24.79/24.48	YES
24.79/24.48	
24.79/24.48	DP problem for innermost termination.
24.79/24.48	P =
24.79/24.48	  init#(x1, x2, x3, x4, x5, x6, x7, x8) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8) 
24.79/24.48	  f4#(I0, I1, I2, I3, I4, I5, I6, I7) -> f2#(I8, I9, I1, I4, I5, I6, I7, I10) [I6 + 2 <= I3 /\ I7 + 2 <= I3 /\ I5 + 2 <= I2 /\ I4 + 2 <= I2 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ I9 <= I3 /\ I8 <= I2 /\ 0 <= I0 - 1 /\ I1 <= I0 - 1]
24.79/24.48	  f3#(I11, I12, I13, I14, I15, I16, I17, I18) -> f4#(I13, I13 - 1, I19, I20, I21, I22, I16, I17) [0 <= I16 + I17 + I15 - I14 - 2 * I22 /\ I16 + I17 + I15 - I14 - 2 * I22 <= 1 /\ I14 + I15 + I16 - I17 - 2 * I21 <= 1 /\ 0 <= I14 + I15 + I16 - I17 - 2 * I21 /\ I17 + 2 <= I12 /\ I16 + 2 <= I12 /\ I15 + 2 <= I11 /\ I14 + 2 <= I11 /\ 0 <= I20 - 1 /\ 0 <= I19 - 1 /\ 0 <= I12 - 1 /\ 0 <= I11 - 1 /\ I20 <= I12 /\ I13 - 1 <= I13 - 1 /\ 0 <= I13 - 1]
24.79/24.48	  f2#(I23, I24, I25, I26, I27, I28, I29, I30) -> f3#(I23, I24, I25, I26, I27, I28, I29, I31) [0 <= I25 - 1 /\ I25 - 1 <= I25 - 1 /\ y2 <= I24 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I26 + 2 <= I23 /\ I27 + 2 <= I23 /\ I29 + 2 <= I24 /\ I28 + 2 <= I24]
24.79/24.48	  f3#(I32, I33, I34, I35, I36, I37, I38, I39) -> f4#(1, 0, I40, I41, I42, I43, I37, I38) [1 = I34 /\ 0 <= I35 + I36 + I37 - I38 - 2 * I42 /\ I35 + I36 + I37 - I38 - 2 * I42 <= 1 /\ I37 + I38 + I36 - I35 - 2 * I43 <= 1 /\ 0 <= I37 + I38 + I36 - I35 - 2 * I43 /\ I38 + 2 <= I33 /\ I37 + 2 <= I33 /\ I36 + 2 <= I32 /\ I35 + 2 <= I32 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I41 <= I33]
24.79/24.48	  f2#(I44, I45, I46, I47, I48, I49, I50, I51) -> f3#(I44, I45, 1, I47, I48, I49, I50, I52) [I53 <= I45 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ 0 <= I54 - 1 /\ 0 <= I53 - 1 /\ I47 + 2 <= I44 /\ I48 + 2 <= I44 /\ I50 + 2 <= I45 /\ I49 + 2 <= I45 /\ 1 = I46]
24.79/24.48	  f3#(I55, I56, I57, I58, I59, I60, I61, I62) -> f2#(I63, I64, I57 - 1, I58, I59, I65, I66, I67) [0 <= I60 + I61 + I59 - I58 - 2 * I66 /\ I60 + I61 + I59 - I58 - 2 * I66 <= 1 /\ I58 + I59 + I60 - I61 - 2 * I65 <= 1 /\ 0 <= I58 + I59 + I60 - I61 - 2 * I65 /\ I61 + 2 <= I56 /\ I60 + 2 <= I56 /\ I59 + 2 <= I55 /\ I58 + 2 <= I55 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I56 - 1 /\ 0 <= I55 - 1 /\ I63 <= I55 /\ I57 - 1 <= I57 - 1 /\ 0 <= I57 - 1]
24.79/24.48	  f2#(I68, I69, I70, I71, I72, I73, I74, I75) -> f3#(I68, I69, I70, I71, I72, I73, I74, I76) [0 <= I70 - 1 /\ I70 - 1 <= I70 - 1 /\ I77 <= I68 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1 /\ 0 <= I77 - 1 /\ 0 <= I78 - 1 /\ I71 + 2 <= I68 /\ I72 + 2 <= I68 /\ I74 + 2 <= I69 /\ I73 + 2 <= I69]
24.79/24.48	  f1#(I79, I80, I81, I82, I83, I84, I85, I86) -> f2#(I87, I88, I80, 0, 0, 200, 200, I89) [201 <= I88 - 1 /\ 1 <= I87 - 1 /\ 0 <= I79 - 1 /\ I88 - 201 <= I79 /\ -1 <= I80 - 1 /\ I87 - 1 <= I79]
24.79/24.48	R = 
