6.68/6.95	YES
6.68/6.95	
6.68/6.95	DP problem for innermost termination.
6.68/6.95	P =
6.68/6.95	  init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 
6.68/6.95	  f6#(I0, I1, I2, I3, I4) -> f5#(I5, I6, I2, I3, I7) [I4 + 2 <= I0 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I6 + 2 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0]
6.68/6.95	  f5#(I8, I9, I10, I11, I12) -> f5#(I13, I14, I10, I11 + 1, I15) [-1 <= I10 - 1 /\ -1 <= I11 - 1 /\ y1 <= 41 /\ -1 <= y1 - 1 /\ I13 + 2 <= I8 /\ I13 + 2 <= I9 /\ I14 + 2 <= I8 /\ I14 + 2 <= I9 /\ 2 <= I8 - 1 /\ 2 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I14 - 1]
6.68/6.95	  f5#(I16, I17, I18, I19, I20) -> f6#(I21, I22, I18, I19 + 1, I23) [-1 <= I18 - 1 /\ -1 <= I19 - 1 /\ I24 <= 41 /\ -1 <= I24 - 1 /\ I21 <= I16 /\ I21 <= I17 /\ I22 + 2 <= I16 /\ I22 + 2 <= I17 /\ 1 <= I16 - 1 /\ 1 <= I17 - 1 /\ 1 <= I21 - 1 /\ -1 <= I22 - 1 /\ I23 + 2 <= I16 /\ I23 + 2 <= I17]
6.68/6.95	  f5#(I25, I26, I27, I28, I29) -> f6#(I30, I31, I27, I28 + 1, I32) [-1 <= I27 - 1 /\ 41 <= I33 - 1 /\ -1 <= I28 - 1 /\ I30 <= I25 /\ I30 <= I26 /\ I31 + 1 <= I25 /\ I31 + 1 <= I26 /\ 0 <= I25 - 1 /\ 0 <= I26 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1 /\ I32 + 2 <= I25 /\ I32 + 2 <= I26]
6.68/6.95	  f2#(I34, I35, I36, I37, I38) -> f5#(I39, I40, I41, I36, I42) [I37 + 2 <= I35 /\ 2 <= I40 - 1 /\ 2 <= I39 - 1 /\ 2 <= I35 - 1 /\ 0 <= I34 - 1 /\ I40 <= I35 /\ 0 <= I41 - 1 /\ I39 <= I35]
6.68/6.95	  f1#(I43, I44, I45, I46, I47) -> f5#(I48, I49, I44, 1, I50) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 0 <= I43 - 1 /\ I49 + 1 <= I43 /\ 0 <= I44 - 1 /\ I48 + 1 <= I43]
6.68/6.95	  f4#(I51, I52, I53, I54, I55) -> f4#(I56, I57, I53 - 1, I54 + 1, I58) [0 <= I53 - 1 /\ 0 <= I59 - 1 /\ -1 <= I54 - 1 /\ I56 - 2 <= I51 /\ I56 - 2 <= I52 /\ I57 - 2 <= I51 /\ I57 - 2 <= I52 /\ 2 <= I51 - 1 /\ 2 <= I52 - 1 /\ 4 <= I56 - 1 /\ 4 <= I57 - 1]
6.68/6.95	  f4#(I60, I61, I62, I63, I64) -> f4#(I65, I66, I62 - 1, I63 + 1, I67) [4 <= I66 - 1 /\ 4 <= I65 - 1 /\ 2 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I61 /\ I66 - 2 <= I60 /\ I65 - 2 <= I61 /\ I65 - 2 <= I60 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1]
6.68/6.95	  f4#(I68, I69, I70, I71, I72) -> f4#(I73, I74, I70 - 1, I71 + 1, I75) [2 <= I74 - 1 /\ 2 <= I73 - 1 /\ 1 <= I69 - 1 /\ 2 <= I68 - 1 /\ 0 <= I70 - 1 /\ -1 <= I71 - 1]
6.68/6.95	  f4#(I76, I77, I78, I79, I80) -> f4#(I81, I82, I78 - 1, I79 + 1, I83) [0 <= I78 - 1 /\ 0 <= I84 - 1 /\ -1 <= I79 - 1 /\ 2 <= I76 - 1 /\ 1 <= I77 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1]
6.68/6.95	  f4#(I85, I86, I87, I88, I89) -> f4#(I90, I91, I87 - 1, I88 + 1, I92) [0 <= I87 - 1 /\ 0 <= I93 - 1 /\ -1 <= I88 - 1 /\ I90 <= I85 /\ I91 + 2 <= I86 /\ 2 <= I85 - 1 /\ 2 <= I86 - 1 /\ 2 <= I90 - 1 /\ 0 <= I91 - 1]
6.68/6.95	  f4#(I94, I95, I96, I97, I98) -> f4#(I99, I100, I96 - 1, I97 + 1, I101) [0 <= I100 - 1 /\ 2 <= I99 - 1 /\ 2 <= I95 - 1 /\ 2 <= I94 - 1 /\ I100 + 2 <= I95 /\ I99 <= I94 /\ 0 <= I96 - 1 /\ -1 <= I97 - 1]
6.68/6.95	  f1#(I102, I103, I104, I105, I106) -> f4#(I107, I108, I109, 1, I110) [2 <= I108 - 1 /\ 2 <= I107 - 1 /\ 0 <= I102 - 1 /\ I108 - 2 <= I102 /\ I107 - 2 <= I102 /\ -1 <= I103 - 1 /\ 0 <= I109 - 1]
6.68/6.95	  f3#(I111, I112, I113, I114, I115) -> f2#(I116, I117, I113, I114, I118) [I114 + 2 <= I112 /\ 2 <= I117 - 1 /\ 0 <= I116 - 1 /\ 2 <= I112 - 1 /\ 0 <= I111 - 1 /\ I117 <= I112 /\ I116 + 2 <= I112 /\ I116 <= I111]
6.68/6.95	  f1#(I119, I120, I121, I122, I123) -> f2#(I124, I125, I126, I127, I128) [2 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I119 - 1 /\ I124 <= I119]
6.68/6.95	R = 
6.68/6.95	  init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 
