15.27/15.52	YES
15.27/15.52	
15.27/15.52	DP problem for innermost termination.
15.27/15.52	P =
15.27/15.52	  f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
15.27/15.52	  f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f4#(I0, I1, I2, I3, I4, I3, 0, 0, I8) 
15.27/15.52	  f2#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4#(I9, I10, I11, I12, I13, I14, 1 + I15, I16, I17) 
15.27/15.52	  f4#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f2#(rnd1, I26, I20, I21, I22, I23, I24, rnd8, I26) [I25 <= 0 /\ 0 <= I25 /\ 0 <= -1 + I23 - I24 /\ y1 = I26 /\ rnd8 = y1 /\ rnd1 = rnd1]
15.27/15.52	  f4#(I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f5#(I47, I48, I49, I50, I51, I52, I53, I54, I55) [I51 = I51]
15.27/15.52	  f3#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f4#(I65, I64, I58, I59, I60, I61, 1 + I62, I66, I64) [I67 = I64 /\ I66 = I67 /\ I65 = I65]
15.27/15.52	  f1#(I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2#(I77, I76, I70, I71, I72, I73, I74, I78, I76) [I79 = I76 /\ I78 = I79 /\ I77 = I77]
15.27/15.52	R = 
15.27/15.52	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
15.27/15.52	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f4(I0, I1, I2, I3, I4, I3, 0, 0, I8) 
15.27/15.52	  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4(I9, I10, I11, I12, I13, I14, 1 + I15, I16, I17) 
15.27/15.52	  f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f2(rnd1, I26, I20, I21, I22, I23, I24, rnd8, I26) [I25 <= 0 /\ 0 <= I25 /\ 0 <= -1 + I23 - I24 /\ y1 = I26 /\ rnd8 = y1 /\ rnd1 = rnd1]
15.27/15.52	  f4(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f7(I36, I28, I34, I30, I31, I32, I33, I34, I35) [I36 = I34 /\ I32 - I33 <= 0 /\ 0 <= I34 /\ I34 <= 0]
15.27/15.52	  f5(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I46, I38, I44, I40, I41, I42, I43, I44, I45) [I46 = I44]
15.27/15.52	  f4(I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f5(I47, I48, I49, I50, I51, I52, I53, I54, I55) [I51 = I51]
15.27/15.52	  f3(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f4(I65, I64, I58, I59, I60, I61, 1 + I62, I66, I64) [I67 = I64 /\ I66 = I67 /\ I65 = I65]
15.27/15.52	  f1(I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2(I77, I76, I70, I71, I72, I73, I74, I78, I76) [I79 = I76 /\ I78 = I79 /\ I77 = I77]
15.27/15.52	
15.27/15.52	The dependency graph for this problem is:
15.27/15.52	  0 -> 1
15.27/15.52	  1 -> 3, 4
15.27/15.52	  2 -> 3, 4
15.27/15.52	  3 -> 2
15.27/15.52	  4 -> 
15.27/15.52	  5 -> 3, 4
15.27/15.52	  6 -> 2
15.27/15.52	Where:
15.27/15.52	  0) f9#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f8#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
15.27/15.52	  1) f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f4#(I0, I1, I2, I3, I4, I3, 0, 0, I8) 
15.27/15.52	  2) f2#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4#(I9, I10, I11, I12, I13, I14, 1 + I15, I16, I17) 
15.27/15.52	  3) f4#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f2#(rnd1, I26, I20, I21, I22, I23, I24, rnd8, I26) [I25 <= 0 /\ 0 <= I25 /\ 0 <= -1 + I23 - I24 /\ y1 = I26 /\ rnd8 = y1 /\ rnd1 = rnd1]
15.27/15.52	  4) f4#(I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f5#(I47, I48, I49, I50, I51, I52, I53, I54, I55) [I51 = I51]
15.27/15.52	  5) f3#(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f4#(I65, I64, I58, I59, I60, I61, 1 + I62, I66, I64) [I67 = I64 /\ I66 = I67 /\ I65 = I65]
15.27/15.52	  6) f1#(I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2#(I77, I76, I70, I71, I72, I73, I74, I78, I76) [I79 = I76 /\ I78 = I79 /\ I77 = I77]
15.27/15.52	
15.27/15.52	We have the following SCCs.
15.27/15.52	  { 2, 3 }
15.27/15.52	
15.27/15.52	DP problem for innermost termination.