24.79/24.48	  init(x1, x2, x3, x4, x5, x6, x7, x8) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8) 
24.79/24.48	  f4(I0, I1, I2, I3, I4, I5, I6, I7) -> f2(I8, I9, I1, I4, I5, I6, I7, I10) [I6 + 2 <= I3 /\ I7 + 2 <= I3 /\ I5 + 2 <= I2 /\ I4 + 2 <= I2 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ I9 <= I3 /\ I8 <= I2 /\ 0 <= I0 - 1 /\ I1 <= I0 - 1]
24.79/24.48	  f3(I11, I12, I13, I14, I15, I16, I17, I18) -> f4(I13, I13 - 1, I19, I20, I21, I22, I16, I17) [0 <= I16 + I17 + I15 - I14 - 2 * I22 /\ I16 + I17 + I15 - I14 - 2 * I22 <= 1 /\ I14 + I15 + I16 - I17 - 2 * I21 <= 1 /\ 0 <= I14 + I15 + I16 - I17 - 2 * I21 /\ I17 + 2 <= I12 /\ I16 + 2 <= I12 /\ I15 + 2 <= I11 /\ I14 + 2 <= I11 /\ 0 <= I20 - 1 /\ 0 <= I19 - 1 /\ 0 <= I12 - 1 /\ 0 <= I11 - 1 /\ I20 <= I12 /\ I13 - 1 <= I13 - 1 /\ 0 <= I13 - 1]
24.79/24.48	  f2(I23, I24, I25, I26, I27, I28, I29, I30) -> f3(I23, I24, I25, I26, I27, I28, I29, I31) [0 <= I25 - 1 /\ I25 - 1 <= I25 - 1 /\ y2 <= I24 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I26 + 2 <= I23 /\ I27 + 2 <= I23 /\ I29 + 2 <= I24 /\ I28 + 2 <= I24]
24.79/24.48	  f3(I32, I33, I34, I35, I36, I37, I38, I39) -> f4(1, 0, I40, I41, I42, I43, I37, I38) [1 = I34 /\ 0 <= I35 + I36 + I37 - I38 - 2 * I42 /\ I35 + I36 + I37 - I38 - 2 * I42 <= 1 /\ I37 + I38 + I36 - I35 - 2 * I43 <= 1 /\ 0 <= I37 + I38 + I36 - I35 - 2 * I43 /\ I38 + 2 <= I33 /\ I37 + 2 <= I33 /\ I36 + 2 <= I32 /\ I35 + 2 <= I32 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I41 <= I33]
24.79/24.48	  f2(I44, I45, I46, I47, I48, I49, I50, I51) -> f3(I44, I45, 1, I47, I48, I49, I50, I52) [I53 <= I45 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ 0 <= I54 - 1 /\ 0 <= I53 - 1 /\ I47 + 2 <= I44 /\ I48 + 2 <= I44 /\ I50 + 2 <= I45 /\ I49 + 2 <= I45 /\ 1 = I46]
24.79/24.48	  f3(I55, I56, I57, I58, I59, I60, I61, I62) -> f2(I63, I64, I57 - 1, I58, I59, I65, I66, I67) [0 <= I60 + I61 + I59 - I58 - 2 * I66 /\ I60 + I61 + I59 - I58 - 2 * I66 <= 1 /\ I58 + I59 + I60 - I61 - 2 * I65 <= 1 /\ 0 <= I58 + I59 + I60 - I61 - 2 * I65 /\ I61 + 2 <= I56 /\ I60 + 2 <= I56 /\ I59 + 2 <= I55 /\ I58 + 2 <= I55 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I56 - 1 /\ 0 <= I55 - 1 /\ I63 <= I55 /\ I57 - 1 <= I57 - 1 /\ 0 <= I57 - 1]
24.79/24.48	  f2(I68, I69, I70, I71, I72, I73, I74, I75) -> f3(I68, I69, I70, I71, I72, I73, I74, I76) [0 <= I70 - 1 /\ I70 - 1 <= I70 - 1 /\ I77 <= I68 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1 /\ 0 <= I77 - 1 /\ 0 <= I78 - 1 /\ I71 + 2 <= I68 /\ I72 + 2 <= I68 /\ I74 + 2 <= I69 /\ I73 + 2 <= I69]
24.79/24.48	  f1(I79, I80, I81, I82, I83, I84, I85, I86) -> f2(I87, I88, I80, 0, 0, 200, 200, I89) [201 <= I88 - 1 /\ 1 <= I87 - 1 /\ 0 <= I79 - 1 /\ I88 - 201 <= I79 /\ -1 <= I80 - 1 /\ I87 - 1 <= I79]
24.79/24.48	
24.79/24.48	The dependency graph for this problem is:
24.79/24.48	  0 -> 8
24.79/24.48	  1 -> 3, 5, 7
24.79/24.48	  2 -> 1
24.79/24.48	  3 -> 2, 4, 6
24.79/24.48	  4 -> 1
24.79/24.48	  5 -> 2, 4, 6
24.79/24.48	  6 -> 3, 5, 7
