3.05/3.08	YES
3.05/3.08	
3.05/3.08	DP problem for innermost termination.
3.05/3.08	P =
3.05/3.08	  init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 
3.05/3.08	  f4#(I0, I1, I2, I3, I4) -> f4#(I5, I6, I2 - 1, I3, I4 + 1) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I5 - 2 <= I0 /\ I5 - 2 <= I1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I5 - 1 /\ 4 <= I6 - 1]
3.05/3.08	  f4#(I7, I8, I9, I10, I11) -> f4#(I12, I13, I9 - 1, I10, I11 + 1) [4 <= I13 - 1 /\ 4 <= I12 - 1 /\ 2 <= I8 - 1 /\ 2 <= I7 - 1 /\ I13 - 2 <= I8 /\ I13 - 2 <= I7 /\ I12 - 2 <= I8 /\ I12 - 2 <= I7 /\ I11 <= I10 - 1 /\ -1 <= I11 - 1 /\ 0 <= I9 - 1]
3.05/3.08	  f4#(I14, I15, I16, I17, I18) -> f4#(I19, I20, I16 - 1, I17, I18 + 1) [2 <= I20 - 1 /\ 2 <= I19 - 1 /\ 1 <= I15 - 1 /\ 2 <= I14 - 1 /\ I18 <= I17 - 1 /\ -1 <= I18 - 1 /\ 0 <= I16 - 1]
3.05/3.08	  f4#(I21, I22, I23, I24, I25) -> f4#(I26, I27, I23 - 1, I24, I25 + 1) [-1 <= I25 - 1 /\ 0 <= I28 - 1 /\ 0 <= I23 - 1 /\ I25 <= I24 - 1 /\ 2 <= I21 - 1 /\ 1 <= I22 - 1 /\ 2 <= I26 - 1 /\ 2 <= I27 - 1]
3.05/3.08	  f4#(I29, I30, I31, I32, I33) -> f4#(I34, I35, I31 - 1, I32, I33 + 1) [-1 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I31 - 1 /\ I33 <= I32 - 1 /\ I34 <= I29 /\ I35 + 2 <= I30 /\ 2 <= I29 - 1 /\ 2 <= I30 - 1 /\ 2 <= I34 - 1 /\ 0 <= I35 - 1]
3.05/3.08	  f4#(I37, I38, I39, I40, I41) -> f4#(I42, I43, I39 - 1, I40, I41 + 1) [0 <= I43 - 1 /\ 2 <= I42 - 1 /\ 2 <= I38 - 1 /\ 2 <= I37 - 1 /\ I43 + 2 <= I38 /\ I42 <= I37 /\ I41 <= I40 - 1 /\ -1 <= I41 - 1 /\ 0 <= I39 - 1]
3.05/3.08	  f1#(I44, I45, I46, I47, I48) -> f4#(I49, I50, I51, I45, 1) [2 <= I50 - 1 /\ 2 <= I49 - 1 /\ 0 <= I44 - 1 /\ I50 - 2 <= I44 /\ I49 - 2 <= I44 /\ 0 <= I51 - 1 /\ 0 <= I45 - 1]
3.05/3.08	  f2#(I52, I53, I54, I55, I56) -> f2#(I57, I58, I59, I60, I61) [-1 <= I58 - 1 /\ 2 <= I57 - 1 /\ 0 <= I53 - 1 /\ 2 <= I52 - 1 /\ I58 + 1 <= I53 /\ I58 + 3 <= I52 /\ I57 - 2 <= I52]
3.05/3.08	  f3#(I62, I63, I64, I65, I66) -> f2#(I67, I68, I69, I70, I71) [I63 + 2 <= I62 /\ -1 <= I68 - 1 /\ 2 <= I67 - 1 /\ 2 <= I62 - 1 /\ I68 + 3 <= I62 /\ I67 <= I62]
3.05/3.08	  f1#(I72, I73, I74, I75, I76) -> f2#(I77, I78, I79, I80, I81) [-1 <= I78 - 1 /\ 2 <= I77 - 1 /\ 0 <= I72 - 1]
3.05/3.08	R = 
3.05/3.08	  init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 
