6.15/6.15	YES
6.15/6.15	
6.15/6.15	DP problem for innermost termination.
6.15/6.15	P =
6.15/6.15	  init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
6.15/6.15	  f6#(I0, I1, I2, I3) -> f2#(I0, I1 - 1, I4, I5) [1 = I2 /\ I1 - 1 <= I1 - 1 /\ 1 <= I1 - 1]
6.15/6.15	  f7#(I6, I7, I8, I9) -> f2#(I6, I10, I11, I12) [0 = I8 /\ 0 <= I7 - 2 * I10 /\ I7 - 2 * I10 <= 1 /\ 0 <= I10 - 1 /\ I10 <= I7 - 1 /\ 1 <= I7 - 1]
6.15/6.15	  f6#(I13, I14, I15, I16) -> f7#(I13, I14, 0, I16) [1 <= I14 - 1 /\ 0 <= y1 - 1 /\ y1 <= I14 - 1 /\ 0 = I15]
6.15/6.15	  f5#(I17, I18, I19, I20) -> f6#(I17, I18, I21, I22) [1 <= I18 - 1 /\ 2 <= I17 - 1 /\ I18 - 2 * I23 <= 1 /\ 0 <= I18 - 2 * I23 /\ I18 - 2 * I23 = I21]
6.15/6.15	  f2#(I24, I25, I26, I27) -> f5#(I24, I25, I28, I29) [1 <= I25 - 1 /\ 2 <= I24 - 1]
6.15/6.15	  f5#(I30, I31, I32, I33) -> f6#(I30, I31, I34, I35) [1 <= I31 - 1 /\ I30 <= 1 /\ I31 - 2 * I36 <= 1 /\ 0 <= I31 - 2 * I36 /\ I31 - 2 * I36 = I34]
6.15/6.15	  f2#(I37, I38, I39, I40) -> f5#(I37, I38, I41, I42) [1 <= I38 - 1 /\ I37 <= 1]
6.15/6.15	  f4#(I43, I44, I45, I46) -> f2#(I44, I45, I47, I48) [0 <= I43 - 1 /\ 1 <= I49 - 1]
6.15/6.15	  f3#(I50, I51, I52, I53) -> f4#(I54, I51, I55, I56) [1 <= I57 - 1 /\ -1 <= I55 - 1 /\ I54 <= I50 /\ 0 <= I50 - 1 /\ 0 <= I54 - 1]
6.15/6.15	  f3#(I58, I59, I60, I61) -> f4#(I62, I59, 0, I63) [I62 <= I58 /\ 1 <= I64 - 1 /\ 0 <= I58 - 1 /\ 0 <= I62 - 1]
6.15/6.15	  f3#(I65, I66, I67, I68) -> f2#(I66, 0, I69, I70) [0 <= I65 - 1]
6.15/6.15	  f1#(I71, I72, I73, I74) -> f3#(I75, I76, I77, I78) [0 <= I75 - 1 /\ 0 <= I71 - 1 /\ I75 <= I71 /\ 0 <= I72 - 1 /\ -1 <= I76 - 1]
6.15/6.15	  f1#(I79, I80, I81, I82) -> f3#(I83, 0, I84, I85) [0 <= I83 - 1 /\ 0 <= I79 - 1 /\ 0 <= I80 - 1 /\ I83 <= I79]
6.15/6.15	  f1#(I86, I87, I88, I89) -> f2#(0, 0, I90, I91) [0 = I87 /\ 0 <= I86 - 1]
6.15/6.15	R = 
6.15/6.15	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
6.15/6.15	  f6(I0, I1, I2, I3) -> f2(I0, I1 - 1, I4, I5) [1 = I2 /\ I1 - 1 <= I1 - 1 /\ 1 <= I1 - 1]