24.79/24.48	  7 -> 2, 4, 6
24.79/24.48	  8 -> 3, 5, 7
24.79/24.48	Where:
24.79/24.48	  0) init#(x1, x2, x3, x4, x5, x6, x7, x8) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8) 
24.79/24.48	  1) f4#(I0, I1, I2, I3, I4, I5, I6, I7) -> f2#(I8, I9, I1, I4, I5, I6, I7, I10) [I6 + 2 <= I3 /\ I7 + 2 <= I3 /\ I5 + 2 <= I2 /\ I4 + 2 <= I2 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ I9 <= I3 /\ I8 <= I2 /\ 0 <= I0 - 1 /\ I1 <= I0 - 1]
24.79/24.48	  2) f3#(I11, I12, I13, I14, I15, I16, I17, I18) -> f4#(I13, I13 - 1, I19, I20, I21, I22, I16, I17) [0 <= I16 + I17 + I15 - I14 - 2 * I22 /\ I16 + I17 + I15 - I14 - 2 * I22 <= 1 /\ I14 + I15 + I16 - I17 - 2 * I21 <= 1 /\ 0 <= I14 + I15 + I16 - I17 - 2 * I21 /\ I17 + 2 <= I12 /\ I16 + 2 <= I12 /\ I15 + 2 <= I11 /\ I14 + 2 <= I11 /\ 0 <= I20 - 1 /\ 0 <= I19 - 1 /\ 0 <= I12 - 1 /\ 0 <= I11 - 1 /\ I20 <= I12 /\ I13 - 1 <= I13 - 1 /\ 0 <= I13 - 1]
24.79/24.48	  3) f2#(I23, I24, I25, I26, I27, I28, I29, I30) -> f3#(I23, I24, I25, I26, I27, I28, I29, I31) [0 <= I25 - 1 /\ I25 - 1 <= I25 - 1 /\ y2 <= I24 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I26 + 2 <= I23 /\ I27 + 2 <= I23 /\ I29 + 2 <= I24 /\ I28 + 2 <= I24]
24.79/24.48	  4) f3#(I32, I33, I34, I35, I36, I37, I38, I39) -> f4#(1, 0, I40, I41, I42, I43, I37, I38) [1 = I34 /\ 0 <= I35 + I36 + I37 - I38 - 2 * I42 /\ I35 + I36 + I37 - I38 - 2 * I42 <= 1 /\ I37 + I38 + I36 - I35 - 2 * I43 <= 1 /\ 0 <= I37 + I38 + I36 - I35 - 2 * I43 /\ I38 + 2 <= I33 /\ I37 + 2 <= I33 /\ I36 + 2 <= I32 /\ I35 + 2 <= I32 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I41 <= I33]
24.79/24.48	  5) f2#(I44, I45, I46, I47, I48, I49, I50, I51) -> f3#(I44, I45, 1, I47, I48, I49, I50, I52) [I53 <= I45 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ 0 <= I54 - 1 /\ 0 <= I53 - 1 /\ I47 + 2 <= I44 /\ I48 + 2 <= I44 /\ I50 + 2 <= I45 /\ I49 + 2 <= I45 /\ 1 = I46]
24.79/24.48	  6) f3#(I55, I56, I57, I58, I59, I60, I61, I62) -> f2#(I63, I64, I57 - 1, I58, I59, I65, I66, I67) [0 <= I60 + I61 + I59 - I58 - 2 * I66 /\ I60 + I61 + I59 - I58 - 2 * I66 <= 1 /\ I58 + I59 + I60 - I61 - 2 * I65 <= 1 /\ 0 <= I58 + I59 + I60 - I61 - 2 * I65 /\ I61 + 2 <= I56 /\ I60 + 2 <= I56 /\ I59 + 2 <= I55 /\ I58 + 2 <= I55 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I56 - 1 /\ 0 <= I55 - 1 /\ I63 <= I55 /\ I57 - 1 <= I57 - 1 /\ 0 <= I57 - 1]
24.79/24.48	  7) f2#(I68, I69, I70, I71, I72, I73, I74, I75) -> f3#(I68, I69, I70, I71, I72, I73, I74, I76) [0 <= I70 - 1 /\ I70 - 1 <= I70 - 1 /\ I77 <= I68 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1 /\ 0 <= I77 - 1 /\ 0 <= I78 - 1 /\ I71 + 2 <= I68 /\ I72 + 2 <= I68 /\ I74 + 2 <= I69 /\ I73 + 2 <= I69]
24.79/24.48	  8) f1#(I79, I80, I81, I82, I83, I84, I85, I86) -> f2#(I87, I88, I80, 0, 0, 200, 200, I89) [201 <= I88 - 1 /\ 1 <= I87 - 1 /\ 0 <= I79 - 1 /\ I88 - 201 <= I79 /\ -1 <= I80 - 1 /\ I87 - 1 <= I79]
24.79/24.48	
24.79/24.48	We have the following SCCs.
