95.98/94.86	MAYBE
95.98/94.86	
95.98/94.86	DP problem for innermost termination.
95.98/94.86	P =
95.98/94.86	  f15#(x1, x2, x3, x4, x5) -> f1#(x1, x2, x3, x4, x5) 
95.98/94.86	  f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f8#(I31, I32, I33, I34, I35) -> f2#(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  f11#(I36, I37, I38, I39, I40) -> f3#(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  f10#(I41, I42, I43, I44, I45) -> f11#(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  f10#(I46, I47, I48, I49, I50) -> f11#(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  f8#(I51, I52, I53, I54, I55) -> f10#(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  f8#(I57, I58, I59, I60, I61) -> f4#(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  f2#(I68, I69, I70, I71, I72) -> f8#(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  f3#(I73, I74, I75, I76, I77) -> f2#(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0]
95.98/94.86	  f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) 
95.98/94.86	  f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	  f1#(I110, I111, I112, I113, I114) -> f2#(I110, I111, I112, I113, I114) 
95.98/94.86	R = 
95.98/94.86	  f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) 
95.98/94.86	  f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) 
95.98/94.86	  f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0]
95.98/94.86	  f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0]
95.98/94.86	  f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) 
95.98/94.86	  f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	  f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) 
95.98/94.86	
95.98/94.86	The dependency graph for this problem is:
95.98/94.86	  0 -> 21
95.98/94.86	  1 -> 14, 19, 20
95.98/94.86	  2 -> 1
95.98/94.86	  3 -> 1
95.98/94.86	  4 -> 2, 3
95.98/94.86	  5 -> 4, 6
95.98/94.86	  6 -> 5
95.98/94.86	  7 -> 13
95.98/94.86	  8 -> 14, 19, 20
95.98/94.86	  9 -> 8
95.98/94.86	  10 -> 8
95.98/94.86	  11 -> 9, 10
95.98/94.86	  12 -> 4, 6
95.98/94.86	  13 -> 7, 11, 12
95.98/94.86	  14 -> 13
95.98/94.86	  15 -> 14, 19, 20
95.98/94.86	  16 -> 15
95.98/94.86	  17 -> 16
95.98/94.86	  18 -> 16
95.98/94.86	  19 -> 17, 18
95.98/94.86	  20 -> 4, 6
95.98/94.86	  21 -> 13
95.98/94.86	Where:
95.98/94.86	  0) f15#(x1, x2, x3, x4, x5) -> f1#(x1, x2, x3, x4, x5) 
95.98/94.86	  1) f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  2) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  3) f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  4) f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  5) f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  6) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  7) f8#(I31, I32, I33, I34, I35) -> f2#(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  8) f11#(I36, I37, I38, I39, I40) -> f3#(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  9) f10#(I41, I42, I43, I44, I45) -> f11#(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  10) f10#(I46, I47, I48, I49, I50) -> f11#(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  11) f8#(I51, I52, I53, I54, I55) -> f10#(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  12) f8#(I57, I58, I59, I60, I61) -> f4#(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  13) f2#(I68, I69, I70, I71, I72) -> f8#(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  14) f3#(I73, I74, I75, I76, I77) -> f2#(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0]
95.98/94.86	  15) f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) 
95.98/94.86	  16) f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  17) f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  18) f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  19) f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  20) f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	  21) f1#(I110, I111, I112, I113, I114) -> f2#(I110, I111, I112, I113, I114) 
95.98/94.86	
95.98/94.86	We have the following SCCs.
95.98/94.86	  { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }
95.98/94.86	
95.98/94.86	DP problem for innermost termination.