6.15/6.15	  f7(I6, I7, I8, I9) -> f2(I6, I10, I11, I12) [0 = I8 /\ 0 <= I7 - 2 * I10 /\ I7 - 2 * I10 <= 1 /\ 0 <= I10 - 1 /\ I10 <= I7 - 1 /\ 1 <= I7 - 1]
6.15/6.15	  f6(I13, I14, I15, I16) -> f7(I13, I14, 0, I16) [1 <= I14 - 1 /\ 0 <= y1 - 1 /\ y1 <= I14 - 1 /\ 0 = I15]
6.15/6.15	  f5(I17, I18, I19, I20) -> f6(I17, I18, I21, I22) [1 <= I18 - 1 /\ 2 <= I17 - 1 /\ I18 - 2 * I23 <= 1 /\ 0 <= I18 - 2 * I23 /\ I18 - 2 * I23 = I21]
6.15/6.15	  f2(I24, I25, I26, I27) -> f5(I24, I25, I28, I29) [1 <= I25 - 1 /\ 2 <= I24 - 1]
6.15/6.15	  f5(I30, I31, I32, I33) -> f6(I30, I31, I34, I35) [1 <= I31 - 1 /\ I30 <= 1 /\ I31 - 2 * I36 <= 1 /\ 0 <= I31 - 2 * I36 /\ I31 - 2 * I36 = I34]
6.15/6.15	  f2(I37, I38, I39, I40) -> f5(I37, I38, I41, I42) [1 <= I38 - 1 /\ I37 <= 1]
6.15/6.15	  f4(I43, I44, I45, I46) -> f2(I44, I45, I47, I48) [0 <= I43 - 1 /\ 1 <= I49 - 1]
6.15/6.15	  f3(I50, I51, I52, I53) -> f4(I54, I51, I55, I56) [1 <= I57 - 1 /\ -1 <= I55 - 1 /\ I54 <= I50 /\ 0 <= I50 - 1 /\ 0 <= I54 - 1]
6.15/6.15	  f3(I58, I59, I60, I61) -> f4(I62, I59, 0, I63) [I62 <= I58 /\ 1 <= I64 - 1 /\ 0 <= I58 - 1 /\ 0 <= I62 - 1]
6.15/6.15	  f3(I65, I66, I67, I68) -> f2(I66, 0, I69, I70) [0 <= I65 - 1]
6.15/6.15	  f1(I71, I72, I73, I74) -> f3(I75, I76, I77, I78) [0 <= I75 - 1 /\ 0 <= I71 - 1 /\ I75 <= I71 /\ 0 <= I72 - 1 /\ -1 <= I76 - 1]
6.15/6.15	  f1(I79, I80, I81, I82) -> f3(I83, 0, I84, I85) [0 <= I83 - 1 /\ 0 <= I79 - 1 /\ 0 <= I80 - 1 /\ I83 <= I79]
6.15/6.15	  f1(I86, I87, I88, I89) -> f2(0, 0, I90, I91) [0 = I87 /\ 0 <= I86 - 1]
6.15/6.15	
6.15/6.15	The dependency graph for this problem is:
6.15/6.15	  0 -> 12, 13, 14
6.15/6.15	  1 -> 5, 7
6.15/6.15	  2 -> 5, 7
6.15/6.15	  3 -> 2
6.15/6.15	  4 -> 1, 3
6.15/6.15	  5 -> 4
6.15/6.15	  6 -> 1, 3
6.15/6.15	  7 -> 6
6.15/6.15	  8 -> 5, 7
6.15/6.15	  9 -> 8
6.15/6.15	  10 -> 8
6.15/6.15	  11 -> 
6.15/6.15	  12 -> 9, 10, 11
6.15/6.15	  13 -> 9, 10, 11