24.79/24.48	  { 1, 2, 3, 4, 5, 6, 7 }
24.79/24.48	
24.79/24.48	DP problem for innermost termination.
24.79/24.48	P =
24.79/24.48	  f4#(I0, I1, I2, I3, I4, I5, I6, I7) -> f2#(I8, I9, I1, I4, I5, I6, I7, I10) [I6 + 2 <= I3 /\ I7 + 2 <= I3 /\ I5 + 2 <= I2 /\ I4 + 2 <= I2 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ I9 <= I3 /\ I8 <= I2 /\ 0 <= I0 - 1 /\ I1 <= I0 - 1]
24.79/24.48	  f3#(I11, I12, I13, I14, I15, I16, I17, I18) -> f4#(I13, I13 - 1, I19, I20, I21, I22, I16, I17) [0 <= I16 + I17 + I15 - I14 - 2 * I22 /\ I16 + I17 + I15 - I14 - 2 * I22 <= 1 /\ I14 + I15 + I16 - I17 - 2 * I21 <= 1 /\ 0 <= I14 + I15 + I16 - I17 - 2 * I21 /\ I17 + 2 <= I12 /\ I16 + 2 <= I12 /\ I15 + 2 <= I11 /\ I14 + 2 <= I11 /\ 0 <= I20 - 1 /\ 0 <= I19 - 1 /\ 0 <= I12 - 1 /\ 0 <= I11 - 1 /\ I20 <= I12 /\ I13 - 1 <= I13 - 1 /\ 0 <= I13 - 1]
24.79/24.48	  f2#(I23, I24, I25, I26, I27, I28, I29, I30) -> f3#(I23, I24, I25, I26, I27, I28, I29, I31) [0 <= I25 - 1 /\ I25 - 1 <= I25 - 1 /\ y2 <= I24 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I26 + 2 <= I23 /\ I27 + 2 <= I23 /\ I29 + 2 <= I24 /\ I28 + 2 <= I24]
24.79/24.48	  f3#(I32, I33, I34, I35, I36, I37, I38, I39) -> f4#(1, 0, I40, I41, I42, I43, I37, I38) [1 = I34 /\ 0 <= I35 + I36 + I37 - I38 - 2 * I42 /\ I35 + I36 + I37 - I38 - 2 * I42 <= 1 /\ I37 + I38 + I36 - I35 - 2 * I43 <= 1 /\ 0 <= I37 + I38 + I36 - I35 - 2 * I43 /\ I38 + 2 <= I33 /\ I37 + 2 <= I33 /\ I36 + 2 <= I32 /\ I35 + 2 <= I32 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I41 <= I33]
24.79/24.48	  f2#(I44, I45, I46, I47, I48, I49, I50, I51) -> f3#(I44, I45, 1, I47, I48, I49, I50, I52) [I53 <= I45 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ 0 <= I54 - 1 /\ 0 <= I53 - 1 /\ I47 + 2 <= I44 /\ I48 + 2 <= I44 /\ I50 + 2 <= I45 /\ I49 + 2 <= I45 /\ 1 = I46]
24.79/24.48	  f3#(I55, I56, I57, I58, I59, I60, I61, I62) -> f2#(I63, I64, I57 - 1, I58, I59, I65, I66, I67) [0 <= I60 + I61 + I59 - I58 - 2 * I66 /\ I60 + I61 + I59 - I58 - 2 * I66 <= 1 /\ I58 + I59 + I60 - I61 - 2 * I65 <= 1 /\ 0 <= I58 + I59 + I60 - I61 - 2 * I65 /\ I61 + 2 <= I56 /\ I60 + 2 <= I56 /\ I59 + 2 <= I55 /\ I58 + 2 <= I55 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I56 - 1 /\ 0 <= I55 - 1 /\ I63 <= I55 /\ I57 - 1 <= I57 - 1 /\ 0 <= I57 - 1]
24.79/24.48	  f2#(I68, I69, I70, I71, I72, I73, I74, I75) -> f3#(I68, I69, I70, I71, I72, I73, I74, I76) [0 <= I70 - 1 /\ I70 - 1 <= I70 - 1 /\ I77 <= I68 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1 /\ 0 <= I77 - 1 /\ 0 <= I78 - 1 /\ I71 + 2 <= I68 /\ I72 + 2 <= I68 /\ I74 + 2 <= I69 /\ I73 + 2 <= I69]
24.79/24.48	R = 