95.98/94.86	P =
95.98/94.86	  f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f8#(I31, I32, I33, I34, I35) -> f2#(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  f11#(I36, I37, I38, I39, I40) -> f3#(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  f10#(I41, I42, I43, I44, I45) -> f11#(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  f10#(I46, I47, I48, I49, I50) -> f11#(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  f8#(I51, I52, I53, I54, I55) -> f10#(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  f8#(I57, I58, I59, I60, I61) -> f4#(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  f2#(I68, I69, I70, I71, I72) -> f8#(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  f3#(I73, I74, I75, I76, I77) -> f2#(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0]
95.98/94.86	  f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) 
95.98/94.86	  f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	R = 
95.98/94.86	  f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) 
95.98/94.86	  f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) 
95.98/94.86	  f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0]
95.98/94.86	  f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0]
95.98/94.86	  f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) 
95.98/94.86	  f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	  f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) 
95.98/94.86	
95.98/94.86	We use the extended value criterion with the projection function NU:
95.98/94.86	  NU[f5#(x0,x1,x2,x3,x4)] = 0
95.98/94.86	  NU[f6#(x0,x1,x2,x3,x4)] = 0
95.98/94.86	  NU[f7#(x0,x1,x2,x3,x4)] = 0
95.98/94.86	  NU[f10#(x0,x1,x2,x3,x4)] = 0
95.98/94.86	  NU[f11#(x0,x1,x2,x3,x4)] = 0
95.98/94.86	  NU[f2#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1
95.98/94.86	  NU[f8#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1
95.98/94.86	  NU[f12#(x0,x1,x2,x3,x4)] = 0
95.98/94.86	  NU[f4#(x0,x1,x2,x3,x4)] = 0
95.98/94.86	  NU[f13#(x0,x1,x2,x3,x4)] = 0
95.98/94.86	  NU[f3#(x0,x1,x2,x3,x4)] = 0
95.98/94.86	  NU[f14#(x0,x1,x2,x3,x4)] = 0
95.98/94.86	
95.98/94.86	This gives the following inequalities:
95.98/94.86	    ==>  0 >= 0
95.98/94.86	  1 <= I6  ==>  0 >= 0
95.98/94.86	  1 + I11 <= 0  ==>  0 >= 0
95.98/94.86	  rnd2 = rnd2 /\ 0 <= -1 - I18 + I19  ==>  0 >= 0
95.98/94.86	    ==>  0 >= 0
95.98/94.86	  0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29  ==>  0 >= 0
95.98/94.86	  -1 * I34 + I35 <= 0  ==>  -I34 + I35 - 1 >= -I34 + I35 - 1
95.98/94.86	    ==>  0 >= 0
95.98/94.86	  1 <= I42  ==>  0 >= 0
95.98/94.86	  1 + I47 <= 0  ==>  0 >= 0
95.98/94.86	  I56 = I56 /\ 0 <= -1 - I54 + I55  ==>  -I54 + I55 - 1 >= 0
95.98/94.86	  0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61  ==>  -I60 + I61 - 1 >= 0
95.98/94.86	  0 <= -1 - I70 + I71  ==>  -I71 + I72 - 1 >= -I71 + I72 - 1
95.98/94.86	  -1 * I76 + I77 <= 0  ==>  0 > -I76 + I77 - 1  with  0 >= 0
95.98/94.86	    ==>  0 >= 0
95.98/94.86	    ==>  0 >= 0
95.98/94.86	  1 <= I89  ==>  0 >= 0
95.98/94.86	  1 + I94 <= 0  ==>  0 >= 0
95.98/94.86	  I103 = I103 /\ 0 <= -1 - I101 + I102  ==>  0 >= 0
95.98/94.86	  0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108  ==>  0 >= 0
95.98/94.86	
95.98/94.86	We remove all the strictly oriented dependency pairs.
95.98/94.86	
95.98/94.86	DP problem for innermost termination.