6.15/6.15	  14 -> 
6.15/6.15	Where:
6.15/6.15	  0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
6.15/6.15	  1) f6#(I0, I1, I2, I3) -> f2#(I0, I1 - 1, I4, I5) [1 = I2 /\ I1 - 1 <= I1 - 1 /\ 1 <= I1 - 1]
6.15/6.15	  2) f7#(I6, I7, I8, I9) -> f2#(I6, I10, I11, I12) [0 = I8 /\ 0 <= I7 - 2 * I10 /\ I7 - 2 * I10 <= 1 /\ 0 <= I10 - 1 /\ I10 <= I7 - 1 /\ 1 <= I7 - 1]
6.15/6.15	  3) f6#(I13, I14, I15, I16) -> f7#(I13, I14, 0, I16) [1 <= I14 - 1 /\ 0 <= y1 - 1 /\ y1 <= I14 - 1 /\ 0 = I15]
6.15/6.15	  4) f5#(I17, I18, I19, I20) -> f6#(I17, I18, I21, I22) [1 <= I18 - 1 /\ 2 <= I17 - 1 /\ I18 - 2 * I23 <= 1 /\ 0 <= I18 - 2 * I23 /\ I18 - 2 * I23 = I21]
6.15/6.15	  5) f2#(I24, I25, I26, I27) -> f5#(I24, I25, I28, I29) [1 <= I25 - 1 /\ 2 <= I24 - 1]
6.15/6.15	  6) f5#(I30, I31, I32, I33) -> f6#(I30, I31, I34, I35) [1 <= I31 - 1 /\ I30 <= 1 /\ I31 - 2 * I36 <= 1 /\ 0 <= I31 - 2 * I36 /\ I31 - 2 * I36 = I34]
6.15/6.15	  7) f2#(I37, I38, I39, I40) -> f5#(I37, I38, I41, I42) [1 <= I38 - 1 /\ I37 <= 1]
6.15/6.15	  8) f4#(I43, I44, I45, I46) -> f2#(I44, I45, I47, I48) [0 <= I43 - 1 /\ 1 <= I49 - 1]
6.15/6.15	  9) f3#(I50, I51, I52, I53) -> f4#(I54, I51, I55, I56) [1 <= I57 - 1 /\ -1 <= I55 - 1 /\ I54 <= I50 /\ 0 <= I50 - 1 /\ 0 <= I54 - 1]
6.15/6.15	  10) f3#(I58, I59, I60, I61) -> f4#(I62, I59, 0, I63) [I62 <= I58 /\ 1 <= I64 - 1 /\ 0 <= I58 - 1 /\ 0 <= I62 - 1]
6.15/6.15	  11) f3#(I65, I66, I67, I68) -> f2#(I66, 0, I69, I70) [0 <= I65 - 1]
6.15/6.15	  12) f1#(I71, I72, I73, I74) -> f3#(I75, I76, I77, I78) [0 <= I75 - 1 /\ 0 <= I71 - 1 /\ I75 <= I71 /\ 0 <= I72 - 1 /\ -1 <= I76 - 1]
6.15/6.15	  13) f1#(I79, I80, I81, I82) -> f3#(I83, 0, I84, I85) [0 <= I83 - 1 /\ 0 <= I79 - 1 /\ 0 <= I80 - 1 /\ I83 <= I79]
6.15/6.15	  14) f1#(I86, I87, I88, I89) -> f2#(0, 0, I90, I91) [0 = I87 /\ 0 <= I86 - 1]
6.15/6.15	
6.15/6.15	We have the following SCCs.
6.15/6.15	  { 1, 2, 3, 4, 5, 6, 7 }
6.15/6.15	
6.15/6.15	DP problem for innermost termination.
