  6) f3#(I31, I32, I33) -> f4#(I31, I32, I33) [-1 <= I33 - 1 /\ 0 <= I32 - 1 /\ I34 <= I33 - 1 /\ I35 <= I32 - 1 /\ I31 - 2 * I36 = 1 /\ y4 <= I31 /\ -1 <= I35 - 1 /\ y5 <= I35 /\ 0 <= I34 - 1]
3.73/3.72	  7) f4#(I37, I38, I39) -> f3#(I40, I41, I42) [-1 <= I43 - 1 /\ 0 <= I38 - 1 /\ I43 <= I42 - 1 /\ -1 <= I39 - 1 /\ I43 <= I39 - 1 /\ I43 <= I44 - 1 /\ I41 <= I38 - 1 /\ I43 <= I41 - 1 /\ I43 <= I45 - 1 /\ I37 - 2 * I46 = 0 /\ I40 <= I37 /\ 0 <= I37 - 2 * I46 /\ I37 - 2 * I46 <= 1 /\ I37 - 2 * I40 <= 1 /\ 0 <= I37 - 2 * I40]
3.73/3.72	  8) f3#(I47, I48, I49) -> f4#(I47, I48, I49) [-1 <= I50 - 1 /\ 0 <= I48 - 1 /\ I50 <= I51 - 1 /\ -1 <= I49 - 1 /\ I50 <= I49 - 1 /\ I50 <= I52 - 1 /\ I53 <= I48 - 1 /\ I50 <= I53 - 1 /\ I50 <= I54 - 1 /\ y6 <= I47 /\ I47 - 2 * y7 = 0]
3.73/3.72	  9) f2#(I55, I56, I57) -> f3#(I55, I56, I56) [0 <= I56 - 1]
3.73/3.72	  10) f1#(I58, I59, I60) -> f2#(I61, I62, I63) [-1 <= I64 - 1 /\ 1 <= I59 - 1 /\ I62 <= 0 /\ -1 <= I61 - 1 /\ 0 <= I58 - 1]
3.73/3.72	  11) f1#(I65, I66, I67) -> f2#(I68, I69, I70) [-1 <= I71 - 1 /\ 1 <= I66 - 1 /\ -1 <= I68 - 1 /\ I69 <= I72 - 1 /\ -1 <= I72 - 1 /\ 0 <= I65 - 1]
3.73/3.72	
3.73/3.72	We have the following SCCs.
3.73/3.72	  { 1 }
3.73/3.72	  { 3, 4, 5, 6, 7, 8 }
3.73/3.72	
3.73/3.72	DP problem for innermost termination.
3.73/3.72	P =
3.73/3.72	  f4#(I11, I12, I13) -> f3#(I14, I15, I16) [-1 <= I13 - 1 /\ 0 <= I12 - 1 /\ I15 <= I13 - 1 /\ I15 <= I12 - 1 /\ I11 - 2 * I17 = 1 /\ I14 <= I11 /\ 0 <= I15 - 1 /\ 0 <= I11 - 2 * I17 /\ I11 - 2 * I17 <= 1 /\ I11 - 2 * I14 <= 1 /\ 0 <= I11 - 2 * I14 /\ I15 = I16]
3.73/3.72	  f3#(I18, I19, I20) -> f4#(I18, I19, I20) [-1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I21 <= I20 - 1 /\ I21 <= I19 - 1 /\ I18 - 2 * I22 = 1 /\ 0 <= I21 - 1 /\ y3 <= I18]
3.73/3.72	  f4#(I23, I24, I25) -> f3#(I26, I27, I28) [-1 <= I25 - 1 /\ 0 <= I24 - 1 /\ I28 <= I25 - 1 /\ I29 <= I24 - 1 /\ I23 - 2 * I30 = 1 /\ I26 <= I23 /\ -1 <= I29 - 1 /\ 0 <= I28 - 1 /\ I27 <= I29 /\ 0 <= I23 - 2 * I30 /\ I23 - 2 * I30 <= 1 /\ I23 - 2 * I26 <= 1 /\ 0 <= I23 - 2 * I26]
3.73/3.72	  f3#(I31, I32, I33) -> f4#(I31, I32, I33) [-1 <= I33 - 1 /\ 0 <= I32 - 1 /\ I34 <= I33 - 1 /\ I35 <= I32 - 1 /\ I31 - 2 * I36 = 1 /\ y4 <= I31 /\ -1 <= I35 - 1 /\ y5 <= I35 /\ 0 <= I34 - 1]