95.98/94.86	P =
95.98/94.86	  f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f8#(I31, I32, I33, I34, I35) -> f2#(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  f11#(I36, I37, I38, I39, I40) -> f3#(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  f10#(I41, I42, I43, I44, I45) -> f11#(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  f10#(I46, I47, I48, I49, I50) -> f11#(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  f8#(I51, I52, I53, I54, I55) -> f10#(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  f8#(I57, I58, I59, I60, I61) -> f4#(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  f2#(I68, I69, I70, I71, I72) -> f8#(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) 
95.98/94.86	  f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	R = 
95.98/94.86	  f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) 
95.98/94.86	  f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) 
95.98/94.86	  f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0]
95.98/94.86	  f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0]
95.98/94.86	  f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) 
95.98/94.86	  f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	  f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) 
95.98/94.86	
95.98/94.86	The dependency graph for this problem is:
95.98/94.86	  1 -> 19, 20
95.98/94.86	  2 -> 1
95.98/94.86	  3 -> 1
95.98/94.86	  4 -> 2, 3
95.98/94.86	  5 -> 4, 6
95.98/94.86	  6 -> 5
95.98/94.86	  7 -> 13
95.98/94.86	  8 -> 19, 20
95.98/94.86	  9 -> 8
95.98/94.86	  10 -> 8
95.98/94.86	  11 -> 9, 10
95.98/94.86	  12 -> 4, 6
95.98/94.86	  13 -> 7, 11, 12
95.98/94.86	  15 -> 19, 20
95.98/94.86	  16 -> 15
95.98/94.86	  17 -> 16
95.98/94.86	  18 -> 16
95.98/94.86	  19 -> 17, 18
95.98/94.86	  20 -> 4, 6
95.98/94.86	Where:
95.98/94.86	  1) f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  2) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  3) f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  4) f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  5) f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  6) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  7) f8#(I31, I32, I33, I34, I35) -> f2#(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  8) f11#(I36, I37, I38, I39, I40) -> f3#(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  9) f10#(I41, I42, I43, I44, I45) -> f11#(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  10) f10#(I46, I47, I48, I49, I50) -> f11#(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  11) f8#(I51, I52, I53, I54, I55) -> f10#(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  12) f8#(I57, I58, I59, I60, I61) -> f4#(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  13) f2#(I68, I69, I70, I71, I72) -> f8#(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  15) f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) 
95.98/94.86	  16) f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  17) f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  18) f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  19) f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  20) f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	
95.98/94.86	We have the following SCCs.
95.98/94.86	  { 7, 13 }
95.98/94.86	  { 1, 2, 3, 4, 5, 6, 15, 16, 17, 18, 19, 20 }
95.98/94.86	
95.98/94.86	DP problem for innermost termination.
95.98/94.86	P =
95.98/94.86	  f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) 
95.98/94.86	  f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3#(I98, I99, I100, I101, I102) -> f5#(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	R = 
95.98/94.86	  f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) 
95.98/94.86	  f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) 
95.98/94.86	  f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0]
95.98/94.86	  f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0]
95.98/94.86	  f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) 
95.98/94.86	  f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	  f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) 
95.98/94.86	
95.98/94.86	We use the extended value criterion with the projection function NU:
95.98/94.86	  NU[f5#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2
95.98/94.86	  NU[f6#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2
95.98/94.86	  NU[f7#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1
95.98/94.86	  NU[f12#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2
95.98/94.86	  NU[f4#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2
95.98/94.86	  NU[f13#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2
95.98/94.86	  NU[f3#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1
95.98/94.86	  NU[f14#(x0,x1,x2,x3,x4)] = -x3 + x4 - 2
95.98/94.86	
95.98/94.86	This gives the following inequalities:
95.98/94.86	    ==>  -I3 + I4 - 2 >= -(1 + I3) + I4 - 1
95.98/94.86	  1 <= I6  ==>  -I8 + I9 - 2 >= -I8 + I9 - 2
95.98/94.86	  1 + I11 <= 0  ==>  -I13 + I14 - 2 >= -I13 + I14 - 2
95.98/94.86	  rnd2 = rnd2 /\ 0 <= -1 - I18 + I19  ==>  -I18 + I19 - 2 >= -I18 + I19 - 2
95.98/94.86	    ==>  -I23 + I24 - 2 >= -I23 + I24 - 2
95.98/94.86	  0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29  ==>  -I28 + I29 - 2 >= -I28 + I29 - 2
95.98/94.86	    ==>  -I81 + I82 - 1 >= -I81 + I82 - 1
95.98/94.86	    ==>  -I86 + I87 - 2 >= -(1 + I86) + I87 - 1
95.98/94.86	  1 <= I89  ==>  -I91 + I92 - 2 >= -I91 + I92 - 2
95.98/94.86	  1 + I94 <= 0  ==>  -I96 + I97 - 2 >= -I96 + I97 - 2
95.98/94.86	  I103 = I103 /\ 0 <= -1 - I101 + I102  ==>  -I101 + I102 - 1 > -I101 + I102 - 2  with  -I101 + I102 - 1 >= 0
95.98/94.86	  0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108  ==>  -I107 + I108 - 1 >= -I107 + I108 - 2
95.98/94.86	
95.98/94.86	We remove all the strictly oriented dependency pairs.
95.98/94.86	
95.98/94.86	DP problem for innermost termination.
