14.34/14.21	YES
14.34/14.21	
14.34/14.21	DP problem for innermost termination.
14.34/14.21	P =
14.34/14.21	  f19#(x1, x2, x3) -> f18#(x1, x2, x3) 
14.34/14.21	  f18#(I0, I1, I2) -> f7#(I0, 0, I2) [y1 = 0]
14.34/14.21	  f3#(I3, I4, I5) -> f17#(I3, I4, I5) 
14.34/14.21	  f3#(I6, I7, I8) -> f13#(I6, I7, I8) 
14.34/14.21	  f3#(I9, I10, I11) -> f17#(I9, I10, I11) 
14.34/14.21	  f17#(I12, I13, I14) -> f16#(I12, I13, I14) 
14.34/14.21	  f16#(I15, I16, I17) -> f15#(I15, I16, I17) 
14.34/14.21	  f16#(I18, I19, I20) -> f14#(I18, I19, I20) 
14.34/14.21	  f16#(I21, I22, I23) -> f14#(I21, I22, I23) 
14.34/14.21	  f15#(I24, I25, I26) -> f13#(I24, I25, I26) 
14.34/14.21	  f14#(I27, I28, I29) -> f15#(I27, I28, I29) 
14.34/14.21	  f2#(I30, I31, I32) -> f11#(I30, I31, I32) 
14.34/14.21	  f13#(I33, I34, I35) -> f7#(I33, 1 + I34, I35) 
14.34/14.21	  f11#(I36, I37, I38) -> f10#(I36, I37, I38) [1 + I37 <= 1000]
14.34/14.21	  f10#(I42, I43, I44) -> f9#(I42, I43, I44) 
14.34/14.21	  f10#(I45, I46, I47) -> f4#(I45, I46, I47) 
14.34/14.21	  f10#(I48, I49, I50) -> f9#(I48, I49, I50) 
14.34/14.21	  f9#(I51, I52, I53) -> f8#(I51, I52, rnd3) [rnd3 = rnd3]
14.34/14.21	  f8#(I54, I55, I56) -> f6#(I54, I55, I56) 
14.34/14.21	  f8#(I57, I58, I59) -> f5#(I57, I58, I59) 
14.34/14.21	  f8#(I60, I61, I62) -> f5#(I60, I61, I62) 
14.34/14.21	  f7#(I63, I64, I65) -> f1#(I63, I64, I65) 
14.34/14.21	  f6#(I66, I67, I68) -> f4#(I66, I67, I68) 
14.34/14.21	  f5#(I69, I70, I71) -> f6#(I69, I70, I71) 
14.34/14.21	  f4#(I72, I73, I74) -> f2#(I72, 1 + I73, I74) 
14.34/14.21	  f1#(I75, I76, I77) -> f3#(I76, I76, I77) [1 + I76 <= 1000]
14.34/14.21	  f1#(I78, I79, I80) -> f2#(I78, 0, I80) [1000 <= I79]
14.34/14.21	R = 
14.34/14.21	  f19(x1, x2, x3) -> f18(x1, x2, x3) 
14.34/14.21	  f18(I0, I1, I2) -> f7(I0, 0, I2) [y1 = 0]
14.34/14.21	  f3(I3, I4, I5) -> f17(I3, I4, I5) 
14.34/14.21	  f3(I6, I7, I8) -> f13(I6, I7, I8) 
14.34/14.21	  f3(I9, I10, I11) -> f17(I9, I10, I11) 
14.34/14.21	  f17(I12, I13, I14) -> f16(I12, I13, I14) 
14.34/14.21	  f16(I15, I16, I17) -> f15(I15, I16, I17) 
14.34/14.21	  f16(I18, I19, I20) -> f14(I18, I19, I20) 
14.34/14.21	  f16(I21, I22, I23) -> f14(I21, I22, I23) 
14.34/14.21	  f15(I24, I25, I26) -> f13(I24, I25, I26) 
14.34/14.21	  f14(I27, I28, I29) -> f15(I27, I28, I29) 