3.73/3.72	  f4#(I37, I38, I39) -> f3#(I40, I41, I42) [-1 <= I43 - 1 /\ 0 <= I38 - 1 /\ I43 <= I42 - 1 /\ -1 <= I39 - 1 /\ I43 <= I39 - 1 /\ I43 <= I44 - 1 /\ I41 <= I38 - 1 /\ I43 <= I41 - 1 /\ I43 <= I45 - 1 /\ I37 - 2 * I46 = 0 /\ I40 <= I37 /\ 0 <= I37 - 2 * I46 /\ I37 - 2 * I46 <= 1 /\ I37 - 2 * I40 <= 1 /\ 0 <= I37 - 2 * I40]
3.73/3.72	  f3#(I47, I48, I49) -> f4#(I47, I48, I49) [-1 <= I50 - 1 /\ 0 <= I48 - 1 /\ I50 <= I51 - 1 /\ -1 <= I49 - 1 /\ I50 <= I49 - 1 /\ I50 <= I52 - 1 /\ I53 <= I48 - 1 /\ I50 <= I53 - 1 /\ I50 <= I54 - 1 /\ y6 <= I47 /\ I47 - 2 * y7 = 0]
3.73/3.72	R = 
3.73/3.72	  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
3.73/3.72	  f5(I0, I1, I2) -> f5(I0 - 1, I3, I4) [0 <= I0 - 1]
3.73/3.72	  f1(I5, I6, I7) -> f5(I8, I9, I10) [-1 <= y2 - 1 /\ 1 <= I6 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ y1 - 1 = I8]
3.73/3.72	  f4(I11, I12, I13) -> f3(I14, I15, I16) [-1 <= I13 - 1 /\ 0 <= I12 - 1 /\ I15 <= I13 - 1 /\ I15 <= I12 - 1 /\ I11 - 2 * I17 = 1 /\ I14 <= I11 /\ 0 <= I15 - 1 /\ 0 <= I11 - 2 * I17 /\ I11 - 2 * I17 <= 1 /\ I11 - 2 * I14 <= 1 /\ 0 <= I11 - 2 * I14 /\ I15 = I16]
3.73/3.72	  f3(I18, I19, I20) -> f4(I18, I19, I20) [-1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I21 <= I20 - 1 /\ I21 <= I19 - 1 /\ I18 - 2 * I22 = 1 /\ 0 <= I21 - 1 /\ y3 <= I18]
3.73/3.72	  f4(I23, I24, I25) -> f3(I26, I27, I28) [-1 <= I25 - 1 /\ 0 <= I24 - 1 /\ I28 <= I25 - 1 /\ I29 <= I24 - 1 /\ I23 - 2 * I30 = 1 /\ I26 <= I23 /\ -1 <= I29 - 1 /\ 0 <= I28 - 1 /\ I27 <= I29 /\ 0 <= I23 - 2 * I30 /\ I23 - 2 * I30 <= 1 /\ I23 - 2 * I26 <= 1 /\ 0 <= I23 - 2 * I26]
3.73/3.72	  f3(I31, I32, I33) -> f4(I31, I32, I33) [-1 <= I33 - 1 /\ 0 <= I32 - 1 /\ I34 <= I33 - 1 /\ I35 <= I32 - 1 /\ I31 - 2 * I36 = 1 /\ y4 <= I31 /\ -1 <= I35 - 1 /\ y5 <= I35 /\ 0 <= I34 - 1]
3.73/3.72	  f4(I37, I38, I39) -> f3(I40, I41, I42) [-1 <= I43 - 1 /\ 0 <= I38 - 1 /\ I43 <= I42 - 1 /\ -1 <= I39 - 1 /\ I43 <= I39 - 1 /\ I43 <= I44 - 1 /\ I41 <= I38 - 1 /\ I43 <= I41 - 1 /\ I43 <= I45 - 1 /\ I37 - 2 * I46 = 0 /\ I40 <= I37 /\ 0 <= I37 - 2 * I46 /\ I37 - 2 * I46 <= 1 /\ I37 - 2 * I40 <= 1 /\ 0 <= I37 - 2 * I40]