95.98/94.86	P =
95.98/94.86	  f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) 
95.98/94.86	  f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	R = 
95.98/94.86	  f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) 
95.98/94.86	  f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) 
95.98/94.86	  f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0]
95.98/94.86	  f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0]
95.98/94.86	  f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) 
95.98/94.86	  f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	  f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) 
95.98/94.86	
95.98/94.86	The dependency graph for this problem is:
95.98/94.86	  1 -> 20
95.98/94.86	  2 -> 1
95.98/94.86	  3 -> 1
95.98/94.86	  4 -> 2, 3
95.98/94.86	  5 -> 4, 6
95.98/94.86	  6 -> 5
95.98/94.86	  15 -> 20
95.98/94.86	  16 -> 15
95.98/94.86	  17 -> 16
95.98/94.86	  18 -> 16
95.98/94.86	  20 -> 4, 6
95.98/94.86	Where:
95.98/94.86	  1) f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  2) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  3) f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  4) f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  5) f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  6) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  15) f7#(I78, I79, I80, I81, I82) -> f3#(I78, I79, I80, I81, I82) 
95.98/94.86	  16) f6#(I83, I84, I85, I86, I87) -> f7#(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  17) f5#(I88, I89, I90, I91, I92) -> f6#(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  18) f5#(I93, I94, I95, I96, I97) -> f6#(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  20) f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	
95.98/94.86	We have the following SCCs.
95.98/94.86	  { 1, 2, 3, 4, 5, 6, 20 }
95.98/94.86	
95.98/94.86	DP problem for innermost termination.
95.98/94.86	P =
95.98/94.86	  f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f3#(I104, I105, I106, I107, I108) -> f4#(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	R = 
95.98/94.86	  f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) 
95.98/94.86	  f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) 
95.98/94.86	  f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0]
95.98/94.86	  f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0]
95.98/94.86	  f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) 
95.98/94.86	  f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	  f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) 
95.98/94.86	
95.98/94.86	We use the extended value criterion with the projection function NU:
95.98/94.86	  NU[f12#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1
95.98/94.86	  NU[f4#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1
95.98/94.86	  NU[f13#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1
95.98/94.86	  NU[f3#(x0,x1,x2,x3,x4)] = -x3 + x4
95.98/94.86	  NU[f14#(x0,x1,x2,x3,x4)] = -x3 + x4 - 1
95.98/94.86	
95.98/94.86	This gives the following inequalities:
95.98/94.86	    ==>  -I3 + I4 - 1 >= -(1 + I3) + I4
95.98/94.86	  1 <= I6  ==>  -I8 + I9 - 1 >= -I8 + I9 - 1
95.98/94.86	  1 + I11 <= 0  ==>  -I13 + I14 - 1 >= -I13 + I14 - 1
95.98/94.86	  rnd2 = rnd2 /\ 0 <= -1 - I18 + I19  ==>  -I18 + I19 - 1 >= -I18 + I19 - 1
95.98/94.86	    ==>  -I23 + I24 - 1 >= -I23 + I24 - 1
95.98/94.86	  0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29  ==>  -I28 + I29 - 1 >= -I28 + I29 - 1
95.98/94.86	  0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108  ==>  -I107 + I108 > -I107 + I108 - 1  with  -I107 + I108 >= 0
95.98/94.86	
95.98/94.86	We remove all the strictly oriented dependency pairs.
95.98/94.86	
95.98/94.86	DP problem for innermost termination.
95.98/94.86	P =
95.98/94.86	  f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	R = 
95.98/94.86	  f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) 
95.98/94.86	  f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) 
95.98/94.86	  f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0]
95.98/94.86	  f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0]
95.98/94.86	  f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) 
95.98/94.86	  f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	  f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) 
95.98/94.86	
95.98/94.86	The dependency graph for this problem is:
95.98/94.86	  1 -> 
95.98/94.86	  2 -> 1
95.98/94.86	  3 -> 1
95.98/94.86	  4 -> 2, 3
95.98/94.86	  5 -> 4, 6
95.98/94.86	  6 -> 5
95.98/94.86	Where:
95.98/94.86	  1) f14#(I0, I1, I2, I3, I4) -> f3#(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  2) f13#(I5, I6, I7, I8, I9) -> f14#(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  3) f13#(I10, I11, I12, I13, I14) -> f14#(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  4) f4#(I15, I16, I17, I18, I19) -> f13#(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  5) f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  6) f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	
95.98/94.86	We have the following SCCs.