6.15/6.15	P =
6.15/6.15	  f6#(I0, I1, I2, I3) -> f2#(I0, I1 - 1, I4, I5) [1 = I2 /\ I1 - 1 <= I1 - 1 /\ 1 <= I1 - 1]
6.15/6.15	  f7#(I6, I7, I8, I9) -> f2#(I6, I10, I11, I12) [0 = I8 /\ 0 <= I7 - 2 * I10 /\ I7 - 2 * I10 <= 1 /\ 0 <= I10 - 1 /\ I10 <= I7 - 1 /\ 1 <= I7 - 1]
6.15/6.15	  f6#(I13, I14, I15, I16) -> f7#(I13, I14, 0, I16) [1 <= I14 - 1 /\ 0 <= y1 - 1 /\ y1 <= I14 - 1 /\ 0 = I15]
6.15/6.15	  f5#(I17, I18, I19, I20) -> f6#(I17, I18, I21, I22) [1 <= I18 - 1 /\ 2 <= I17 - 1 /\ I18 - 2 * I23 <= 1 /\ 0 <= I18 - 2 * I23 /\ I18 - 2 * I23 = I21]
6.15/6.15	  f2#(I24, I25, I26, I27) -> f5#(I24, I25, I28, I29) [1 <= I25 - 1 /\ 2 <= I24 - 1]
6.15/6.15	  f5#(I30, I31, I32, I33) -> f6#(I30, I31, I34, I35) [1 <= I31 - 1 /\ I30 <= 1 /\ I31 - 2 * I36 <= 1 /\ 0 <= I31 - 2 * I36 /\ I31 - 2 * I36 = I34]
6.15/6.15	  f2#(I37, I38, I39, I40) -> f5#(I37, I38, I41, I42) [1 <= I38 - 1 /\ I37 <= 1]
6.15/6.15	R = 
6.15/6.15	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
6.15/6.15	  f6(I0, I1, I2, I3) -> f2(I0, I1 - 1, I4, I5) [1 = I2 /\ I1 - 1 <= I1 - 1 /\ 1 <= I1 - 1]
6.15/6.15	  f7(I6, I7, I8, I9) -> f2(I6, I10, I11, I12) [0 = I8 /\ 0 <= I7 - 2 * I10 /\ I7 - 2 * I10 <= 1 /\ 0 <= I10 - 1 /\ I10 <= I7 - 1 /\ 1 <= I7 - 1]
6.15/6.15	  f6(I13, I14, I15, I16) -> f7(I13, I14, 0, I16) [1 <= I14 - 1 /\ 0 <= y1 - 1 /\ y1 <= I14 - 1 /\ 0 = I15]
6.15/6.15	  f5(I17, I18, I19, I20) -> f6(I17, I18, I21, I22) [1 <= I18 - 1 /\ 2 <= I17 - 1 /\ I18 - 2 * I23 <= 1 /\ 0 <= I18 - 2 * I23 /\ I18 - 2 * I23 = I21]
6.15/6.15	  f2(I24, I25, I26, I27) -> f5(I24, I25, I28, I29) [1 <= I25 - 1 /\ 2 <= I24 - 1]
6.15/6.15	  f5(I30, I31, I32, I33) -> f6(I30, I31, I34, I35) [1 <= I31 - 1 /\ I30 <= 1 /\ I31 - 2 * I36 <= 1 /\ 0 <= I31 - 2 * I36 /\ I31 - 2 * I36 = I34]
6.15/6.15	  f2(I37, I38, I39, I40) -> f5(I37, I38, I41, I42) [1 <= I38 - 1 /\ I37 <= 1]
6.15/6.15	  f4(I43, I44, I45, I46) -> f2(I44, I45, I47, I48) [0 <= I43 - 1 /\ 1 <= I49 - 1]
6.15/6.15	  f3(I50, I51, I52, I53) -> f4(I54, I51, I55, I56) [1 <= I57 - 1 /\ -1 <= I55 - 1 /\ I54 <= I50 /\ 0 <= I50 - 1 /\ 0 <= I54 - 1]
6.15/6.15	  f3(I58, I59, I60, I61) -> f4(I62, I59, 0, I63) [I62 <= I58 /\ 1 <= I64 - 1 /\ 0 <= I58 - 1 /\ 0 <= I62 - 1]
6.15/6.15	  f3(I65, I66, I67, I68) -> f2(I66, 0, I69, I70) [0 <= I65 - 1]