15.27/15.52	P =
15.27/15.52	  f2#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4#(I9, I10, I11, I12, I13, I14, 1 + I15, I16, I17) 
15.27/15.52	  f4#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f2#(rnd1, I26, I20, I21, I22, I23, I24, rnd8, I26) [I25 <= 0 /\ 0 <= I25 /\ 0 <= -1 + I23 - I24 /\ y1 = I26 /\ rnd8 = y1 /\ rnd1 = rnd1]
15.27/15.52	R = 
15.27/15.52	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
15.27/15.52	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f4(I0, I1, I2, I3, I4, I3, 0, 0, I8) 
15.27/15.52	  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4(I9, I10, I11, I12, I13, I14, 1 + I15, I16, I17) 
15.27/15.52	  f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f2(rnd1, I26, I20, I21, I22, I23, I24, rnd8, I26) [I25 <= 0 /\ 0 <= I25 /\ 0 <= -1 + I23 - I24 /\ y1 = I26 /\ rnd8 = y1 /\ rnd1 = rnd1]
15.27/15.52	  f4(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f7(I36, I28, I34, I30, I31, I32, I33, I34, I35) [I36 = I34 /\ I32 - I33 <= 0 /\ 0 <= I34 /\ I34 <= 0]
15.27/15.52	  f5(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I46, I38, I44, I40, I41, I42, I43, I44, I45) [I46 = I44]
15.27/15.52	  f4(I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f5(I47, I48, I49, I50, I51, I52, I53, I54, I55) [I51 = I51]
15.27/15.52	  f3(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f4(I65, I64, I58, I59, I60, I61, 1 + I62, I66, I64) [I67 = I64 /\ I66 = I67 /\ I65 = I65]
15.27/15.52	  f1(I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2(I77, I76, I70, I71, I72, I73, I74, I78, I76) [I79 = I76 /\ I78 = I79 /\ I77 = I77]
15.27/15.52	
15.27/15.52	We use the reverse value criterion with the projection function NU:
15.27/15.52	  NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = -1 + z6 - z7 + -1 * 0
15.27/15.52	  NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = -1 + z6 - (1 + z7) + -1 * 0
15.27/15.52	
15.27/15.52	This gives the following inequalities:
15.27/15.52	    ==>  -1 + I14 - (1 + I15) + -1 * 0 >= -1 + I14 - (1 + I15) + -1 * 0
15.27/15.52	  I25 <= 0 /\ 0 <= I25 /\ 0 <= -1 + I23 - I24 /\ y1 = I26 /\ rnd8 = y1 /\ rnd1 = rnd1  ==>  -1 + I23 - I24 + -1 * 0 > -1 + I23 - (1 + I24) + -1 * 0  with  -1 + I23 - I24 + -1 * 0 >= 0
15.27/15.52	
15.27/15.52	We remove all the strictly oriented dependency pairs.
15.27/15.52	
15.27/15.52	DP problem for innermost termination.
15.27/15.52	P =
15.27/15.52	  f2#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4#(I9, I10, I11, I12, I13, I14, 1 + I15, I16, I17) 
15.27/15.52	R = 
15.27/15.52	  f9(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f8(x1, x2, x3, x4, x5, x6, x7, x8, x9) 
15.27/15.52	  f8(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f4(I0, I1, I2, I3, I4, I3, 0, 0, I8) 
15.27/15.52	  f2(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4(I9, I10, I11, I12, I13, I14, 1 + I15, I16, I17) 
15.27/15.52	  f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f2(rnd1, I26, I20, I21, I22, I23, I24, rnd8, I26) [I25 <= 0 /\ 0 <= I25 /\ 0 <= -1 + I23 - I24 /\ y1 = I26 /\ rnd8 = y1 /\ rnd1 = rnd1]
15.27/15.52	  f4(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f7(I36, I28, I34, I30, I31, I32, I33, I34, I35) [I36 = I34 /\ I32 - I33 <= 0 /\ 0 <= I34 /\ I34 <= 0]
15.27/15.52	  f5(I37, I38, I39, I40, I41, I42, I43, I44, I45) -> f6(I46, I38, I44, I40, I41, I42, I43, I44, I45) [I46 = I44]
15.27/15.52	  f4(I47, I48, I49, I50, I51, I52, I53, I54, I55) -> f5(I47, I48, I49, I50, I51, I52, I53, I54, I55) [I51 = I51]
15.27/15.52	  f3(I56, I57, I58, I59, I60, I61, I62, I63, I64) -> f4(I65, I64, I58, I59, I60, I61, 1 + I62, I66, I64) [I67 = I64 /\ I66 = I67 /\ I65 = I65]
15.27/15.52	  f1(I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f2(I77, I76, I70, I71, I72, I73, I74, I78, I76) [I79 = I76 /\ I78 = I79 /\ I77 = I77]
15.27/15.52	
15.27/15.52	The dependency graph for this problem is:
15.27/15.52	  2 -> 
15.27/15.52	Where:
15.27/15.52	  2) f2#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f4#(I9, I10, I11, I12, I13, I14, 1 + I15, I16, I17) 
15.27/15.52	
15.27/15.52	We have the following SCCs.
15.27/15.52	  
15.27/18.49	EOF