24.79/24.48	  init(x1, x2, x3, x4, x5, x6, x7, x8) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8) 
24.79/24.48	  f4(I0, I1, I2, I3, I4, I5, I6, I7) -> f2(I8, I9, I1, I4, I5, I6, I7, I10) [I6 + 2 <= I3 /\ I7 + 2 <= I3 /\ I5 + 2 <= I2 /\ I4 + 2 <= I2 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ I9 <= I3 /\ I8 <= I2 /\ 0 <= I0 - 1 /\ I1 <= I0 - 1]
24.79/24.48	  f3(I11, I12, I13, I14, I15, I16, I17, I18) -> f4(I13, I13 - 1, I19, I20, I21, I22, I16, I17) [0 <= I16 + I17 + I15 - I14 - 2 * I22 /\ I16 + I17 + I15 - I14 - 2 * I22 <= 1 /\ I14 + I15 + I16 - I17 - 2 * I21 <= 1 /\ 0 <= I14 + I15 + I16 - I17 - 2 * I21 /\ I17 + 2 <= I12 /\ I16 + 2 <= I12 /\ I15 + 2 <= I11 /\ I14 + 2 <= I11 /\ 0 <= I20 - 1 /\ 0 <= I19 - 1 /\ 0 <= I12 - 1 /\ 0 <= I11 - 1 /\ I20 <= I12 /\ I13 - 1 <= I13 - 1 /\ 0 <= I13 - 1]
24.79/24.48	  f2(I23, I24, I25, I26, I27, I28, I29, I30) -> f3(I23, I24, I25, I26, I27, I28, I29, I31) [0 <= I25 - 1 /\ I25 - 1 <= I25 - 1 /\ y2 <= I24 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I26 + 2 <= I23 /\ I27 + 2 <= I23 /\ I29 + 2 <= I24 /\ I28 + 2 <= I24]
24.79/24.48	  f3(I32, I33, I34, I35, I36, I37, I38, I39) -> f4(1, 0, I40, I41, I42, I43, I37, I38) [1 = I34 /\ 0 <= I35 + I36 + I37 - I38 - 2 * I42 /\ I35 + I36 + I37 - I38 - 2 * I42 <= 1 /\ I37 + I38 + I36 - I35 - 2 * I43 <= 1 /\ 0 <= I37 + I38 + I36 - I35 - 2 * I43 /\ I38 + 2 <= I33 /\ I37 + 2 <= I33 /\ I36 + 2 <= I32 /\ I35 + 2 <= I32 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I41 <= I33]
24.79/24.48	  f2(I44, I45, I46, I47, I48, I49, I50, I51) -> f3(I44, I45, 1, I47, I48, I49, I50, I52) [I53 <= I45 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ 0 <= I54 - 1 /\ 0 <= I53 - 1 /\ I47 + 2 <= I44 /\ I48 + 2 <= I44 /\ I50 + 2 <= I45 /\ I49 + 2 <= I45 /\ 1 = I46]
24.79/24.48	  f3(I55, I56, I57, I58, I59, I60, I61, I62) -> f2(I63, I64, I57 - 1, I58, I59, I65, I66, I67) [0 <= I60 + I61 + I59 - I58 - 2 * I66 /\ I60 + I61 + I59 - I58 - 2 * I66 <= 1 /\ I58 + I59 + I60 - I61 - 2 * I65 <= 1 /\ 0 <= I58 + I59 + I60 - I61 - 2 * I65 /\ I61 + 2 <= I56 /\ I60 + 2 <= I56 /\ I59 + 2 <= I55 /\ I58 + 2 <= I55 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I56 - 1 /\ 0 <= I55 - 1 /\ I63 <= I55 /\ I57 - 1 <= I57 - 1 /\ 0 <= I57 - 1]
24.79/24.48	  f2(I68, I69, I70, I71, I72, I73, I74, I75) -> f3(I68, I69, I70, I71, I72, I73, I74, I76) [0 <= I70 - 1 /\ I70 - 1 <= I70 - 1 /\ I77 <= I68 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1 /\ 0 <= I77 - 1 /\ 0 <= I78 - 1 /\ I71 + 2 <= I68 /\ I72 + 2 <= I68 /\ I74 + 2 <= I69 /\ I73 + 2 <= I69]