3.05/3.08	  f4(I0, I1, I2, I3, I4) -> f4(I5, I6, I2 - 1, I3, I4 + 1) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I5 - 2 <= I0 /\ I5 - 2 <= I1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I5 - 1 /\ 4 <= I6 - 1]
3.05/3.08	  f4(I7, I8, I9, I10, I11) -> f4(I12, I13, I9 - 1, I10, I11 + 1) [4 <= I13 - 1 /\ 4 <= I12 - 1 /\ 2 <= I8 - 1 /\ 2 <= I7 - 1 /\ I13 - 2 <= I8 /\ I13 - 2 <= I7 /\ I12 - 2 <= I8 /\ I12 - 2 <= I7 /\ I11 <= I10 - 1 /\ -1 <= I11 - 1 /\ 0 <= I9 - 1]
3.05/3.08	  f4(I14, I15, I16, I17, I18) -> f4(I19, I20, I16 - 1, I17, I18 + 1) [2 <= I20 - 1 /\ 2 <= I19 - 1 /\ 1 <= I15 - 1 /\ 2 <= I14 - 1 /\ I18 <= I17 - 1 /\ -1 <= I18 - 1 /\ 0 <= I16 - 1]
3.05/3.08	  f4(I21, I22, I23, I24, I25) -> f4(I26, I27, I23 - 1, I24, I25 + 1) [-1 <= I25 - 1 /\ 0 <= I28 - 1 /\ 0 <= I23 - 1 /\ I25 <= I24 - 1 /\ 2 <= I21 - 1 /\ 1 <= I22 - 1 /\ 2 <= I26 - 1 /\ 2 <= I27 - 1]
3.05/3.08	  f4(I29, I30, I31, I32, I33) -> f4(I34, I35, I31 - 1, I32, I33 + 1) [-1 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I31 - 1 /\ I33 <= I32 - 1 /\ I34 <= I29 /\ I35 + 2 <= I30 /\ 2 <= I29 - 1 /\ 2 <= I30 - 1 /\ 2 <= I34 - 1 /\ 0 <= I35 - 1]
3.05/3.08	  f4(I37, I38, I39, I40, I41) -> f4(I42, I43, I39 - 1, I40, I41 + 1) [0 <= I43 - 1 /\ 2 <= I42 - 1 /\ 2 <= I38 - 1 /\ 2 <= I37 - 1 /\ I43 + 2 <= I38 /\ I42 <= I37 /\ I41 <= I40 - 1 /\ -1 <= I41 - 1 /\ 0 <= I39 - 1]
3.05/3.08	  f1(I44, I45, I46, I47, I48) -> f4(I49, I50, I51, I45, 1) [2 <= I50 - 1 /\ 2 <= I49 - 1 /\ 0 <= I44 - 1 /\ I50 - 2 <= I44 /\ I49 - 2 <= I44 /\ 0 <= I51 - 1 /\ 0 <= I45 - 1]
3.05/3.08	  f2(I52, I53, I54, I55, I56) -> f2(I57, I58, I59, I60, I61) [-1 <= I58 - 1 /\ 2 <= I57 - 1 /\ 0 <= I53 - 1 /\ 2 <= I52 - 1 /\ I58 + 1 <= I53 /\ I58 + 3 <= I52 /\ I57 - 2 <= I52]
3.05/3.08	  f3(I62, I63, I64, I65, I66) -> f2(I67, I68, I69, I70, I71) [I63 + 2 <= I62 /\ -1 <= I68 - 1 /\ 2 <= I67 - 1 /\ 2 <= I62 - 1 /\ I68 + 3 <= I62 /\ I67 <= I62]
3.05/3.08	  f1(I72, I73, I74, I75, I76) -> f2(I77, I78, I79, I80, I81) [-1 <= I78 - 1 /\ 2 <= I77 - 1 /\ 0 <= I72 - 1]
3.05/3.08	
3.05/3.08	The dependency graph for this problem is:
3.05/3.08	  0 -> 7, 10
3.05/3.08	  1 -> 1, 2, 3, 4, 5, 6
3.05/3.08	  2 -> 1, 2, 3, 4, 5, 6
3.05/3.08	  3 -> 1, 2, 3, 4, 5, 6
3.05/3.08	  4 -> 1, 2, 3, 4, 5, 6
3.05/3.08	  5 -> 1, 2, 3, 4, 5, 6
3.05/3.08	  6 -> 1, 2, 3, 4, 5, 6
3.05/3.08	  7 -> 1, 2, 3, 4, 5, 6
3.05/3.08	  8 -> 8
3.05/3.08	  9 -> 8