6.68/6.95	  f6(I0, I1, I2, I3, I4) -> f5(I5, I6, I2, I3, I7) [I4 + 2 <= I0 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I6 + 2 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0]
6.68/6.95	  f5(I8, I9, I10, I11, I12) -> f5(I13, I14, I10, I11 + 1, I15) [-1 <= I10 - 1 /\ -1 <= I11 - 1 /\ y1 <= 41 /\ -1 <= y1 - 1 /\ I13 + 2 <= I8 /\ I13 + 2 <= I9 /\ I14 + 2 <= I8 /\ I14 + 2 <= I9 /\ 2 <= I8 - 1 /\ 2 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I14 - 1]
6.68/6.95	  f5(I16, I17, I18, I19, I20) -> f6(I21, I22, I18, I19 + 1, I23) [-1 <= I18 - 1 /\ -1 <= I19 - 1 /\ I24 <= 41 /\ -1 <= I24 - 1 /\ I21 <= I16 /\ I21 <= I17 /\ I22 + 2 <= I16 /\ I22 + 2 <= I17 /\ 1 <= I16 - 1 /\ 1 <= I17 - 1 /\ 1 <= I21 - 1 /\ -1 <= I22 - 1 /\ I23 + 2 <= I16 /\ I23 + 2 <= I17]
6.68/6.95	  f5(I25, I26, I27, I28, I29) -> f6(I30, I31, I27, I28 + 1, I32) [-1 <= I27 - 1 /\ 41 <= I33 - 1 /\ -1 <= I28 - 1 /\ I30 <= I25 /\ I30 <= I26 /\ I31 + 1 <= I25 /\ I31 + 1 <= I26 /\ 0 <= I25 - 1 /\ 0 <= I26 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1 /\ I32 + 2 <= I25 /\ I32 + 2 <= I26]
6.68/6.95	  f2(I34, I35, I36, I37, I38) -> f5(I39, I40, I41, I36, I42) [I37 + 2 <= I35 /\ 2 <= I40 - 1 /\ 2 <= I39 - 1 /\ 2 <= I35 - 1 /\ 0 <= I34 - 1 /\ I40 <= I35 /\ 0 <= I41 - 1 /\ I39 <= I35]
6.68/6.95	  f1(I43, I44, I45, I46, I47) -> f5(I48, I49, I44, 1, I50) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 0 <= I43 - 1 /\ I49 + 1 <= I43 /\ 0 <= I44 - 1 /\ I48 + 1 <= I43]
6.68/6.95	  f4(I51, I52, I53, I54, I55) -> f4(I56, I57, I53 - 1, I54 + 1, I58) [0 <= I53 - 1 /\ 0 <= I59 - 1 /\ -1 <= I54 - 1 /\ I56 - 2 <= I51 /\ I56 - 2 <= I52 /\ I57 - 2 <= I51 /\ I57 - 2 <= I52 /\ 2 <= I51 - 1 /\ 2 <= I52 - 1 /\ 4 <= I56 - 1 /\ 4 <= I57 - 1]
6.68/6.95	  f4(I60, I61, I62, I63, I64) -> f4(I65, I66, I62 - 1, I63 + 1, I67) [4 <= I66 - 1 /\ 4 <= I65 - 1 /\ 2 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I61 /\ I66 - 2 <= I60 /\ I65 - 2 <= I61 /\ I65 - 2 <= I60 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1]
6.68/6.95	  f4(I68, I69, I70, I71, I72) -> f4(I73, I74, I70 - 1, I71 + 1, I75) [2 <= I74 - 1 /\ 2 <= I73 - 1 /\ 1 <= I69 - 1 /\ 2 <= I68 - 1 /\ 0 <= I70 - 1 /\ -1 <= I71 - 1]
6.68/6.95	  f4(I76, I77, I78, I79, I80) -> f4(I81, I82, I78 - 1, I79 + 1, I83) [0 <= I78 - 1 /\ 0 <= I84 - 1 /\ -1 <= I79 - 1 /\ 2 <= I76 - 1 /\ 1 <= I77 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1]
6.68/6.95	  f4(I85, I86, I87, I88, I89) -> f4(I90, I91, I87 - 1, I88 + 1, I92) [0 <= I87 - 1 /\ 0 <= I93 - 1 /\ -1 <= I88 - 1 /\ I90 <= I85 /\ I91 + 2 <= I86 /\ 2 <= I85 - 1 /\ 2 <= I86 - 1 /\ 2 <= I90 - 1 /\ 0 <= I91 - 1]
6.68/6.95	  f4(I94, I95, I96, I97, I98) -> f4(I99, I100, I96 - 1, I97 + 1, I101) [0 <= I100 - 1 /\ 2 <= I99 - 1 /\ 2 <= I95 - 1 /\ 2 <= I94 - 1 /\ I100 + 2 <= I95 /\ I99 <= I94 /\ 0 <= I96 - 1 /\ -1 <= I97 - 1]
6.68/6.95	  f1(I102, I103, I104, I105, I106) -> f4(I107, I108, I109, 1, I110) [2 <= I108 - 1 /\ 2 <= I107 - 1 /\ 0 <= I102 - 1 /\ I108 - 2 <= I102 /\ I107 - 2 <= I102 /\ -1 <= I103 - 1 /\ 0 <= I109 - 1]
6.68/6.95	  f3(I111, I112, I113, I114, I115) -> f2(I116, I117, I113, I114, I118) [I114 + 2 <= I112 /\ 2 <= I117 - 1 /\ 0 <= I116 - 1 /\ 2 <= I112 - 1 /\ 0 <= I111 - 1 /\ I117 <= I112 /\ I116 + 2 <= I112 /\ I116 <= I111]
6.68/6.95	  f1(I119, I120, I121, I122, I123) -> f2(I124, I125, I126, I127, I128) [2 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I119 - 1 /\ I124 <= I119]
6.68/6.95	
6.68/6.95	The dependency graph for this problem is:
6.68/6.95	  0 -> 6, 13, 15
6.68/6.95	  1 -> 2, 3, 4
6.68/6.95	  2 -> 2, 3, 4
6.68/6.95	  3 -> 1
6.68/6.95	  4 -> 1
6.68/6.95	  5 -> 2, 3, 4
6.68/6.95	  6 -> 2, 3, 4
6.68/6.95	  7 -> 7, 8, 9, 10, 11, 12
6.68/6.95	  8 -> 7, 8, 9, 10, 11, 12
6.68/6.95	  9 -> 7, 8, 9, 10, 11, 12
6.68/6.95	  10 -> 7, 8, 9, 10, 11, 12
6.68/6.95	  11 -> 7, 8, 9, 10, 11, 12