6.15/6.15	  f1(I71, I72, I73, I74) -> f3(I75, I76, I77, I78) [0 <= I75 - 1 /\ 0 <= I71 - 1 /\ I75 <= I71 /\ 0 <= I72 - 1 /\ -1 <= I76 - 1]
6.15/6.15	  f1(I79, I80, I81, I82) -> f3(I83, 0, I84, I85) [0 <= I83 - 1 /\ 0 <= I79 - 1 /\ 0 <= I80 - 1 /\ I83 <= I79]
6.15/6.15	  f1(I86, I87, I88, I89) -> f2(0, 0, I90, I91) [0 = I87 /\ 0 <= I86 - 1]
6.15/6.15	
6.15/6.15	We use the basic value criterion with the projection function NU:
6.15/6.15	  NU[f5#(z1,z2,z3,z4)] = z2
6.15/6.15	  NU[f7#(z1,z2,z3,z4)] = z2
6.15/6.15	  NU[f2#(z1,z2,z3,z4)] = z2
6.15/6.15	  NU[f6#(z1,z2,z3,z4)] = z2
6.15/6.15	
6.15/6.15	This gives the following inequalities:
6.15/6.15	  1 = I2 /\ I1 - 1 <= I1 - 1 /\ 1 <= I1 - 1  ==>  I1 >! I1 - 1
6.15/6.15	  0 = I8 /\ 0 <= I7 - 2 * I10 /\ I7 - 2 * I10 <= 1 /\ 0 <= I10 - 1 /\ I10 <= I7 - 1 /\ 1 <= I7 - 1  ==>  I7 >! I10
6.15/6.15	  1 <= I14 - 1 /\ 0 <= y1 - 1 /\ y1 <= I14 - 1 /\ 0 = I15  ==>  I14 (>! \union =) I14
6.15/6.15	  1 <= I18 - 1 /\ 2 <= I17 - 1 /\ I18 - 2 * I23 <= 1 /\ 0 <= I18 - 2 * I23 /\ I18 - 2 * I23 = I21  ==>  I18 (>! \union =) I18
6.15/6.15	  1 <= I25 - 1 /\ 2 <= I24 - 1  ==>  I25 (>! \union =) I25
6.15/6.15	  1 <= I31 - 1 /\ I30 <= 1 /\ I31 - 2 * I36 <= 1 /\ 0 <= I31 - 2 * I36 /\ I31 - 2 * I36 = I34  ==>  I31 (>! \union =) I31
6.15/6.15	  1 <= I38 - 1 /\ I37 <= 1  ==>  I38 (>! \union =) I38
6.15/6.15	
6.15/6.15	We remove all the strictly oriented dependency pairs.
6.15/6.15	
6.15/6.15	DP problem for innermost termination.
6.15/6.15	P =
6.15/6.15	  f6#(I13, I14, I15, I16) -> f7#(I13, I14, 0, I16) [1 <= I14 - 1 /\ 0 <= y1 - 1 /\ y1 <= I14 - 1 /\ 0 = I15]
6.15/6.15	  f5#(I17, I18, I19, I20) -> f6#(I17, I18, I21, I22) [1 <= I18 - 1 /\ 2 <= I17 - 1 /\ I18 - 2 * I23 <= 1 /\ 0 <= I18 - 2 * I23 /\ I18 - 2 * I23 = I21]
6.15/6.15	  f2#(I24, I25, I26, I27) -> f5#(I24, I25, I28, I29) [1 <= I25 - 1 /\ 2 <= I24 - 1]
6.15/6.15	  f5#(I30, I31, I32, I33) -> f6#(I30, I31, I34, I35) [1 <= I31 - 1 /\ I30 <= 1 /\ I31 - 2 * I36 <= 1 /\ 0 <= I31 - 2 * I36 /\ I31 - 2 * I36 = I34]
6.15/6.15	  f2#(I37, I38, I39, I40) -> f5#(I37, I38, I41, I42) [1 <= I38 - 1 /\ I37 <= 1]
6.15/6.15	R = 
6.15/6.15	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
6.15/6.15	  f6(I0, I1, I2, I3) -> f2(I0, I1 - 1, I4, I5) [1 = I2 /\ I1 - 1 <= I1 - 1 /\ 1 <= I1 - 1]
6.15/6.15	  f7(I6, I7, I8, I9) -> f2(I6, I10, I11, I12) [0 = I8 /\ 0 <= I7 - 2 * I10 /\ I7 - 2 * I10 <= 1 /\ 0 <= I10 - 1 /\ I10 <= I7 - 1 /\ 1 <= I7 - 1]