14.34/14.21	  f2(I30, I31, I32) -> f11(I30, I31, I32) 
14.34/14.21	  f13(I33, I34, I35) -> f7(I33, 1 + I34, I35) 
14.34/14.21	  f11(I36, I37, I38) -> f10(I36, I37, I38) [1 + I37 <= 1000]
14.34/14.21	  f11(I39, I40, I41) -> f12(I39, I40, I41) [1000 <= I40]
14.34/14.21	  f10(I42, I43, I44) -> f9(I42, I43, I44) 
14.34/14.21	  f10(I45, I46, I47) -> f4(I45, I46, I47) 
14.34/14.21	  f10(I48, I49, I50) -> f9(I48, I49, I50) 
14.34/14.21	  f9(I51, I52, I53) -> f8(I51, I52, rnd3) [rnd3 = rnd3]
14.34/14.21	  f8(I54, I55, I56) -> f6(I54, I55, I56) 
14.34/14.21	  f8(I57, I58, I59) -> f5(I57, I58, I59) 
14.34/14.21	  f8(I60, I61, I62) -> f5(I60, I61, I62) 
14.34/14.21	  f7(I63, I64, I65) -> f1(I63, I64, I65) 
14.34/14.21	  f6(I66, I67, I68) -> f4(I66, I67, I68) 
14.34/14.21	  f5(I69, I70, I71) -> f6(I69, I70, I71) 
14.34/14.21	  f4(I72, I73, I74) -> f2(I72, 1 + I73, I74) 
14.34/14.21	  f1(I75, I76, I77) -> f3(I76, I76, I77) [1 + I76 <= 1000]
14.34/14.21	  f1(I78, I79, I80) -> f2(I78, 0, I80) [1000 <= I79]
14.34/14.21	
14.34/14.21	The dependency graph for this problem is:
14.34/14.21	  0 -> 1
14.34/14.21	  1 -> 21
14.34/14.21	  2 -> 5
14.34/14.21	  3 -> 12
14.34/14.21	  4 -> 5
14.34/14.21	  5 -> 6, 7, 8
14.34/14.21	  6 -> 9
14.34/14.21	  7 -> 10
14.34/14.21	  8 -> 10
14.34/14.21	  9 -> 12
14.34/14.21	  10 -> 9
14.34/14.21	  11 -> 13
14.34/14.21	  12 -> 21
14.34/14.21	  13 -> 14, 15, 16
14.34/14.21	  14 -> 17
14.34/14.21	  15 -> 24
14.34/14.21	  16 -> 17
14.34/14.21	  17 -> 18, 19, 20
14.34/14.21	  18 -> 22
14.34/14.21	  19 -> 23
14.34/14.21	  20 -> 23
14.34/14.21	  21 -> 25, 26
14.34/14.21	  22 -> 24
14.34/14.21	  23 -> 22
14.34/14.21	  24 -> 11
14.34/14.21	  25 -> 2, 3, 4
14.34/14.21	  26 -> 11
14.34/14.21	Where:
14.34/14.21	  0) f19#(x1, x2, x3) -> f18#(x1, x2, x3) 
14.34/14.21	  1) f18#(I0, I1, I2) -> f7#(I0, 0, I2) [y1 = 0]
14.34/14.21	  2) f3#(I3, I4, I5) -> f17#(I3, I4, I5) 
14.34/14.21	  3) f3#(I6, I7, I8) -> f13#(I6, I7, I8) 
14.34/14.21	  4) f3#(I9, I10, I11) -> f17#(I9, I10, I11) 
14.34/14.21	  5) f17#(I12, I13, I14) -> f16#(I12, I13, I14) 
14.34/14.21	  6) f16#(I15, I16, I17) -> f15#(I15, I16, I17) 
14.34/14.21	  7) f16#(I18, I19, I20) -> f14#(I18, I19, I20) 
14.34/14.21	  8) f16#(I21, I22, I23) -> f14#(I21, I22, I23) 