6.68/6.95	  12 -> 7, 8, 9, 10, 11, 12
6.68/6.95	  13 -> 7, 8, 9, 10, 11, 12
6.68/6.95	  14 -> 5
6.68/6.95	  15 -> 5
6.68/6.95	Where:
6.68/6.95	  0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 
6.68/6.95	  1) f6#(I0, I1, I2, I3, I4) -> f5#(I5, I6, I2, I3, I7) [I4 + 2 <= I0 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I6 + 2 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0]
6.68/6.95	  2) f5#(I8, I9, I10, I11, I12) -> f5#(I13, I14, I10, I11 + 1, I15) [-1 <= I10 - 1 /\ -1 <= I11 - 1 /\ y1 <= 41 /\ -1 <= y1 - 1 /\ I13 + 2 <= I8 /\ I13 + 2 <= I9 /\ I14 + 2 <= I8 /\ I14 + 2 <= I9 /\ 2 <= I8 - 1 /\ 2 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I14 - 1]
6.68/6.95	  3) f5#(I16, I17, I18, I19, I20) -> f6#(I21, I22, I18, I19 + 1, I23) [-1 <= I18 - 1 /\ -1 <= I19 - 1 /\ I24 <= 41 /\ -1 <= I24 - 1 /\ I21 <= I16 /\ I21 <= I17 /\ I22 + 2 <= I16 /\ I22 + 2 <= I17 /\ 1 <= I16 - 1 /\ 1 <= I17 - 1 /\ 1 <= I21 - 1 /\ -1 <= I22 - 1 /\ I23 + 2 <= I16 /\ I23 + 2 <= I17]
6.68/6.95	  4) f5#(I25, I26, I27, I28, I29) -> f6#(I30, I31, I27, I28 + 1, I32) [-1 <= I27 - 1 /\ 41 <= I33 - 1 /\ -1 <= I28 - 1 /\ I30 <= I25 /\ I30 <= I26 /\ I31 + 1 <= I25 /\ I31 + 1 <= I26 /\ 0 <= I25 - 1 /\ 0 <= I26 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1 /\ I32 + 2 <= I25 /\ I32 + 2 <= I26]
6.68/6.95	  5) f2#(I34, I35, I36, I37, I38) -> f5#(I39, I40, I41, I36, I42) [I37 + 2 <= I35 /\ 2 <= I40 - 1 /\ 2 <= I39 - 1 /\ 2 <= I35 - 1 /\ 0 <= I34 - 1 /\ I40 <= I35 /\ 0 <= I41 - 1 /\ I39 <= I35]
6.68/6.95	  6) f1#(I43, I44, I45, I46, I47) -> f5#(I48, I49, I44, 1, I50) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 0 <= I43 - 1 /\ I49 + 1 <= I43 /\ 0 <= I44 - 1 /\ I48 + 1 <= I43]
6.68/6.95	  7) f4#(I51, I52, I53, I54, I55) -> f4#(I56, I57, I53 - 1, I54 + 1, I58) [0 <= I53 - 1 /\ 0 <= I59 - 1 /\ -1 <= I54 - 1 /\ I56 - 2 <= I51 /\ I56 - 2 <= I52 /\ I57 - 2 <= I51 /\ I57 - 2 <= I52 /\ 2 <= I51 - 1 /\ 2 <= I52 - 1 /\ 4 <= I56 - 1 /\ 4 <= I57 - 1]
6.68/6.95	  8) f4#(I60, I61, I62, I63, I64) -> f4#(I65, I66, I62 - 1, I63 + 1, I67) [4 <= I66 - 1 /\ 4 <= I65 - 1 /\ 2 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I61 /\ I66 - 2 <= I60 /\ I65 - 2 <= I61 /\ I65 - 2 <= I60 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1]
6.68/6.95	  9) f4#(I68, I69, I70, I71, I72) -> f4#(I73, I74, I70 - 1, I71 + 1, I75) [2 <= I74 - 1 /\ 2 <= I73 - 1 /\ 1 <= I69 - 1 /\ 2 <= I68 - 1 /\ 0 <= I70 - 1 /\ -1 <= I71 - 1]
6.68/6.95	  10) f4#(I76, I77, I78, I79, I80) -> f4#(I81, I82, I78 - 1, I79 + 1, I83) [0 <= I78 - 1 /\ 0 <= I84 - 1 /\ -1 <= I79 - 1 /\ 2 <= I76 - 1 /\ 1 <= I77 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1]
6.68/6.95	  11) f4#(I85, I86, I87, I88, I89) -> f4#(I90, I91, I87 - 1, I88 + 1, I92) [0 <= I87 - 1 /\ 0 <= I93 - 1 /\ -1 <= I88 - 1 /\ I90 <= I85 /\ I91 + 2 <= I86 /\ 2 <= I85 - 1 /\ 2 <= I86 - 1 /\ 2 <= I90 - 1 /\ 0 <= I91 - 1]
6.68/6.95	  12) f4#(I94, I95, I96, I97, I98) -> f4#(I99, I100, I96 - 1, I97 + 1, I101) [0 <= I100 - 1 /\ 2 <= I99 - 1 /\ 2 <= I95 - 1 /\ 2 <= I94 - 1 /\ I100 + 2 <= I95 /\ I99 <= I94 /\ 0 <= I96 - 1 /\ -1 <= I97 - 1]
6.68/6.95	  13) f1#(I102, I103, I104, I105, I106) -> f4#(I107, I108, I109, 1, I110) [2 <= I108 - 1 /\ 2 <= I107 - 1 /\ 0 <= I102 - 1 /\ I108 - 2 <= I102 /\ I107 - 2 <= I102 /\ -1 <= I103 - 1 /\ 0 <= I109 - 1]
6.68/6.95	  14) f3#(I111, I112, I113, I114, I115) -> f2#(I116, I117, I113, I114, I118) [I114 + 2 <= I112 /\ 2 <= I117 - 1 /\ 0 <= I116 - 1 /\ 2 <= I112 - 1 /\ 0 <= I111 - 1 /\ I117 <= I112 /\ I116 + 2 <= I112 /\ I116 <= I111]
6.68/6.95	  15) f1#(I119, I120, I121, I122, I123) -> f2#(I124, I125, I126, I127, I128) [2 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I119 - 1 /\ I124 <= I119]
6.68/6.95	
6.68/6.95	We have the following SCCs.