3.73/3.72	  f3(I47, I48, I49) -> f4(I47, I48, I49) [-1 <= I50 - 1 /\ 0 <= I48 - 1 /\ I50 <= I51 - 1 /\ -1 <= I49 - 1 /\ I50 <= I49 - 1 /\ I50 <= I52 - 1 /\ I53 <= I48 - 1 /\ I50 <= I53 - 1 /\ I50 <= I54 - 1 /\ y6 <= I47 /\ I47 - 2 * y7 = 0]
3.73/3.72	  f2(I55, I56, I57) -> f3(I55, I56, I56) [0 <= I56 - 1]
3.73/3.72	  f1(I58, I59, I60) -> f2(I61, I62, I63) [-1 <= I64 - 1 /\ 1 <= I59 - 1 /\ I62 <= 0 /\ -1 <= I61 - 1 /\ 0 <= I58 - 1]
3.73/3.72	  f1(I65, I66, I67) -> f2(I68, I69, I70) [-1 <= I71 - 1 /\ 1 <= I66 - 1 /\ -1 <= I68 - 1 /\ I69 <= I72 - 1 /\ -1 <= I72 - 1 /\ 0 <= I65 - 1]
3.73/3.72	
3.73/3.72	We use the basic value criterion with the projection function NU:
3.73/3.72	  NU[f3#(z1,z2,z3)] = z2
3.73/3.72	  NU[f4#(z1,z2,z3)] = z2
3.73/3.72	
3.73/3.72	This gives the following inequalities:
3.73/3.72	  -1 <= I13 - 1 /\ 0 <= I12 - 1 /\ I15 <= I13 - 1 /\ I15 <= I12 - 1 /\ I11 - 2 * I17 = 1 /\ I14 <= I11 /\ 0 <= I15 - 1 /\ 0 <= I11 - 2 * I17 /\ I11 - 2 * I17 <= 1 /\ I11 - 2 * I14 <= 1 /\ 0 <= I11 - 2 * I14 /\ I15 = I16  ==>  I12 >! I15
3.73/3.72	  -1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I21 <= I20 - 1 /\ I21 <= I19 - 1 /\ I18 - 2 * I22 = 1 /\ 0 <= I21 - 1 /\ y3 <= I18  ==>  I19 (>! \union =) I19
3.73/3.72	  -1 <= I25 - 1 /\ 0 <= I24 - 1 /\ I28 <= I25 - 1 /\ I29 <= I24 - 1 /\ I23 - 2 * I30 = 1 /\ I26 <= I23 /\ -1 <= I29 - 1 /\ 0 <= I28 - 1 /\ I27 <= I29 /\ 0 <= I23 - 2 * I30 /\ I23 - 2 * I30 <= 1 /\ I23 - 2 * I26 <= 1 /\ 0 <= I23 - 2 * I26  ==>  I24 >! I27
3.73/3.72	  -1 <= I33 - 1 /\ 0 <= I32 - 1 /\ I34 <= I33 - 1 /\ I35 <= I32 - 1 /\ I31 - 2 * I36 = 1 /\ y4 <= I31 /\ -1 <= I35 - 1 /\ y5 <= I35 /\ 0 <= I34 - 1  ==>  I32 (>! \union =) I32
3.73/3.72	  -1 <= I43 - 1 /\ 0 <= I38 - 1 /\ I43 <= I42 - 1 /\ -1 <= I39 - 1 /\ I43 <= I39 - 1 /\ I43 <= I44 - 1 /\ I41 <= I38 - 1 /\ I43 <= I41 - 1 /\ I43 <= I45 - 1 /\ I37 - 2 * I46 = 0 /\ I40 <= I37 /\ 0 <= I37 - 2 * I46 /\ I37 - 2 * I46 <= 1 /\ I37 - 2 * I40 <= 1 /\ 0 <= I37 - 2 * I40  ==>  I38 >! I41
3.73/3.72	  -1 <= I50 - 1 /\ 0 <= I48 - 1 /\ I50 <= I51 - 1 /\ -1 <= I49 - 1 /\ I50 <= I49 - 1 /\ I50 <= I52 - 1 /\ I53 <= I48 - 1 /\ I50 <= I53 - 1 /\ I50 <= I54 - 1 /\ y6 <= I47 /\ I47 - 2 * y7 = 0  ==>  I48 (>! \union =) I48
3.73/3.72	
3.73/3.72	We remove all the strictly oriented dependency pairs.