24.79/24.48	  f1(I79, I80, I81, I82, I83, I84, I85, I86) -> f2(I87, I88, I80, 0, 0, 200, 200, I89) [201 <= I88 - 1 /\ 1 <= I87 - 1 /\ 0 <= I79 - 1 /\ I88 - 201 <= I79 /\ -1 <= I80 - 1 /\ I87 - 1 <= I79]
24.79/24.48	
24.79/24.48	We use the basic value criterion with the projection function NU:
24.79/24.48	  NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8)] = z3
24.79/24.48	  NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8)] = z3
24.79/24.48	  NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8)] = z1
24.79/24.48	
24.79/24.48	This gives the following inequalities:
24.79/24.48	  I6 + 2 <= I3 /\ I7 + 2 <= I3 /\ I5 + 2 <= I2 /\ I4 + 2 <= I2 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ I9 <= I3 /\ I8 <= I2 /\ 0 <= I0 - 1 /\ I1 <= I0 - 1  ==>  I0 >! I1
24.79/24.48	  0 <= I16 + I17 + I15 - I14 - 2 * I22 /\ I16 + I17 + I15 - I14 - 2 * I22 <= 1 /\ I14 + I15 + I16 - I17 - 2 * I21 <= 1 /\ 0 <= I14 + I15 + I16 - I17 - 2 * I21 /\ I17 + 2 <= I12 /\ I16 + 2 <= I12 /\ I15 + 2 <= I11 /\ I14 + 2 <= I11 /\ 0 <= I20 - 1 /\ 0 <= I19 - 1 /\ 0 <= I12 - 1 /\ 0 <= I11 - 1 /\ I20 <= I12 /\ I13 - 1 <= I13 - 1 /\ 0 <= I13 - 1  ==>  I13 (>! \union =) I13
24.79/24.48	  0 <= I25 - 1 /\ I25 - 1 <= I25 - 1 /\ y2 <= I24 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I26 + 2 <= I23 /\ I27 + 2 <= I23 /\ I29 + 2 <= I24 /\ I28 + 2 <= I24  ==>  I25 (>! \union =) I25
24.79/24.48	  1 = I34 /\ 0 <= I35 + I36 + I37 - I38 - 2 * I42 /\ I35 + I36 + I37 - I38 - 2 * I42 <= 1 /\ I37 + I38 + I36 - I35 - 2 * I43 <= 1 /\ 0 <= I37 + I38 + I36 - I35 - 2 * I43 /\ I38 + 2 <= I33 /\ I37 + 2 <= I33 /\ I36 + 2 <= I32 /\ I35 + 2 <= I32 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I41 <= I33  ==>  I34 (>! \union =) 1
24.79/24.48	  I53 <= I45 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ 0 <= I54 - 1 /\ 0 <= I53 - 1 /\ I47 + 2 <= I44 /\ I48 + 2 <= I44 /\ I50 + 2 <= I45 /\ I49 + 2 <= I45 /\ 1 = I46  ==>  I46 (>! \union =) 1
24.79/24.48	  0 <= I60 + I61 + I59 - I58 - 2 * I66 /\ I60 + I61 + I59 - I58 - 2 * I66 <= 1 /\ I58 + I59 + I60 - I61 - 2 * I65 <= 1 /\ 0 <= I58 + I59 + I60 - I61 - 2 * I65 /\ I61 + 2 <= I56 /\ I60 + 2 <= I56 /\ I59 + 2 <= I55 /\ I58 + 2 <= I55 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I56 - 1 /\ 0 <= I55 - 1 /\ I63 <= I55 /\ I57 - 1 <= I57 - 1 /\ 0 <= I57 - 1  ==>  I57 >! I57 - 1
24.79/24.48	  0 <= I70 - 1 /\ I70 - 1 <= I70 - 1 /\ I77 <= I68 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1 /\ 0 <= I77 - 1 /\ 0 <= I78 - 1 /\ I71 + 2 <= I68 /\ I72 + 2 <= I68 /\ I74 + 2 <= I69 /\ I73 + 2 <= I69  ==>  I70 (>! \union =) I70
24.79/24.48	
24.79/24.48	We remove all the strictly oriented dependency pairs.
24.79/24.48	
24.79/24.48	DP problem for innermost termination.