6.68/6.95	  { 7, 8, 9, 10, 11, 12 }
6.68/6.95	  { 1, 2, 3, 4 }
6.68/6.95	
6.68/6.95	DP problem for innermost termination.
6.68/6.95	P =
6.68/6.95	  f6#(I0, I1, I2, I3, I4) -> f5#(I5, I6, I2, I3, I7) [I4 + 2 <= I0 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I6 + 2 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0]
6.68/6.95	  f5#(I8, I9, I10, I11, I12) -> f5#(I13, I14, I10, I11 + 1, I15) [-1 <= I10 - 1 /\ -1 <= I11 - 1 /\ y1 <= 41 /\ -1 <= y1 - 1 /\ I13 + 2 <= I8 /\ I13 + 2 <= I9 /\ I14 + 2 <= I8 /\ I14 + 2 <= I9 /\ 2 <= I8 - 1 /\ 2 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I14 - 1]
6.68/6.95	  f5#(I16, I17, I18, I19, I20) -> f6#(I21, I22, I18, I19 + 1, I23) [-1 <= I18 - 1 /\ -1 <= I19 - 1 /\ I24 <= 41 /\ -1 <= I24 - 1 /\ I21 <= I16 /\ I21 <= I17 /\ I22 + 2 <= I16 /\ I22 + 2 <= I17 /\ 1 <= I16 - 1 /\ 1 <= I17 - 1 /\ 1 <= I21 - 1 /\ -1 <= I22 - 1 /\ I23 + 2 <= I16 /\ I23 + 2 <= I17]
6.68/6.95	  f5#(I25, I26, I27, I28, I29) -> f6#(I30, I31, I27, I28 + 1, I32) [-1 <= I27 - 1 /\ 41 <= I33 - 1 /\ -1 <= I28 - 1 /\ I30 <= I25 /\ I30 <= I26 /\ I31 + 1 <= I25 /\ I31 + 1 <= I26 /\ 0 <= I25 - 1 /\ 0 <= I26 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1 /\ I32 + 2 <= I25 /\ I32 + 2 <= I26]
6.68/6.95	R = 
6.68/6.95	  init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 
6.68/6.95	  f6(I0, I1, I2, I3, I4) -> f5(I5, I6, I2, I3, I7) [I4 + 2 <= I0 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I6 + 2 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0]
6.68/6.95	  f5(I8, I9, I10, I11, I12) -> f5(I13, I14, I10, I11 + 1, I15) [-1 <= I10 - 1 /\ -1 <= I11 - 1 /\ y1 <= 41 /\ -1 <= y1 - 1 /\ I13 + 2 <= I8 /\ I13 + 2 <= I9 /\ I14 + 2 <= I8 /\ I14 + 2 <= I9 /\ 2 <= I8 - 1 /\ 2 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I14 - 1]
6.68/6.95	  f5(I16, I17, I18, I19, I20) -> f6(I21, I22, I18, I19 + 1, I23) [-1 <= I18 - 1 /\ -1 <= I19 - 1 /\ I24 <= 41 /\ -1 <= I24 - 1 /\ I21 <= I16 /\ I21 <= I17 /\ I22 + 2 <= I16 /\ I22 + 2 <= I17 /\ 1 <= I16 - 1 /\ 1 <= I17 - 1 /\ 1 <= I21 - 1 /\ -1 <= I22 - 1 /\ I23 + 2 <= I16 /\ I23 + 2 <= I17]
6.68/6.95	  f5(I25, I26, I27, I28, I29) -> f6(I30, I31, I27, I28 + 1, I32) [-1 <= I27 - 1 /\ 41 <= I33 - 1 /\ -1 <= I28 - 1 /\ I30 <= I25 /\ I30 <= I26 /\ I31 + 1 <= I25 /\ I31 + 1 <= I26 /\ 0 <= I25 - 1 /\ 0 <= I26 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1 /\ I32 + 2 <= I25 /\ I32 + 2 <= I26]
6.68/6.95	  f2(I34, I35, I36, I37, I38) -> f5(I39, I40, I41, I36, I42) [I37 + 2 <= I35 /\ 2 <= I40 - 1 /\ 2 <= I39 - 1 /\ 2 <= I35 - 1 /\ 0 <= I34 - 1 /\ I40 <= I35 /\ 0 <= I41 - 1 /\ I39 <= I35]
6.68/6.95	  f1(I43, I44, I45, I46, I47) -> f5(I48, I49, I44, 1, I50) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 0 <= I43 - 1 /\ I49 + 1 <= I43 /\ 0 <= I44 - 1 /\ I48 + 1 <= I43]
6.68/6.95	  f4(I51, I52, I53, I54, I55) -> f4(I56, I57, I53 - 1, I54 + 1, I58) [0 <= I53 - 1 /\ 0 <= I59 - 1 /\ -1 <= I54 - 1 /\ I56 - 2 <= I51 /\ I56 - 2 <= I52 /\ I57 - 2 <= I51 /\ I57 - 2 <= I52 /\ 2 <= I51 - 1 /\ 2 <= I52 - 1 /\ 4 <= I56 - 1 /\ 4 <= I57 - 1]