3.73/3.72	
3.73/3.72	DP problem for innermost termination.
3.73/3.72	P =
3.73/3.72	  f3#(I18, I19, I20) -> f4#(I18, I19, I20) [-1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I21 <= I20 - 1 /\ I21 <= I19 - 1 /\ I18 - 2 * I22 = 1 /\ 0 <= I21 - 1 /\ y3 <= I18]
3.73/3.72	  f3#(I31, I32, I33) -> f4#(I31, I32, I33) [-1 <= I33 - 1 /\ 0 <= I32 - 1 /\ I34 <= I33 - 1 /\ I35 <= I32 - 1 /\ I31 - 2 * I36 = 1 /\ y4 <= I31 /\ -1 <= I35 - 1 /\ y5 <= I35 /\ 0 <= I34 - 1]
3.73/3.72	  f3#(I47, I48, I49) -> f4#(I47, I48, I49) [-1 <= I50 - 1 /\ 0 <= I48 - 1 /\ I50 <= I51 - 1 /\ -1 <= I49 - 1 /\ I50 <= I49 - 1 /\ I50 <= I52 - 1 /\ I53 <= I48 - 1 /\ I50 <= I53 - 1 /\ I50 <= I54 - 1 /\ y6 <= I47 /\ I47 - 2 * y7 = 0]
3.73/3.72	R = 
3.73/3.72	  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
3.73/3.72	  f5(I0, I1, I2) -> f5(I0 - 1, I3, I4) [0 <= I0 - 1]
3.73/3.72	  f1(I5, I6, I7) -> f5(I8, I9, I10) [-1 <= y2 - 1 /\ 1 <= I6 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ y1 - 1 = I8]
3.73/3.72	  f4(I11, I12, I13) -> f3(I14, I15, I16) [-1 <= I13 - 1 /\ 0 <= I12 - 1 /\ I15 <= I13 - 1 /\ I15 <= I12 - 1 /\ I11 - 2 * I17 = 1 /\ I14 <= I11 /\ 0 <= I15 - 1 /\ 0 <= I11 - 2 * I17 /\ I11 - 2 * I17 <= 1 /\ I11 - 2 * I14 <= 1 /\ 0 <= I11 - 2 * I14 /\ I15 = I16]
3.73/3.72	  f3(I18, I19, I20) -> f4(I18, I19, I20) [-1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I21 <= I20 - 1 /\ I21 <= I19 - 1 /\ I18 - 2 * I22 = 1 /\ 0 <= I21 - 1 /\ y3 <= I18]
3.73/3.72	  f4(I23, I24, I25) -> f3(I26, I27, I28) [-1 <= I25 - 1 /\ 0 <= I24 - 1 /\ I28 <= I25 - 1 /\ I29 <= I24 - 1 /\ I23 - 2 * I30 = 1 /\ I26 <= I23 /\ -1 <= I29 - 1 /\ 0 <= I28 - 1 /\ I27 <= I29 /\ 0 <= I23 - 2 * I30 /\ I23 - 2 * I30 <= 1 /\ I23 - 2 * I26 <= 1 /\ 0 <= I23 - 2 * I26]
3.73/3.72	  f3(I31, I32, I33) -> f4(I31, I32, I33) [-1 <= I33 - 1 /\ 0 <= I32 - 1 /\ I34 <= I33 - 1 /\ I35 <= I32 - 1 /\ I31 - 2 * I36 = 1 /\ y4 <= I31 /\ -1 <= I35 - 1 /\ y5 <= I35 /\ 0 <= I34 - 1]