95.98/94.86	  { 5, 6 }
95.98/94.86	
95.98/94.86	DP problem for innermost termination.
95.98/94.86	P =
95.98/94.86	  f12#(I20, I21, I22, I23, I24) -> f4#(I20, I21, I22, I23, I24) 
95.98/94.86	  f4#(I25, I26, I27, I28, I29) -> f12#(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	R = 
95.98/94.86	  f15(x1, x2, x3, x4, x5) -> f1(x1, x2, x3, x4, x5) 
95.98/94.86	  f14(I0, I1, I2, I3, I4) -> f3(I0, I1, I2, 1 + I3, I4) 
95.98/94.86	  f13(I5, I6, I7, I8, I9) -> f14(I5, I6, I7, I8, I9) [1 <= I6]
95.98/94.86	  f13(I10, I11, I12, I13, I14) -> f14(I10, I11, I12, I13, I14) [1 + I11 <= 0]
95.98/94.86	  f4(I15, I16, I17, I18, I19) -> f13(I15, rnd2, I17, I18, I19) [rnd2 = rnd2 /\ 0 <= -1 - I18 + I19]
95.98/94.86	  f12(I20, I21, I22, I23, I24) -> f4(I20, I21, I22, I23, I24) 
95.98/94.86	  f4(I25, I26, I27, I28, I29) -> f12(I25, I30, I27, I28, I29) [0 <= I30 /\ I30 <= 0 /\ I30 = I30 /\ 0 <= -1 - I28 + I29]
95.98/94.86	  f8(I31, I32, I33, I34, I35) -> f2(I31, I32, 1 + I33, I34, I35) [-1 * I34 + I35 <= 0]
95.98/94.86	  f11(I36, I37, I38, I39, I40) -> f3(I36, I37, I38, 1 + I39, I40) 
95.98/94.86	  f10(I41, I42, I43, I44, I45) -> f11(I41, I42, I43, I44, I45) [1 <= I42]
95.98/94.86	  f10(I46, I47, I48, I49, I50) -> f11(I46, I47, I48, I49, I50) [1 + I47 <= 0]
95.98/94.86	  f8(I51, I52, I53, I54, I55) -> f10(I51, I56, I53, I54, I55) [I56 = I56 /\ 0 <= -1 - I54 + I55]
95.98/94.86	  f8(I57, I58, I59, I60, I61) -> f4(I57, I62, I59, I60, I61) [0 <= I62 /\ I62 <= 0 /\ I62 = I62 /\ 0 <= -1 - I60 + I61]
95.98/94.86	  f2(I63, I64, I65, I66, I67) -> f9(rnd1, I64, I65, I66, I67) [rnd1 = rnd1 /\ -1 * I65 + I66 <= 0]
95.98/94.86	  f2(I68, I69, I70, I71, I72) -> f8(I68, I69, I70, I71, I72) [0 <= -1 - I70 + I71]
95.98/94.86	  f3(I73, I74, I75, I76, I77) -> f2(I73, I74, 1 + I75, I76, I77) [-1 * I76 + I77 <= 0]
95.98/94.86	  f7(I78, I79, I80, I81, I82) -> f3(I78, I79, I80, I81, I82) 
95.98/94.86	  f6(I83, I84, I85, I86, I87) -> f7(I83, I84, I85, 1 + I86, I87) 
95.98/94.86	  f5(I88, I89, I90, I91, I92) -> f6(I88, I89, I90, I91, I92) [1 <= I89]
95.98/94.86	  f5(I93, I94, I95, I96, I97) -> f6(I93, I94, I95, I96, I97) [1 + I94 <= 0]
95.98/94.86	  f3(I98, I99, I100, I101, I102) -> f5(I98, I103, I100, I101, I102) [I103 = I103 /\ 0 <= -1 - I101 + I102]
95.98/94.86	  f3(I104, I105, I106, I107, I108) -> f4(I104, I109, I106, I107, I108) [0 <= I109 /\ I109 <= 0 /\ I109 = I109 /\ 0 <= -1 - I107 + I108]
95.98/94.86	  f1(I110, I111, I112, I113, I114) -> f2(I110, I111, I112, I113, I114) 
95.98/94.86	
95.98/97.84	EOF