6.68/6.95	  f4(I60, I61, I62, I63, I64) -> f4(I65, I66, I62 - 1, I63 + 1, I67) [4 <= I66 - 1 /\ 4 <= I65 - 1 /\ 2 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I61 /\ I66 - 2 <= I60 /\ I65 - 2 <= I61 /\ I65 - 2 <= I60 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1]
6.68/6.95	  f4(I68, I69, I70, I71, I72) -> f4(I73, I74, I70 - 1, I71 + 1, I75) [2 <= I74 - 1 /\ 2 <= I73 - 1 /\ 1 <= I69 - 1 /\ 2 <= I68 - 1 /\ 0 <= I70 - 1 /\ -1 <= I71 - 1]
6.68/6.95	  f4(I76, I77, I78, I79, I80) -> f4(I81, I82, I78 - 1, I79 + 1, I83) [0 <= I78 - 1 /\ 0 <= I84 - 1 /\ -1 <= I79 - 1 /\ 2 <= I76 - 1 /\ 1 <= I77 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1]
6.68/6.95	  f4(I85, I86, I87, I88, I89) -> f4(I90, I91, I87 - 1, I88 + 1, I92) [0 <= I87 - 1 /\ 0 <= I93 - 1 /\ -1 <= I88 - 1 /\ I90 <= I85 /\ I91 + 2 <= I86 /\ 2 <= I85 - 1 /\ 2 <= I86 - 1 /\ 2 <= I90 - 1 /\ 0 <= I91 - 1]
6.68/6.95	  f4(I94, I95, I96, I97, I98) -> f4(I99, I100, I96 - 1, I97 + 1, I101) [0 <= I100 - 1 /\ 2 <= I99 - 1 /\ 2 <= I95 - 1 /\ 2 <= I94 - 1 /\ I100 + 2 <= I95 /\ I99 <= I94 /\ 0 <= I96 - 1 /\ -1 <= I97 - 1]
6.68/6.95	  f1(I102, I103, I104, I105, I106) -> f4(I107, I108, I109, 1, I110) [2 <= I108 - 1 /\ 2 <= I107 - 1 /\ 0 <= I102 - 1 /\ I108 - 2 <= I102 /\ I107 - 2 <= I102 /\ -1 <= I103 - 1 /\ 0 <= I109 - 1]
6.68/6.95	  f3(I111, I112, I113, I114, I115) -> f2(I116, I117, I113, I114, I118) [I114 + 2 <= I112 /\ 2 <= I117 - 1 /\ 0 <= I116 - 1 /\ 2 <= I112 - 1 /\ 0 <= I111 - 1 /\ I117 <= I112 /\ I116 + 2 <= I112 /\ I116 <= I111]
6.68/6.95	  f1(I119, I120, I121, I122, I123) -> f2(I124, I125, I126, I127, I128) [2 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I119 - 1 /\ I124 <= I119]
6.68/6.95	
6.68/6.95	We use the basic value criterion with the projection function NU:
6.68/6.95	  NU[f5#(z1,z2,z3,z4,z5)] = z2
6.68/6.95	  NU[f6#(z1,z2,z3,z4,z5)] = z1
6.68/6.95	
6.68/6.95	This gives the following inequalities:
6.68/6.95	  I4 + 2 <= I0 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I6 + 2 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0  ==>  I0 >! I6
6.68/6.95	  -1 <= I10 - 1 /\ -1 <= I11 - 1 /\ y1 <= 41 /\ -1 <= y1 - 1 /\ I13 + 2 <= I8 /\ I13 + 2 <= I9 /\ I14 + 2 <= I8 /\ I14 + 2 <= I9 /\ 2 <= I8 - 1 /\ 2 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I14 - 1  ==>  I9 >! I14
6.68/6.95	  -1 <= I18 - 1 /\ -1 <= I19 - 1 /\ I24 <= 41 /\ -1 <= I24 - 1 /\ I21 <= I16 /\ I21 <= I17 /\ I22 + 2 <= I16 /\ I22 + 2 <= I17 /\ 1 <= I16 - 1 /\ 1 <= I17 - 1 /\ 1 <= I21 - 1 /\ -1 <= I22 - 1 /\ I23 + 2 <= I16 /\ I23 + 2 <= I17  ==>  I17 (>! \union =) I21
6.68/6.95	  -1 <= I27 - 1 /\ 41 <= I33 - 1 /\ -1 <= I28 - 1 /\ I30 <= I25 /\ I30 <= I26 /\ I31 + 1 <= I25 /\ I31 + 1 <= I26 /\ 0 <= I25 - 1 /\ 0 <= I26 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1 /\ I32 + 2 <= I25 /\ I32 + 2 <= I26  ==>  I26 (>! \union =) I30
6.68/6.95	
6.68/6.95	We remove all the strictly oriented dependency pairs.
6.68/6.95	
6.68/6.95	DP problem for innermost termination.