24.79/24.48	P =
24.79/24.48	  f3#(I11, I12, I13, I14, I15, I16, I17, I18) -> f4#(I13, I13 - 1, I19, I20, I21, I22, I16, I17) [0 <= I16 + I17 + I15 - I14 - 2 * I22 /\ I16 + I17 + I15 - I14 - 2 * I22 <= 1 /\ I14 + I15 + I16 - I17 - 2 * I21 <= 1 /\ 0 <= I14 + I15 + I16 - I17 - 2 * I21 /\ I17 + 2 <= I12 /\ I16 + 2 <= I12 /\ I15 + 2 <= I11 /\ I14 + 2 <= I11 /\ 0 <= I20 - 1 /\ 0 <= I19 - 1 /\ 0 <= I12 - 1 /\ 0 <= I11 - 1 /\ I20 <= I12 /\ I13 - 1 <= I13 - 1 /\ 0 <= I13 - 1]
24.79/24.48	  f2#(I23, I24, I25, I26, I27, I28, I29, I30) -> f3#(I23, I24, I25, I26, I27, I28, I29, I31) [0 <= I25 - 1 /\ I25 - 1 <= I25 - 1 /\ y2 <= I24 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I26 + 2 <= I23 /\ I27 + 2 <= I23 /\ I29 + 2 <= I24 /\ I28 + 2 <= I24]
24.79/24.48	  f3#(I32, I33, I34, I35, I36, I37, I38, I39) -> f4#(1, 0, I40, I41, I42, I43, I37, I38) [1 = I34 /\ 0 <= I35 + I36 + I37 - I38 - 2 * I42 /\ I35 + I36 + I37 - I38 - 2 * I42 <= 1 /\ I37 + I38 + I36 - I35 - 2 * I43 <= 1 /\ 0 <= I37 + I38 + I36 - I35 - 2 * I43 /\ I38 + 2 <= I33 /\ I37 + 2 <= I33 /\ I36 + 2 <= I32 /\ I35 + 2 <= I32 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I41 <= I33]
24.79/24.48	  f2#(I44, I45, I46, I47, I48, I49, I50, I51) -> f3#(I44, I45, 1, I47, I48, I49, I50, I52) [I53 <= I45 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ 0 <= I54 - 1 /\ 0 <= I53 - 1 /\ I47 + 2 <= I44 /\ I48 + 2 <= I44 /\ I50 + 2 <= I45 /\ I49 + 2 <= I45 /\ 1 = I46]
24.79/24.48	  f2#(I68, I69, I70, I71, I72, I73, I74, I75) -> f3#(I68, I69, I70, I71, I72, I73, I74, I76) [0 <= I70 - 1 /\ I70 - 1 <= I70 - 1 /\ I77 <= I68 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1 /\ 0 <= I77 - 1 /\ 0 <= I78 - 1 /\ I71 + 2 <= I68 /\ I72 + 2 <= I68 /\ I74 + 2 <= I69 /\ I73 + 2 <= I69]
24.79/24.48	R = 
24.79/24.48	  init(x1, x2, x3, x4, x5, x6, x7, x8) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8) 
24.79/24.48	  f4(I0, I1, I2, I3, I4, I5, I6, I7) -> f2(I8, I9, I1, I4, I5, I6, I7, I10) [I6 + 2 <= I3 /\ I7 + 2 <= I3 /\ I5 + 2 <= I2 /\ I4 + 2 <= I2 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ I9 <= I3 /\ I8 <= I2 /\ 0 <= I0 - 1 /\ I1 <= I0 - 1]
24.79/24.48	  f3(I11, I12, I13, I14, I15, I16, I17, I18) -> f4(I13, I13 - 1, I19, I20, I21, I22, I16, I17) [0 <= I16 + I17 + I15 - I14 - 2 * I22 /\ I16 + I17 + I15 - I14 - 2 * I22 <= 1 /\ I14 + I15 + I16 - I17 - 2 * I21 <= 1 /\ 0 <= I14 + I15 + I16 - I17 - 2 * I21 /\ I17 + 2 <= I12 /\ I16 + 2 <= I12 /\ I15 + 2 <= I11 /\ I14 + 2 <= I11 /\ 0 <= I20 - 1 /\ 0 <= I19 - 1 /\ 0 <= I12 - 1 /\ 0 <= I11 - 1 /\ I20 <= I12 /\ I13 - 1 <= I13 - 1 /\ 0 <= I13 - 1]
24.79/24.48	  f2(I23, I24, I25, I26, I27, I28, I29, I30) -> f3(I23, I24, I25, I26, I27, I28, I29, I31) [0 <= I25 - 1 /\ I25 - 1 <= I25 - 1 /\ y2 <= I24 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I26 + 2 <= I23 /\ I27 + 2 <= I23 /\ I29 + 2 <= I24 /\ I28 + 2 <= I24]
24.79/24.48	  f3(I32, I33, I34, I35, I36, I37, I38, I39) -> f4(1, 0, I40, I41, I42, I43, I37, I38) [1 = I34 /\ 0 <= I35 + I36 + I37 - I38 - 2 * I42 /\ I35 + I36 + I37 - I38 - 2 * I42 <= 1 /\ I37 + I38 + I36 - I35 - 2 * I43 <= 1 /\ 0 <= I37 + I38 + I36 - I35 - 2 * I43 /\ I38 + 2 <= I33 /\ I37 + 2 <= I33 /\ I36 + 2 <= I32 /\ I35 + 2 <= I32 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I41 <= I33]