6.15/6.15	  f6(I13, I14, I15, I16) -> f7(I13, I14, 0, I16) [1 <= I14 - 1 /\ 0 <= y1 - 1 /\ y1 <= I14 - 1 /\ 0 = I15]
6.15/6.15	  f5(I17, I18, I19, I20) -> f6(I17, I18, I21, I22) [1 <= I18 - 1 /\ 2 <= I17 - 1 /\ I18 - 2 * I23 <= 1 /\ 0 <= I18 - 2 * I23 /\ I18 - 2 * I23 = I21]
6.15/6.15	  f2(I24, I25, I26, I27) -> f5(I24, I25, I28, I29) [1 <= I25 - 1 /\ 2 <= I24 - 1]
6.15/6.15	  f5(I30, I31, I32, I33) -> f6(I30, I31, I34, I35) [1 <= I31 - 1 /\ I30 <= 1 /\ I31 - 2 * I36 <= 1 /\ 0 <= I31 - 2 * I36 /\ I31 - 2 * I36 = I34]
6.15/6.15	  f2(I37, I38, I39, I40) -> f5(I37, I38, I41, I42) [1 <= I38 - 1 /\ I37 <= 1]
6.15/6.15	  f4(I43, I44, I45, I46) -> f2(I44, I45, I47, I48) [0 <= I43 - 1 /\ 1 <= I49 - 1]
6.15/6.15	  f3(I50, I51, I52, I53) -> f4(I54, I51, I55, I56) [1 <= I57 - 1 /\ -1 <= I55 - 1 /\ I54 <= I50 /\ 0 <= I50 - 1 /\ 0 <= I54 - 1]
6.15/6.15	  f3(I58, I59, I60, I61) -> f4(I62, I59, 0, I63) [I62 <= I58 /\ 1 <= I64 - 1 /\ 0 <= I58 - 1 /\ 0 <= I62 - 1]
6.15/6.15	  f3(I65, I66, I67, I68) -> f2(I66, 0, I69, I70) [0 <= I65 - 1]
6.15/6.15	  f1(I71, I72, I73, I74) -> f3(I75, I76, I77, I78) [0 <= I75 - 1 /\ 0 <= I71 - 1 /\ I75 <= I71 /\ 0 <= I72 - 1 /\ -1 <= I76 - 1]
6.15/6.15	  f1(I79, I80, I81, I82) -> f3(I83, 0, I84, I85) [0 <= I83 - 1 /\ 0 <= I79 - 1 /\ 0 <= I80 - 1 /\ I83 <= I79]
6.15/6.15	  f1(I86, I87, I88, I89) -> f2(0, 0, I90, I91) [0 = I87 /\ 0 <= I86 - 1]
6.15/6.15	
6.15/6.15	The dependency graph for this problem is:
6.15/6.15	  3 -> 
6.15/6.15	  4 -> 3
6.15/6.15	  5 -> 4
6.15/6.15	  6 -> 3
6.15/6.15	  7 -> 6
6.15/6.15	Where:
6.15/6.15	  3) f6#(I13, I14, I15, I16) -> f7#(I13, I14, 0, I16) [1 <= I14 - 1 /\ 0 <= y1 - 1 /\ y1 <= I14 - 1 /\ 0 = I15]
6.15/6.15	  4) f5#(I17, I18, I19, I20) -> f6#(I17, I18, I21, I22) [1 <= I18 - 1 /\ 2 <= I17 - 1 /\ I18 - 2 * I23 <= 1 /\ 0 <= I18 - 2 * I23 /\ I18 - 2 * I23 = I21]
6.15/6.15	  5) f2#(I24, I25, I26, I27) -> f5#(I24, I25, I28, I29) [1 <= I25 - 1 /\ 2 <= I24 - 1]
6.15/6.15	  6) f5#(I30, I31, I32, I33) -> f6#(I30, I31, I34, I35) [1 <= I31 - 1 /\ I30 <= 1 /\ I31 - 2 * I36 <= 1 /\ 0 <= I31 - 2 * I36 /\ I31 - 2 * I36 = I34]
6.15/6.15	  7) f2#(I37, I38, I39, I40) -> f5#(I37, I38, I41, I42) [1 <= I38 - 1 /\ I37 <= 1]
6.15/6.15	
6.15/6.15	We have the following SCCs.
6.15/6.15	  
6.15/9.13	EOF