3.05/3.08	  10 -> 8
3.05/3.08	Where:
3.05/3.08	  0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 
3.05/3.08	  1) f4#(I0, I1, I2, I3, I4) -> f4#(I5, I6, I2 - 1, I3, I4 + 1) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I5 - 2 <= I0 /\ I5 - 2 <= I1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I5 - 1 /\ 4 <= I6 - 1]
3.05/3.08	  2) f4#(I7, I8, I9, I10, I11) -> f4#(I12, I13, I9 - 1, I10, I11 + 1) [4 <= I13 - 1 /\ 4 <= I12 - 1 /\ 2 <= I8 - 1 /\ 2 <= I7 - 1 /\ I13 - 2 <= I8 /\ I13 - 2 <= I7 /\ I12 - 2 <= I8 /\ I12 - 2 <= I7 /\ I11 <= I10 - 1 /\ -1 <= I11 - 1 /\ 0 <= I9 - 1]
3.05/3.08	  3) f4#(I14, I15, I16, I17, I18) -> f4#(I19, I20, I16 - 1, I17, I18 + 1) [2 <= I20 - 1 /\ 2 <= I19 - 1 /\ 1 <= I15 - 1 /\ 2 <= I14 - 1 /\ I18 <= I17 - 1 /\ -1 <= I18 - 1 /\ 0 <= I16 - 1]
3.05/3.08	  4) f4#(I21, I22, I23, I24, I25) -> f4#(I26, I27, I23 - 1, I24, I25 + 1) [-1 <= I25 - 1 /\ 0 <= I28 - 1 /\ 0 <= I23 - 1 /\ I25 <= I24 - 1 /\ 2 <= I21 - 1 /\ 1 <= I22 - 1 /\ 2 <= I26 - 1 /\ 2 <= I27 - 1]
3.05/3.08	  5) f4#(I29, I30, I31, I32, I33) -> f4#(I34, I35, I31 - 1, I32, I33 + 1) [-1 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I31 - 1 /\ I33 <= I32 - 1 /\ I34 <= I29 /\ I35 + 2 <= I30 /\ 2 <= I29 - 1 /\ 2 <= I30 - 1 /\ 2 <= I34 - 1 /\ 0 <= I35 - 1]
3.05/3.08	  6) f4#(I37, I38, I39, I40, I41) -> f4#(I42, I43, I39 - 1, I40, I41 + 1) [0 <= I43 - 1 /\ 2 <= I42 - 1 /\ 2 <= I38 - 1 /\ 2 <= I37 - 1 /\ I43 + 2 <= I38 /\ I42 <= I37 /\ I41 <= I40 - 1 /\ -1 <= I41 - 1 /\ 0 <= I39 - 1]
3.05/3.08	  7) f1#(I44, I45, I46, I47, I48) -> f4#(I49, I50, I51, I45, 1) [2 <= I50 - 1 /\ 2 <= I49 - 1 /\ 0 <= I44 - 1 /\ I50 - 2 <= I44 /\ I49 - 2 <= I44 /\ 0 <= I51 - 1 /\ 0 <= I45 - 1]
3.05/3.08	  8) f2#(I52, I53, I54, I55, I56) -> f2#(I57, I58, I59, I60, I61) [-1 <= I58 - 1 /\ 2 <= I57 - 1 /\ 0 <= I53 - 1 /\ 2 <= I52 - 1 /\ I58 + 1 <= I53 /\ I58 + 3 <= I52 /\ I57 - 2 <= I52]
3.05/3.08	  9) f3#(I62, I63, I64, I65, I66) -> f2#(I67, I68, I69, I70, I71) [I63 + 2 <= I62 /\ -1 <= I68 - 1 /\ 2 <= I67 - 1 /\ 2 <= I62 - 1 /\ I68 + 3 <= I62 /\ I67 <= I62]
3.05/3.08	  10) f1#(I72, I73, I74, I75, I76) -> f2#(I77, I78, I79, I80, I81) [-1 <= I78 - 1 /\ 2 <= I77 - 1 /\ 0 <= I72 - 1]
3.05/3.08	
3.05/3.08	We have the following SCCs.
3.05/3.08	  { 1, 2, 3, 4, 5, 6 }
3.05/3.08	  { 8 }
3.05/3.08	
3.05/3.08	DP problem for innermost termination.