6.68/6.95	P =
6.68/6.95	  f5#(I16, I17, I18, I19, I20) -> f6#(I21, I22, I18, I19 + 1, I23) [-1 <= I18 - 1 /\ -1 <= I19 - 1 /\ I24 <= 41 /\ -1 <= I24 - 1 /\ I21 <= I16 /\ I21 <= I17 /\ I22 + 2 <= I16 /\ I22 + 2 <= I17 /\ 1 <= I16 - 1 /\ 1 <= I17 - 1 /\ 1 <= I21 - 1 /\ -1 <= I22 - 1 /\ I23 + 2 <= I16 /\ I23 + 2 <= I17]
6.68/6.95	  f5#(I25, I26, I27, I28, I29) -> f6#(I30, I31, I27, I28 + 1, I32) [-1 <= I27 - 1 /\ 41 <= I33 - 1 /\ -1 <= I28 - 1 /\ I30 <= I25 /\ I30 <= I26 /\ I31 + 1 <= I25 /\ I31 + 1 <= I26 /\ 0 <= I25 - 1 /\ 0 <= I26 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1 /\ I32 + 2 <= I25 /\ I32 + 2 <= I26]
6.68/6.95	R = 
6.68/6.95	  init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 
6.68/6.95	  f6(I0, I1, I2, I3, I4) -> f5(I5, I6, I2, I3, I7) [I4 + 2 <= I0 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I6 + 2 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0]
6.68/6.95	  f5(I8, I9, I10, I11, I12) -> f5(I13, I14, I10, I11 + 1, I15) [-1 <= I10 - 1 /\ -1 <= I11 - 1 /\ y1 <= 41 /\ -1 <= y1 - 1 /\ I13 + 2 <= I8 /\ I13 + 2 <= I9 /\ I14 + 2 <= I8 /\ I14 + 2 <= I9 /\ 2 <= I8 - 1 /\ 2 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I14 - 1]
6.68/6.95	  f5(I16, I17, I18, I19, I20) -> f6(I21, I22, I18, I19 + 1, I23) [-1 <= I18 - 1 /\ -1 <= I19 - 1 /\ I24 <= 41 /\ -1 <= I24 - 1 /\ I21 <= I16 /\ I21 <= I17 /\ I22 + 2 <= I16 /\ I22 + 2 <= I17 /\ 1 <= I16 - 1 /\ 1 <= I17 - 1 /\ 1 <= I21 - 1 /\ -1 <= I22 - 1 /\ I23 + 2 <= I16 /\ I23 + 2 <= I17]
6.68/6.95	  f5(I25, I26, I27, I28, I29) -> f6(I30, I31, I27, I28 + 1, I32) [-1 <= I27 - 1 /\ 41 <= I33 - 1 /\ -1 <= I28 - 1 /\ I30 <= I25 /\ I30 <= I26 /\ I31 + 1 <= I25 /\ I31 + 1 <= I26 /\ 0 <= I25 - 1 /\ 0 <= I26 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1 /\ I32 + 2 <= I25 /\ I32 + 2 <= I26]
6.68/6.95	  f2(I34, I35, I36, I37, I38) -> f5(I39, I40, I41, I36, I42) [I37 + 2 <= I35 /\ 2 <= I40 - 1 /\ 2 <= I39 - 1 /\ 2 <= I35 - 1 /\ 0 <= I34 - 1 /\ I40 <= I35 /\ 0 <= I41 - 1 /\ I39 <= I35]
6.68/6.95	  f1(I43, I44, I45, I46, I47) -> f5(I48, I49, I44, 1, I50) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 0 <= I43 - 1 /\ I49 + 1 <= I43 /\ 0 <= I44 - 1 /\ I48 + 1 <= I43]
6.68/6.95	  f4(I51, I52, I53, I54, I55) -> f4(I56, I57, I53 - 1, I54 + 1, I58) [0 <= I53 - 1 /\ 0 <= I59 - 1 /\ -1 <= I54 - 1 /\ I56 - 2 <= I51 /\ I56 - 2 <= I52 /\ I57 - 2 <= I51 /\ I57 - 2 <= I52 /\ 2 <= I51 - 1 /\ 2 <= I52 - 1 /\ 4 <= I56 - 1 /\ 4 <= I57 - 1]
6.68/6.95	  f4(I60, I61, I62, I63, I64) -> f4(I65, I66, I62 - 1, I63 + 1, I67) [4 <= I66 - 1 /\ 4 <= I65 - 1 /\ 2 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I61 /\ I66 - 2 <= I60 /\ I65 - 2 <= I61 /\ I65 - 2 <= I60 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1]
6.68/6.95	  f4(I68, I69, I70, I71, I72) -> f4(I73, I74, I70 - 1, I71 + 1, I75) [2 <= I74 - 1 /\ 2 <= I73 - 1 /\ 1 <= I69 - 1 /\ 2 <= I68 - 1 /\ 0 <= I70 - 1 /\ -1 <= I71 - 1]
6.68/6.95	  f4(I76, I77, I78, I79, I80) -> f4(I81, I82, I78 - 1, I79 + 1, I83) [0 <= I78 - 1 /\ 0 <= I84 - 1 /\ -1 <= I79 - 1 /\ 2 <= I76 - 1 /\ 1 <= I77 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1]
6.68/6.95	  f4(I85, I86, I87, I88, I89) -> f4(I90, I91, I87 - 1, I88 + 1, I92) [0 <= I87 - 1 /\ 0 <= I93 - 1 /\ -1 <= I88 - 1 /\ I90 <= I85 /\ I91 + 2 <= I86 /\ 2 <= I85 - 1 /\ 2 <= I86 - 1 /\ 2 <= I90 - 1 /\ 0 <= I91 - 1]
6.68/6.95	  f4(I94, I95, I96, I97, I98) -> f4(I99, I100, I96 - 1, I97 + 1, I101) [0 <= I100 - 1 /\ 2 <= I99 - 1 /\ 2 <= I95 - 1 /\ 2 <= I94 - 1 /\ I100 + 2 <= I95 /\ I99 <= I94 /\ 0 <= I96 - 1 /\ -1 <= I97 - 1]
6.68/6.95	  f1(I102, I103, I104, I105, I106) -> f4(I107, I108, I109, 1, I110) [2 <= I108 - 1 /\ 2 <= I107 - 1 /\ 0 <= I102 - 1 /\ I108 - 2 <= I102 /\ I107 - 2 <= I102 /\ -1 <= I103 - 1 /\ 0 <= I109 - 1]
6.68/6.95	  f3(I111, I112, I113, I114, I115) -> f2(I116, I117, I113, I114, I118) [I114 + 2 <= I112 /\ 2 <= I117 - 1 /\ 0 <= I116 - 1 /\ 2 <= I112 - 1 /\ 0 <= I111 - 1 /\ I117 <= I112 /\ I116 + 2 <= I112 /\ I116 <= I111]
6.68/6.95	  f1(I119, I120, I121, I122, I123) -> f2(I124, I125, I126, I127, I128) [2 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I119 - 1 /\ I124 <= I119]
6.68/6.95	
6.68/6.95	The dependency graph for this problem is:
6.68/6.95	  3 -> 
6.68/6.95	  4 -> 
6.68/6.95	Where:
6.68/6.95	  3) f5#(I16, I17, I18, I19, I20) -> f6#(I21, I22, I18, I19 + 1, I23) [-1 <= I18 - 1 /\ -1 <= I19 - 1 /\ I24 <= 41 /\ -1 <= I24 - 1 /\ I21 <= I16 /\ I21 <= I17 /\ I22 + 2 <= I16 /\ I22 + 2 <= I17 /\ 1 <= I16 - 1 /\ 1 <= I17 - 1 /\ 1 <= I21 - 1 /\ -1 <= I22 - 1 /\ I23 + 2 <= I16 /\ I23 + 2 <= I17]
6.68/6.95	  4) f5#(I25, I26, I27, I28, I29) -> f6#(I30, I31, I27, I28 + 1, I32) [-1 <= I27 - 1 /\ 41 <= I33 - 1 /\ -1 <= I28 - 1 /\ I30 <= I25 /\ I30 <= I26 /\ I31 + 1 <= I25 /\ I31 + 1 <= I26 /\ 0 <= I25 - 1 /\ 0 <= I26 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1 /\ I32 + 2 <= I25 /\ I32 + 2 <= I26]
6.68/6.95	
6.68/6.95	We have the following SCCs.