24.79/24.48	  f2(I44, I45, I46, I47, I48, I49, I50, I51) -> f3(I44, I45, 1, I47, I48, I49, I50, I52) [I53 <= I45 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ 0 <= I54 - 1 /\ 0 <= I53 - 1 /\ I47 + 2 <= I44 /\ I48 + 2 <= I44 /\ I50 + 2 <= I45 /\ I49 + 2 <= I45 /\ 1 = I46]
24.79/24.48	  f3(I55, I56, I57, I58, I59, I60, I61, I62) -> f2(I63, I64, I57 - 1, I58, I59, I65, I66, I67) [0 <= I60 + I61 + I59 - I58 - 2 * I66 /\ I60 + I61 + I59 - I58 - 2 * I66 <= 1 /\ I58 + I59 + I60 - I61 - 2 * I65 <= 1 /\ 0 <= I58 + I59 + I60 - I61 - 2 * I65 /\ I61 + 2 <= I56 /\ I60 + 2 <= I56 /\ I59 + 2 <= I55 /\ I58 + 2 <= I55 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I56 - 1 /\ 0 <= I55 - 1 /\ I63 <= I55 /\ I57 - 1 <= I57 - 1 /\ 0 <= I57 - 1]
24.79/24.48	  f2(I68, I69, I70, I71, I72, I73, I74, I75) -> f3(I68, I69, I70, I71, I72, I73, I74, I76) [0 <= I70 - 1 /\ I70 - 1 <= I70 - 1 /\ I77 <= I68 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1 /\ 0 <= I77 - 1 /\ 0 <= I78 - 1 /\ I71 + 2 <= I68 /\ I72 + 2 <= I68 /\ I74 + 2 <= I69 /\ I73 + 2 <= I69]
24.79/24.48	  f1(I79, I80, I81, I82, I83, I84, I85, I86) -> f2(I87, I88, I80, 0, 0, 200, 200, I89) [201 <= I88 - 1 /\ 1 <= I87 - 1 /\ 0 <= I79 - 1 /\ I88 - 201 <= I79 /\ -1 <= I80 - 1 /\ I87 - 1 <= I79]
24.79/24.48	
24.79/24.48	The dependency graph for this problem is:
24.79/24.48	  2 -> 
24.79/24.48	  3 -> 2, 4
24.79/24.48	  4 -> 
24.79/24.48	  5 -> 2, 4
24.79/24.48	  7 -> 2, 4
24.79/24.48	Where:
24.79/24.48	  2) f3#(I11, I12, I13, I14, I15, I16, I17, I18) -> f4#(I13, I13 - 1, I19, I20, I21, I22, I16, I17) [0 <= I16 + I17 + I15 - I14 - 2 * I22 /\ I16 + I17 + I15 - I14 - 2 * I22 <= 1 /\ I14 + I15 + I16 - I17 - 2 * I21 <= 1 /\ 0 <= I14 + I15 + I16 - I17 - 2 * I21 /\ I17 + 2 <= I12 /\ I16 + 2 <= I12 /\ I15 + 2 <= I11 /\ I14 + 2 <= I11 /\ 0 <= I20 - 1 /\ 0 <= I19 - 1 /\ 0 <= I12 - 1 /\ 0 <= I11 - 1 /\ I20 <= I12 /\ I13 - 1 <= I13 - 1 /\ 0 <= I13 - 1]
24.79/24.48	  3) f2#(I23, I24, I25, I26, I27, I28, I29, I30) -> f3#(I23, I24, I25, I26, I27, I28, I29, I31) [0 <= I25 - 1 /\ I25 - 1 <= I25 - 1 /\ y2 <= I24 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= y1 - 1 /\ 0 <= y2 - 1 /\ I26 + 2 <= I23 /\ I27 + 2 <= I23 /\ I29 + 2 <= I24 /\ I28 + 2 <= I24]
24.79/24.48	  4) f3#(I32, I33, I34, I35, I36, I37, I38, I39) -> f4#(1, 0, I40, I41, I42, I43, I37, I38) [1 = I34 /\ 0 <= I35 + I36 + I37 - I38 - 2 * I42 /\ I35 + I36 + I37 - I38 - 2 * I42 <= 1 /\ I37 + I38 + I36 - I35 - 2 * I43 <= 1 /\ 0 <= I37 + I38 + I36 - I35 - 2 * I43 /\ I38 + 2 <= I33 /\ I37 + 2 <= I33 /\ I36 + 2 <= I32 /\ I35 + 2 <= I32 /\ 0 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I41 <= I33]
24.79/24.48	  5) f2#(I44, I45, I46, I47, I48, I49, I50, I51) -> f3#(I44, I45, 1, I47, I48, I49, I50, I52) [I53 <= I45 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ 0 <= I54 - 1 /\ 0 <= I53 - 1 /\ I47 + 2 <= I44 /\ I48 + 2 <= I44 /\ I50 + 2 <= I45 /\ I49 + 2 <= I45 /\ 1 = I46]
24.79/24.48	  7) f2#(I68, I69, I70, I71, I72, I73, I74, I75) -> f3#(I68, I69, I70, I71, I72, I73, I74, I76) [0 <= I70 - 1 /\ I70 - 1 <= I70 - 1 /\ I77 <= I68 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1 /\ 0 <= I77 - 1 /\ 0 <= I78 - 1 /\ I71 + 2 <= I68 /\ I72 + 2 <= I68 /\ I74 + 2 <= I69 /\ I73 + 2 <= I69]
24.79/24.48	
24.79/24.48	We have the following SCCs.
24.79/24.48	  
24.79/27.45	EOF