3.73/3.72	  f4(I37, I38, I39) -> f3(I40, I41, I42) [-1 <= I43 - 1 /\ 0 <= I38 - 1 /\ I43 <= I42 - 1 /\ -1 <= I39 - 1 /\ I43 <= I39 - 1 /\ I43 <= I44 - 1 /\ I41 <= I38 - 1 /\ I43 <= I41 - 1 /\ I43 <= I45 - 1 /\ I37 - 2 * I46 = 0 /\ I40 <= I37 /\ 0 <= I37 - 2 * I46 /\ I37 - 2 * I46 <= 1 /\ I37 - 2 * I40 <= 1 /\ 0 <= I37 - 2 * I40]
3.73/3.72	  f3(I47, I48, I49) -> f4(I47, I48, I49) [-1 <= I50 - 1 /\ 0 <= I48 - 1 /\ I50 <= I51 - 1 /\ -1 <= I49 - 1 /\ I50 <= I49 - 1 /\ I50 <= I52 - 1 /\ I53 <= I48 - 1 /\ I50 <= I53 - 1 /\ I50 <= I54 - 1 /\ y6 <= I47 /\ I47 - 2 * y7 = 0]
3.73/3.72	  f2(I55, I56, I57) -> f3(I55, I56, I56) [0 <= I56 - 1]
3.73/3.72	  f1(I58, I59, I60) -> f2(I61, I62, I63) [-1 <= I64 - 1 /\ 1 <= I59 - 1 /\ I62 <= 0 /\ -1 <= I61 - 1 /\ 0 <= I58 - 1]
3.73/3.72	  f1(I65, I66, I67) -> f2(I68, I69, I70) [-1 <= I71 - 1 /\ 1 <= I66 - 1 /\ -1 <= I68 - 1 /\ I69 <= I72 - 1 /\ -1 <= I72 - 1 /\ 0 <= I65 - 1]
3.73/3.72	
3.73/3.72	The dependency graph for this problem is:
3.73/3.72	  4 -> 
3.73/3.72	  6 -> 
3.73/3.72	  8 -> 
3.73/3.72	Where:
3.73/3.72	  4) f3#(I18, I19, I20) -> f4#(I18, I19, I20) [-1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I21 <= I20 - 1 /\ I21 <= I19 - 1 /\ I18 - 2 * I22 = 1 /\ 0 <= I21 - 1 /\ y3 <= I18]
3.73/3.72	  6) f3#(I31, I32, I33) -> f4#(I31, I32, I33) [-1 <= I33 - 1 /\ 0 <= I32 - 1 /\ I34 <= I33 - 1 /\ I35 <= I32 - 1 /\ I31 - 2 * I36 = 1 /\ y4 <= I31 /\ -1 <= I35 - 1 /\ y5 <= I35 /\ 0 <= I34 - 1]
3.73/3.72	  8) f3#(I47, I48, I49) -> f4#(I47, I48, I49) [-1 <= I50 - 1 /\ 0 <= I48 - 1 /\ I50 <= I51 - 1 /\ -1 <= I49 - 1 /\ I50 <= I49 - 1 /\ I50 <= I52 - 1 /\ I53 <= I48 - 1 /\ I50 <= I53 - 1 /\ I50 <= I54 - 1 /\ y6 <= I47 /\ I47 - 2 * y7 = 0]
3.73/3.72	
3.73/3.72	We have the following SCCs.
3.73/3.72	  
3.73/3.72	
3.73/3.72	DP problem for innermost termination.