3.05/3.08	P =
3.05/3.08	  f2#(I52, I53, I54, I55, I56) -> f2#(I57, I58, I59, I60, I61) [-1 <= I58 - 1 /\ 2 <= I57 - 1 /\ 0 <= I53 - 1 /\ 2 <= I52 - 1 /\ I58 + 1 <= I53 /\ I58 + 3 <= I52 /\ I57 - 2 <= I52]
3.05/3.08	R = 
3.05/3.08	  init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 
3.05/3.08	  f4(I0, I1, I2, I3, I4) -> f4(I5, I6, I2 - 1, I3, I4 + 1) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I5 - 2 <= I0 /\ I5 - 2 <= I1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I5 - 1 /\ 4 <= I6 - 1]
3.05/3.08	  f4(I7, I8, I9, I10, I11) -> f4(I12, I13, I9 - 1, I10, I11 + 1) [4 <= I13 - 1 /\ 4 <= I12 - 1 /\ 2 <= I8 - 1 /\ 2 <= I7 - 1 /\ I13 - 2 <= I8 /\ I13 - 2 <= I7 /\ I12 - 2 <= I8 /\ I12 - 2 <= I7 /\ I11 <= I10 - 1 /\ -1 <= I11 - 1 /\ 0 <= I9 - 1]
3.05/3.08	  f4(I14, I15, I16, I17, I18) -> f4(I19, I20, I16 - 1, I17, I18 + 1) [2 <= I20 - 1 /\ 2 <= I19 - 1 /\ 1 <= I15 - 1 /\ 2 <= I14 - 1 /\ I18 <= I17 - 1 /\ -1 <= I18 - 1 /\ 0 <= I16 - 1]
3.05/3.08	  f4(I21, I22, I23, I24, I25) -> f4(I26, I27, I23 - 1, I24, I25 + 1) [-1 <= I25 - 1 /\ 0 <= I28 - 1 /\ 0 <= I23 - 1 /\ I25 <= I24 - 1 /\ 2 <= I21 - 1 /\ 1 <= I22 - 1 /\ 2 <= I26 - 1 /\ 2 <= I27 - 1]
3.05/3.08	  f4(I29, I30, I31, I32, I33) -> f4(I34, I35, I31 - 1, I32, I33 + 1) [-1 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I31 - 1 /\ I33 <= I32 - 1 /\ I34 <= I29 /\ I35 + 2 <= I30 /\ 2 <= I29 - 1 /\ 2 <= I30 - 1 /\ 2 <= I34 - 1 /\ 0 <= I35 - 1]
3.05/3.08	  f4(I37, I38, I39, I40, I41) -> f4(I42, I43, I39 - 1, I40, I41 + 1) [0 <= I43 - 1 /\ 2 <= I42 - 1 /\ 2 <= I38 - 1 /\ 2 <= I37 - 1 /\ I43 + 2 <= I38 /\ I42 <= I37 /\ I41 <= I40 - 1 /\ -1 <= I41 - 1 /\ 0 <= I39 - 1]
3.05/3.08	  f1(I44, I45, I46, I47, I48) -> f4(I49, I50, I51, I45, 1) [2 <= I50 - 1 /\ 2 <= I49 - 1 /\ 0 <= I44 - 1 /\ I50 - 2 <= I44 /\ I49 - 2 <= I44 /\ 0 <= I51 - 1 /\ 0 <= I45 - 1]
3.05/3.08	  f2(I52, I53, I54, I55, I56) -> f2(I57, I58, I59, I60, I61) [-1 <= I58 - 1 /\ 2 <= I57 - 1 /\ 0 <= I53 - 1 /\ 2 <= I52 - 1 /\ I58 + 1 <= I53 /\ I58 + 3 <= I52 /\ I57 - 2 <= I52]
3.05/3.08	  f3(I62, I63, I64, I65, I66) -> f2(I67, I68, I69, I70, I71) [I63 + 2 <= I62 /\ -1 <= I68 - 1 /\ 2 <= I67 - 1 /\ 2 <= I62 - 1 /\ I68 + 3 <= I62 /\ I67 <= I62]
3.05/3.08	  f1(I72, I73, I74, I75, I76) -> f2(I77, I78, I79, I80, I81) [-1 <= I78 - 1 /\ 2 <= I77 - 1 /\ 0 <= I72 - 1]
3.05/3.08	
3.05/3.08	We use the basic value criterion with the projection function NU:
3.05/3.08	  NU[f2#(z1,z2,z3,z4,z5)] = z2
3.05/3.08	
3.05/3.08	This gives the following inequalities:
3.05/3.08	  -1 <= I58 - 1 /\ 2 <= I57 - 1 /\ 0 <= I53 - 1 /\ 2 <= I52 - 1 /\ I58 + 1 <= I53 /\ I58 + 3 <= I52 /\ I57 - 2 <= I52  ==>  I53 >! I58
3.05/3.08	
3.05/3.08	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
3.05/3.08	
3.05/3.08	DP problem for innermost termination.