6.68/6.95	  
6.68/6.95	
6.68/6.95	DP problem for innermost termination.
6.68/6.95	P =
6.68/6.95	  f4#(I51, I52, I53, I54, I55) -> f4#(I56, I57, I53 - 1, I54 + 1, I58) [0 <= I53 - 1 /\ 0 <= I59 - 1 /\ -1 <= I54 - 1 /\ I56 - 2 <= I51 /\ I56 - 2 <= I52 /\ I57 - 2 <= I51 /\ I57 - 2 <= I52 /\ 2 <= I51 - 1 /\ 2 <= I52 - 1 /\ 4 <= I56 - 1 /\ 4 <= I57 - 1]
6.68/6.95	  f4#(I60, I61, I62, I63, I64) -> f4#(I65, I66, I62 - 1, I63 + 1, I67) [4 <= I66 - 1 /\ 4 <= I65 - 1 /\ 2 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I61 /\ I66 - 2 <= I60 /\ I65 - 2 <= I61 /\ I65 - 2 <= I60 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1]
6.68/6.95	  f4#(I68, I69, I70, I71, I72) -> f4#(I73, I74, I70 - 1, I71 + 1, I75) [2 <= I74 - 1 /\ 2 <= I73 - 1 /\ 1 <= I69 - 1 /\ 2 <= I68 - 1 /\ 0 <= I70 - 1 /\ -1 <= I71 - 1]
6.68/6.95	  f4#(I76, I77, I78, I79, I80) -> f4#(I81, I82, I78 - 1, I79 + 1, I83) [0 <= I78 - 1 /\ 0 <= I84 - 1 /\ -1 <= I79 - 1 /\ 2 <= I76 - 1 /\ 1 <= I77 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1]
6.68/6.95	  f4#(I85, I86, I87, I88, I89) -> f4#(I90, I91, I87 - 1, I88 + 1, I92) [0 <= I87 - 1 /\ 0 <= I93 - 1 /\ -1 <= I88 - 1 /\ I90 <= I85 /\ I91 + 2 <= I86 /\ 2 <= I85 - 1 /\ 2 <= I86 - 1 /\ 2 <= I90 - 1 /\ 0 <= I91 - 1]
6.68/6.95	  f4#(I94, I95, I96, I97, I98) -> f4#(I99, I100, I96 - 1, I97 + 1, I101) [0 <= I100 - 1 /\ 2 <= I99 - 1 /\ 2 <= I95 - 1 /\ 2 <= I94 - 1 /\ I100 + 2 <= I95 /\ I99 <= I94 /\ 0 <= I96 - 1 /\ -1 <= I97 - 1]
6.68/6.95	R = 
6.68/6.95	  init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 
6.68/6.95	  f6(I0, I1, I2, I3, I4) -> f5(I5, I6, I2, I3, I7) [I4 + 2 <= I0 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I6 + 2 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0]
6.68/6.95	  f5(I8, I9, I10, I11, I12) -> f5(I13, I14, I10, I11 + 1, I15) [-1 <= I10 - 1 /\ -1 <= I11 - 1 /\ y1 <= 41 /\ -1 <= y1 - 1 /\ I13 + 2 <= I8 /\ I13 + 2 <= I9 /\ I14 + 2 <= I8 /\ I14 + 2 <= I9 /\ 2 <= I8 - 1 /\ 2 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I14 - 1]
6.68/6.95	  f5(I16, I17, I18, I19, I20) -> f6(I21, I22, I18, I19 + 1, I23) [-1 <= I18 - 1 /\ -1 <= I19 - 1 /\ I24 <= 41 /\ -1 <= I24 - 1 /\ I21 <= I16 /\ I21 <= I17 /\ I22 + 2 <= I16 /\ I22 + 2 <= I17 /\ 1 <= I16 - 1 /\ 1 <= I17 - 1 /\ 1 <= I21 - 1 /\ -1 <= I22 - 1 /\ I23 + 2 <= I16 /\ I23 + 2 <= I17]
6.68/6.95	  f5(I25, I26, I27, I28, I29) -> f6(I30, I31, I27, I28 + 1, I32) [-1 <= I27 - 1 /\ 41 <= I33 - 1 /\ -1 <= I28 - 1 /\ I30 <= I25 /\ I30 <= I26 /\ I31 + 1 <= I25 /\ I31 + 1 <= I26 /\ 0 <= I25 - 1 /\ 0 <= I26 - 1 /\ 0 <= I30 - 1 /\ -1 <= I31 - 1 /\ I32 + 2 <= I25 /\ I32 + 2 <= I26]
6.68/6.95	  f2(I34, I35, I36, I37, I38) -> f5(I39, I40, I41, I36, I42) [I37 + 2 <= I35 /\ 2 <= I40 - 1 /\ 2 <= I39 - 1 /\ 2 <= I35 - 1 /\ 0 <= I34 - 1 /\ I40 <= I35 /\ 0 <= I41 - 1 /\ I39 <= I35]
6.68/6.95	  f1(I43, I44, I45, I46, I47) -> f5(I48, I49, I44, 1, I50) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 0 <= I43 - 1 /\ I49 + 1 <= I43 /\ 0 <= I44 - 1 /\ I48 + 1 <= I43]
6.68/6.95	  f4(I51, I52, I53, I54, I55) -> f4(I56, I57, I53 - 1, I54 + 1, I58) [0 <= I53 - 1 /\ 0 <= I59 - 1 /\ -1 <= I54 - 1 /\ I56 - 2 <= I51 /\ I56 - 2 <= I52 /\ I57 - 2 <= I51 /\ I57 - 2 <= I52 /\ 2 <= I51 - 1 /\ 2 <= I52 - 1 /\ 4 <= I56 - 1 /\ 4 <= I57 - 1]
