48.61/48.21	YES
48.61/48.21	
48.61/48.21	DP problem for innermost termination.
48.61/48.21	P =
48.61/48.21	  f7#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f6#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 
48.61/48.21	  f6#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f2#(0, I3, I2, I3, I4, 0, I6, I7, I8, I9, I10) 
48.61/48.21	  f2#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f4#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
48.61/48.21	  f4#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f3#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [1 + I22 <= 32]
48.61/48.21	  f3#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1#(I44, I45, I46, I47, I48, I49, I50, I51, 1, I53, I54) 
48.61/48.21	  f3#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f1#(I55, I56, I57, I58, I59, I60, I61, I62, 0, I64, I65) 
48.61/48.21	  f1#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2#(1 + I66, I67, I68, I69, I70, I71 + I74, I72, I73, I74, I75, I76) 
48.61/48.21	R = 
48.61/48.21	  f7(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 
48.61/48.21	  f6(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f2(0, I3, I2, I3, I4, 0, I6, I7, I8, I9, I10) 
48.61/48.21	  f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f4(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
48.61/48.21	  f4(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [1 + I22 <= 32]
48.61/48.21	  f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f5(I33, I34, I36, I36, rnd5, I38, I38, rnd8, I41, I38, rnd11) [32 <= I33 /\ y1 = I36 /\ y2 = y2 /\ y3 = y3 /\ y4 = y4 /\ y5 = y5 /\ rnd5 = rnd5 /\ rnd8 = rnd5 /\ rnd11 = rnd8]
48.61/48.21	  f3(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, I49, I50, I51, 1, I53, I54) 
48.61/48.21	  f3(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f1(I55, I56, I57, I58, I59, I60, I61, I62, 0, I64, I65) 
48.61/48.21	  f1(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2(1 + I66, I67, I68, I69, I70, I71 + I74, I72, I73, I74, I75, I76) 
48.61/48.21	
48.61/48.21	The dependency graph for this problem is:
48.61/48.21	  0 -> 1
48.61/48.21	  1 -> 2
48.61/48.21	  2 -> 3
48.61/48.21	  3 -> 4, 5
48.61/48.21	  4 -> 6
48.61/48.21	  5 -> 6
48.61/48.21	  6 -> 2
48.61/48.21	Where:
48.61/48.21	  0) f7#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f6#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 
48.61/48.21	  1) f6#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f2#(0, I3, I2, I3, I4, 0, I6, I7, I8, I9, I10) 
48.61/48.21	  2) f2#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f4#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
48.61/48.21	  3) f4#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f3#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [1 + I22 <= 32]
48.61/48.21	  4) f3#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1#(I44, I45, I46, I47, I48, I49, I50, I51, 1, I53, I54) 
48.61/48.21	  5) f3#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f1#(I55, I56, I57, I58, I59, I60, I61, I62, 0, I64, I65) 
48.61/48.21	  6) f1#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2#(1 + I66, I67, I68, I69, I70, I71 + I74, I72, I73, I74, I75, I76) 
48.61/48.21	
48.61/48.21	We have the following SCCs.
48.61/48.21	  { 2, 3, 4, 5, 6 }
48.61/48.21	
48.61/48.21	DP problem for innermost termination.