3.05/3.08	P =
3.05/3.08	  f4#(I0, I1, I2, I3, I4) -> f4#(I5, I6, I2 - 1, I3, I4 + 1) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I5 - 2 <= I0 /\ I5 - 2 <= I1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I5 - 1 /\ 4 <= I6 - 1]
3.05/3.08	  f4#(I7, I8, I9, I10, I11) -> f4#(I12, I13, I9 - 1, I10, I11 + 1) [4 <= I13 - 1 /\ 4 <= I12 - 1 /\ 2 <= I8 - 1 /\ 2 <= I7 - 1 /\ I13 - 2 <= I8 /\ I13 - 2 <= I7 /\ I12 - 2 <= I8 /\ I12 - 2 <= I7 /\ I11 <= I10 - 1 /\ -1 <= I11 - 1 /\ 0 <= I9 - 1]
3.05/3.08	  f4#(I14, I15, I16, I17, I18) -> f4#(I19, I20, I16 - 1, I17, I18 + 1) [2 <= I20 - 1 /\ 2 <= I19 - 1 /\ 1 <= I15 - 1 /\ 2 <= I14 - 1 /\ I18 <= I17 - 1 /\ -1 <= I18 - 1 /\ 0 <= I16 - 1]
3.05/3.08	  f4#(I21, I22, I23, I24, I25) -> f4#(I26, I27, I23 - 1, I24, I25 + 1) [-1 <= I25 - 1 /\ 0 <= I28 - 1 /\ 0 <= I23 - 1 /\ I25 <= I24 - 1 /\ 2 <= I21 - 1 /\ 1 <= I22 - 1 /\ 2 <= I26 - 1 /\ 2 <= I27 - 1]
3.05/3.08	  f4#(I29, I30, I31, I32, I33) -> f4#(I34, I35, I31 - 1, I32, I33 + 1) [-1 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I31 - 1 /\ I33 <= I32 - 1 /\ I34 <= I29 /\ I35 + 2 <= I30 /\ 2 <= I29 - 1 /\ 2 <= I30 - 1 /\ 2 <= I34 - 1 /\ 0 <= I35 - 1]
3.05/3.08	  f4#(I37, I38, I39, I40, I41) -> f4#(I42, I43, I39 - 1, I40, I41 + 1) [0 <= I43 - 1 /\ 2 <= I42 - 1 /\ 2 <= I38 - 1 /\ 2 <= I37 - 1 /\ I43 + 2 <= I38 /\ I42 <= I37 /\ I41 <= I40 - 1 /\ -1 <= I41 - 1 /\ 0 <= I39 - 1]
3.05/3.08	R = 
3.05/3.08	  init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 
3.05/3.08	  f4(I0, I1, I2, I3, I4) -> f4(I5, I6, I2 - 1, I3, I4 + 1) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I5 - 2 <= I0 /\ I5 - 2 <= I1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I5 - 1 /\ 4 <= I6 - 1]
3.05/3.08	  f4(I7, I8, I9, I10, I11) -> f4(I12, I13, I9 - 1, I10, I11 + 1) [4 <= I13 - 1 /\ 4 <= I12 - 1 /\ 2 <= I8 - 1 /\ 2 <= I7 - 1 /\ I13 - 2 <= I8 /\ I13 - 2 <= I7 /\ I12 - 2 <= I8 /\ I12 - 2 <= I7 /\ I11 <= I10 - 1 /\ -1 <= I11 - 1 /\ 0 <= I9 - 1]
3.05/3.08	  f4(I14, I15, I16, I17, I18) -> f4(I19, I20, I16 - 1, I17, I18 + 1) [2 <= I20 - 1 /\ 2 <= I19 - 1 /\ 1 <= I15 - 1 /\ 2 <= I14 - 1 /\ I18 <= I17 - 1 /\ -1 <= I18 - 1 /\ 0 <= I16 - 1]
3.05/3.08	  f4(I21, I22, I23, I24, I25) -> f4(I26, I27, I23 - 1, I24, I25 + 1) [-1 <= I25 - 1 /\ 0 <= I28 - 1 /\ 0 <= I23 - 1 /\ I25 <= I24 - 1 /\ 2 <= I21 - 1 /\ 1 <= I22 - 1 /\ 2 <= I26 - 1 /\ 2 <= I27 - 1]