3.73/3.72	P =
3.73/3.72	  f5#(I0, I1, I2) -> f5#(I0 - 1, I3, I4) [0 <= I0 - 1]
3.73/3.72	R = 
3.73/3.72	  init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 
3.73/3.72	  f5(I0, I1, I2) -> f5(I0 - 1, I3, I4) [0 <= I0 - 1]
3.73/3.72	  f1(I5, I6, I7) -> f5(I8, I9, I10) [-1 <= y2 - 1 /\ 1 <= I6 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ y1 - 1 = I8]
3.73/3.72	  f4(I11, I12, I13) -> f3(I14, I15, I16) [-1 <= I13 - 1 /\ 0 <= I12 - 1 /\ I15 <= I13 - 1 /\ I15 <= I12 - 1 /\ I11 - 2 * I17 = 1 /\ I14 <= I11 /\ 0 <= I15 - 1 /\ 0 <= I11 - 2 * I17 /\ I11 - 2 * I17 <= 1 /\ I11 - 2 * I14 <= 1 /\ 0 <= I11 - 2 * I14 /\ I15 = I16]
3.73/3.72	  f3(I18, I19, I20) -> f4(I18, I19, I20) [-1 <= I20 - 1 /\ 0 <= I19 - 1 /\ I21 <= I20 - 1 /\ I21 <= I19 - 1 /\ I18 - 2 * I22 = 1 /\ 0 <= I21 - 1 /\ y3 <= I18]
3.73/3.72	  f4(I23, I24, I25) -> f3(I26, I27, I28) [-1 <= I25 - 1 /\ 0 <= I24 - 1 /\ I28 <= I25 - 1 /\ I29 <= I24 - 1 /\ I23 - 2 * I30 = 1 /\ I26 <= I23 /\ -1 <= I29 - 1 /\ 0 <= I28 - 1 /\ I27 <= I29 /\ 0 <= I23 - 2 * I30 /\ I23 - 2 * I30 <= 1 /\ I23 - 2 * I26 <= 1 /\ 0 <= I23 - 2 * I26]
3.73/3.72	  f3(I31, I32, I33) -> f4(I31, I32, I33) [-1 <= I33 - 1 /\ 0 <= I32 - 1 /\ I34 <= I33 - 1 /\ I35 <= I32 - 1 /\ I31 - 2 * I36 = 1 /\ y4 <= I31 /\ -1 <= I35 - 1 /\ y5 <= I35 /\ 0 <= I34 - 1]
3.73/3.72	  f4(I37, I38, I39) -> f3(I40, I41, I42) [-1 <= I43 - 1 /\ 0 <= I38 - 1 /\ I43 <= I42 - 1 /\ -1 <= I39 - 1 /\ I43 <= I39 - 1 /\ I43 <= I44 - 1 /\ I41 <= I38 - 1 /\ I43 <= I41 - 1 /\ I43 <= I45 - 1 /\ I37 - 2 * I46 = 0 /\ I40 <= I37 /\ 0 <= I37 - 2 * I46 /\ I37 - 2 * I46 <= 1 /\ I37 - 2 * I40 <= 1 /\ 0 <= I37 - 2 * I40]
3.73/3.72	  f3(I47, I48, I49) -> f4(I47, I48, I49) [-1 <= I50 - 1 /\ 0 <= I48 - 1 /\ I50 <= I51 - 1 /\ -1 <= I49 - 1 /\ I50 <= I49 - 1 /\ I50 <= I52 - 1 /\ I53 <= I48 - 1 /\ I50 <= I53 - 1 /\ I50 <= I54 - 1 /\ y6 <= I47 /\ I47 - 2 * y7 = 0]
3.73/3.72	  f2(I55, I56, I57) -> f3(I55, I56, I56) [0 <= I56 - 1]
3.73/3.72	  f1(I58, I59, I60) -> f2(I61, I62, I63) [-1 <= I64 - 1 /\ 1 <= I59 - 1 /\ I62 <= 0 /\ -1 <= I61 - 1 /\ 0 <= I58 - 1]
3.73/3.72	  f1(I65, I66, I67) -> f2(I68, I69, I70) [-1 <= I71 - 1 /\ 1 <= I66 - 1 /\ -1 <= I68 - 1 /\ I69 <= I72 - 1 /\ -1 <= I72 - 1 /\ 0 <= I65 - 1]
3.73/3.72	
3.73/3.72	We use the basic value criterion with the projection function NU:
3.73/3.72	  NU[f5#(z1,z2,z3)] = z1
3.73/3.72	
3.73/3.72	This gives the following inequalities:
3.73/3.72	  0 <= I0 - 1  ==>  I0 >! I0 - 1
3.73/3.72	
3.73/3.72	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
3.73/6.71	EOF