48.61/48.21	P =
48.61/48.21	  f2#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f4#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
48.61/48.21	  f4#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f3#(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [1 + I22 <= 32]
48.61/48.21	  f3#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1#(I44, I45, I46, I47, I48, I49, I50, I51, 1, I53, I54) 
48.61/48.21	  f3#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f1#(I55, I56, I57, I58, I59, I60, I61, I62, 0, I64, I65) 
48.61/48.21	  f1#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2#(1 + I66, I67, I68, I69, I70, I71 + I74, I72, I73, I74, I75, I76) 
48.61/48.21	R = 
48.61/48.21	  f7(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 
48.61/48.21	  f6(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f2(0, I3, I2, I3, I4, 0, I6, I7, I8, I9, I10) 
48.61/48.21	  f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f4(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
48.61/48.21	  f4(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [1 + I22 <= 32]
48.61/48.21	  f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f5(I33, I34, I36, I36, rnd5, I38, I38, rnd8, I41, I38, rnd11) [32 <= I33 /\ y1 = I36 /\ y2 = y2 /\ y3 = y3 /\ y4 = y4 /\ y5 = y5 /\ rnd5 = rnd5 /\ rnd8 = rnd5 /\ rnd11 = rnd8]
48.61/48.21	  f3(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, I49, I50, I51, 1, I53, I54) 
48.61/48.21	  f3(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f1(I55, I56, I57, I58, I59, I60, I61, I62, 0, I64, I65) 
48.61/48.21	  f1(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2(1 + I66, I67, I68, I69, I70, I71 + I74, I72, I73, I74, I75, I76) 
48.61/48.21	
48.61/48.21	We use the extended value criterion with the projection function NU:
48.61/48.21	  NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x0 + 30
48.61/48.21	  NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x0 + 30
48.61/48.21	  NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x0 + 31
48.61/48.21	  NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x0 + 31
48.61/48.21	
48.61/48.21	This gives the following inequalities:
48.61/48.21	    ==>  -I11 + 31 >= -I11 + 31
48.61/48.21	  1 + I22 <= 32  ==>  -I22 + 31 > -I22 + 30  with  -I22 + 31 >= 0
48.61/48.21	    ==>  -I44 + 30 >= -I44 + 30
48.61/48.21	    ==>  -I55 + 30 >= -I55 + 30
48.61/48.21	    ==>  -I66 + 30 >= -(1 + I66) + 31
48.61/48.21	
48.61/48.21	We remove all the strictly oriented dependency pairs.
48.61/48.21	
48.61/48.21	DP problem for innermost termination.
48.61/48.21	P =
48.61/48.21	  f2#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f4#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
48.61/48.21	  f3#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1#(I44, I45, I46, I47, I48, I49, I50, I51, 1, I53, I54) 
48.61/48.21	  f3#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f1#(I55, I56, I57, I58, I59, I60, I61, I62, 0, I64, I65) 
48.61/48.21	  f1#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2#(1 + I66, I67, I68, I69, I70, I71 + I74, I72, I73, I74, I75, I76) 
48.61/48.21	R = 
48.61/48.21	  f7(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f6(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 
48.61/48.21	  f6(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f2(0, I3, I2, I3, I4, 0, I6, I7, I8, I9, I10) 
48.61/48.21	  f2(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f4(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
48.61/48.21	  f4(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f3(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [1 + I22 <= 32]
48.61/48.21	  f4(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f5(I33, I34, I36, I36, rnd5, I38, I38, rnd8, I41, I38, rnd11) [32 <= I33 /\ y1 = I36 /\ y2 = y2 /\ y3 = y3 /\ y4 = y4 /\ y5 = y5 /\ rnd5 = rnd5 /\ rnd8 = rnd5 /\ rnd11 = rnd8]
48.61/48.21	  f3(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1(I44, I45, I46, I47, I48, I49, I50, I51, 1, I53, I54) 
48.61/48.21	  f3(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f1(I55, I56, I57, I58, I59, I60, I61, I62, 0, I64, I65) 
48.61/48.21	  f1(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2(1 + I66, I67, I68, I69, I70, I71 + I74, I72, I73, I74, I75, I76) 
48.61/48.21	
48.61/48.21	The dependency graph for this problem is:
48.61/48.21	  2 -> 
48.61/48.21	  4 -> 6
48.61/48.21	  5 -> 6
48.61/48.21	  6 -> 2
48.61/48.21	Where:
48.61/48.21	  2) f2#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f4#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) 
48.61/48.21	  4) f3#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f1#(I44, I45, I46, I47, I48, I49, I50, I51, 1, I53, I54) 
48.61/48.21	  5) f3#(I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65) -> f1#(I55, I56, I57, I58, I59, I60, I61, I62, 0, I64, I65) 
48.61/48.21	  6) f1#(I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2#(1 + I66, I67, I68, I69, I70, I71 + I74, I72, I73, I74, I75, I76) 
48.61/48.21	
48.61/48.21	We have the following SCCs.
48.61/48.21	  
48.61/51.18	EOF