6.68/6.95	  f4(I60, I61, I62, I63, I64) -> f4(I65, I66, I62 - 1, I63 + 1, I67) [4 <= I66 - 1 /\ 4 <= I65 - 1 /\ 2 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I61 /\ I66 - 2 <= I60 /\ I65 - 2 <= I61 /\ I65 - 2 <= I60 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1]
6.68/6.95	  f4(I68, I69, I70, I71, I72) -> f4(I73, I74, I70 - 1, I71 + 1, I75) [2 <= I74 - 1 /\ 2 <= I73 - 1 /\ 1 <= I69 - 1 /\ 2 <= I68 - 1 /\ 0 <= I70 - 1 /\ -1 <= I71 - 1]
6.68/6.95	  f4(I76, I77, I78, I79, I80) -> f4(I81, I82, I78 - 1, I79 + 1, I83) [0 <= I78 - 1 /\ 0 <= I84 - 1 /\ -1 <= I79 - 1 /\ 2 <= I76 - 1 /\ 1 <= I77 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1]
6.68/6.96	  f4(I85, I86, I87, I88, I89) -> f4(I90, I91, I87 - 1, I88 + 1, I92) [0 <= I87 - 1 /\ 0 <= I93 - 1 /\ -1 <= I88 - 1 /\ I90 <= I85 /\ I91 + 2 <= I86 /\ 2 <= I85 - 1 /\ 2 <= I86 - 1 /\ 2 <= I90 - 1 /\ 0 <= I91 - 1]
6.68/6.96	  f4(I94, I95, I96, I97, I98) -> f4(I99, I100, I96 - 1, I97 + 1, I101) [0 <= I100 - 1 /\ 2 <= I99 - 1 /\ 2 <= I95 - 1 /\ 2 <= I94 - 1 /\ I100 + 2 <= I95 /\ I99 <= I94 /\ 0 <= I96 - 1 /\ -1 <= I97 - 1]
6.68/6.96	  f1(I102, I103, I104, I105, I106) -> f4(I107, I108, I109, 1, I110) [2 <= I108 - 1 /\ 2 <= I107 - 1 /\ 0 <= I102 - 1 /\ I108 - 2 <= I102 /\ I107 - 2 <= I102 /\ -1 <= I103 - 1 /\ 0 <= I109 - 1]
6.68/6.96	  f3(I111, I112, I113, I114, I115) -> f2(I116, I117, I113, I114, I118) [I114 + 2 <= I112 /\ 2 <= I117 - 1 /\ 0 <= I116 - 1 /\ 2 <= I112 - 1 /\ 0 <= I111 - 1 /\ I117 <= I112 /\ I116 + 2 <= I112 /\ I116 <= I111]
6.68/6.96	  f1(I119, I120, I121, I122, I123) -> f2(I124, I125, I126, I127, I128) [2 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I119 - 1 /\ I124 <= I119]
6.68/6.96	
6.68/6.96	We use the basic value criterion with the projection function NU:
6.68/6.96	  NU[f4#(z1,z2,z3,z4,z5)] = z3
6.68/6.96	
6.68/6.96	This gives the following inequalities:
6.68/6.96	  0 <= I53 - 1 /\ 0 <= I59 - 1 /\ -1 <= I54 - 1 /\ I56 - 2 <= I51 /\ I56 - 2 <= I52 /\ I57 - 2 <= I51 /\ I57 - 2 <= I52 /\ 2 <= I51 - 1 /\ 2 <= I52 - 1 /\ 4 <= I56 - 1 /\ 4 <= I57 - 1  ==>  I53 >! I53 - 1
6.68/6.96	  4 <= I66 - 1 /\ 4 <= I65 - 1 /\ 2 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I61 /\ I66 - 2 <= I60 /\ I65 - 2 <= I61 /\ I65 - 2 <= I60 /\ 0 <= I62 - 1 /\ -1 <= I63 - 1  ==>  I62 >! I62 - 1
6.68/6.96	  2 <= I74 - 1 /\ 2 <= I73 - 1 /\ 1 <= I69 - 1 /\ 2 <= I68 - 1 /\ 0 <= I70 - 1 /\ -1 <= I71 - 1  ==>  I70 >! I70 - 1
6.68/6.96	  0 <= I78 - 1 /\ 0 <= I84 - 1 /\ -1 <= I79 - 1 /\ 2 <= I76 - 1 /\ 1 <= I77 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1  ==>  I78 >! I78 - 1
6.68/6.96	  0 <= I87 - 1 /\ 0 <= I93 - 1 /\ -1 <= I88 - 1 /\ I90 <= I85 /\ I91 + 2 <= I86 /\ 2 <= I85 - 1 /\ 2 <= I86 - 1 /\ 2 <= I90 - 1 /\ 0 <= I91 - 1  ==>  I87 >! I87 - 1
6.68/6.96	  0 <= I100 - 1 /\ 2 <= I99 - 1 /\ 2 <= I95 - 1 /\ 2 <= I94 - 1 /\ I100 + 2 <= I95 /\ I99 <= I94 /\ 0 <= I96 - 1 /\ -1 <= I97 - 1  ==>  I96 >! I96 - 1
6.68/6.96	
6.68/6.96	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
6.68/6.96	EOF