3.05/3.08	  f4(I29, I30, I31, I32, I33) -> f4(I34, I35, I31 - 1, I32, I33 + 1) [-1 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I31 - 1 /\ I33 <= I32 - 1 /\ I34 <= I29 /\ I35 + 2 <= I30 /\ 2 <= I29 - 1 /\ 2 <= I30 - 1 /\ 2 <= I34 - 1 /\ 0 <= I35 - 1]
3.05/3.08	  f4(I37, I38, I39, I40, I41) -> f4(I42, I43, I39 - 1, I40, I41 + 1) [0 <= I43 - 1 /\ 2 <= I42 - 1 /\ 2 <= I38 - 1 /\ 2 <= I37 - 1 /\ I43 + 2 <= I38 /\ I42 <= I37 /\ I41 <= I40 - 1 /\ -1 <= I41 - 1 /\ 0 <= I39 - 1]
3.05/3.08	  f1(I44, I45, I46, I47, I48) -> f4(I49, I50, I51, I45, 1) [2 <= I50 - 1 /\ 2 <= I49 - 1 /\ 0 <= I44 - 1 /\ I50 - 2 <= I44 /\ I49 - 2 <= I44 /\ 0 <= I51 - 1 /\ 0 <= I45 - 1]
3.05/3.08	  f2(I52, I53, I54, I55, I56) -> f2(I57, I58, I59, I60, I61) [-1 <= I58 - 1 /\ 2 <= I57 - 1 /\ 0 <= I53 - 1 /\ 2 <= I52 - 1 /\ I58 + 1 <= I53 /\ I58 + 3 <= I52 /\ I57 - 2 <= I52]
3.05/3.08	  f3(I62, I63, I64, I65, I66) -> f2(I67, I68, I69, I70, I71) [I63 + 2 <= I62 /\ -1 <= I68 - 1 /\ 2 <= I67 - 1 /\ 2 <= I62 - 1 /\ I68 + 3 <= I62 /\ I67 <= I62]
3.05/3.08	  f1(I72, I73, I74, I75, I76) -> f2(I77, I78, I79, I80, I81) [-1 <= I78 - 1 /\ 2 <= I77 - 1 /\ 0 <= I72 - 1]
3.05/3.08	
3.05/3.08	We use the basic value criterion with the projection function NU:
3.05/3.08	  NU[f4#(z1,z2,z3,z4,z5)] = z3
3.05/3.08	
3.05/3.08	This gives the following inequalities:
3.05/3.08	  -1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I5 - 2 <= I0 /\ I5 - 2 <= I1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I5 - 1 /\ 4 <= I6 - 1  ==>  I2 >! I2 - 1
3.05/3.08	  4 <= I13 - 1 /\ 4 <= I12 - 1 /\ 2 <= I8 - 1 /\ 2 <= I7 - 1 /\ I13 - 2 <= I8 /\ I13 - 2 <= I7 /\ I12 - 2 <= I8 /\ I12 - 2 <= I7 /\ I11 <= I10 - 1 /\ -1 <= I11 - 1 /\ 0 <= I9 - 1  ==>  I9 >! I9 - 1
3.05/3.08	  2 <= I20 - 1 /\ 2 <= I19 - 1 /\ 1 <= I15 - 1 /\ 2 <= I14 - 1 /\ I18 <= I17 - 1 /\ -1 <= I18 - 1 /\ 0 <= I16 - 1  ==>  I16 >! I16 - 1
3.05/3.08	  -1 <= I25 - 1 /\ 0 <= I28 - 1 /\ 0 <= I23 - 1 /\ I25 <= I24 - 1 /\ 2 <= I21 - 1 /\ 1 <= I22 - 1 /\ 2 <= I26 - 1 /\ 2 <= I27 - 1  ==>  I23 >! I23 - 1
3.05/3.08	  -1 <= I33 - 1 /\ 0 <= I36 - 1 /\ 0 <= I31 - 1 /\ I33 <= I32 - 1 /\ I34 <= I29 /\ I35 + 2 <= I30 /\ 2 <= I29 - 1 /\ 2 <= I30 - 1 /\ 2 <= I34 - 1 /\ 0 <= I35 - 1  ==>  I31 >! I31 - 1
3.05/3.08	  0 <= I43 - 1 /\ 2 <= I42 - 1 /\ 2 <= I38 - 1 /\ 2 <= I37 - 1 /\ I43 + 2 <= I38 /\ I42 <= I37 /\ I41 <= I40 - 1 /\ -1 <= I41 - 1 /\ 0 <= I39 - 1  ==>  I39 >! I39 - 1
3.05/3.08	
3.05/3.08	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
3.05/6.06	EOF