14.34/14.21	  9) f15#(I24, I25, I26) -> f13#(I24, I25, I26) 
14.34/14.21	  10) f14#(I27, I28, I29) -> f15#(I27, I28, I29) 
14.34/14.21	  11) f2#(I30, I31, I32) -> f11#(I30, I31, I32) 
14.34/14.21	  12) f13#(I33, I34, I35) -> f7#(I33, 1 + I34, I35) 
14.34/14.21	  13) f11#(I36, I37, I38) -> f10#(I36, I37, I38) [1 + I37 <= 1000]
14.34/14.21	  14) f10#(I42, I43, I44) -> f9#(I42, I43, I44) 
14.34/14.21	  15) f10#(I45, I46, I47) -> f4#(I45, I46, I47) 
14.34/14.21	  16) f10#(I48, I49, I50) -> f9#(I48, I49, I50) 
14.34/14.21	  17) f9#(I51, I52, I53) -> f8#(I51, I52, rnd3) [rnd3 = rnd3]
14.34/14.21	  18) f8#(I54, I55, I56) -> f6#(I54, I55, I56) 
14.34/14.21	  19) f8#(I57, I58, I59) -> f5#(I57, I58, I59) 
14.34/14.21	  20) f8#(I60, I61, I62) -> f5#(I60, I61, I62) 
14.34/14.21	  21) f7#(I63, I64, I65) -> f1#(I63, I64, I65) 
14.34/14.21	  22) f6#(I66, I67, I68) -> f4#(I66, I67, I68) 
14.34/14.21	  23) f5#(I69, I70, I71) -> f6#(I69, I70, I71) 
14.34/14.21	  24) f4#(I72, I73, I74) -> f2#(I72, 1 + I73, I74) 
14.34/14.21	  25) f1#(I75, I76, I77) -> f3#(I76, I76, I77) [1 + I76 <= 1000]
14.34/14.21	  26) f1#(I78, I79, I80) -> f2#(I78, 0, I80) [1000 <= I79]
14.34/14.21	
14.34/14.21	We have the following SCCs.
14.34/14.21	  { 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 21, 25 }
14.34/14.21	  { 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24 }
14.34/14.21	
14.34/14.21	DP problem for innermost termination.
14.34/14.21	P =
14.34/14.21	  f2#(I30, I31, I32) -> f11#(I30, I31, I32) 
14.34/14.21	  f11#(I36, I37, I38) -> f10#(I36, I37, I38) [1 + I37 <= 1000]
14.34/14.21	  f10#(I42, I43, I44) -> f9#(I42, I43, I44) 
14.34/14.21	  f10#(I45, I46, I47) -> f4#(I45, I46, I47) 
14.34/14.21	  f10#(I48, I49, I50) -> f9#(I48, I49, I50) 
14.34/14.21	  f9#(I51, I52, I53) -> f8#(I51, I52, rnd3) [rnd3 = rnd3]
14.34/14.21	  f8#(I54, I55, I56) -> f6#(I54, I55, I56) 
14.34/14.21	  f8#(I57, I58, I59) -> f5#(I57, I58, I59) 
14.34/14.21	  f8#(I60, I61, I62) -> f5#(I60, I61, I62) 
14.34/14.21	  f6#(I66, I67, I68) -> f4#(I66, I67, I68) 
14.34/14.21	  f5#(I69, I70, I71) -> f6#(I69, I70, I71) 
14.34/14.21	  f4#(I72, I73, I74) -> f2#(I72, 1 + I73, I74) 
14.34/14.21	R = 
14.34/14.21	  f19(x1, x2, x3) -> f18(x1, x2, x3) 
14.34/14.21	  f18(I0, I1, I2) -> f7(I0, 0, I2) [y1 = 0]
14.42/14.21	  f3(I3, I4, I5) -> f17(I3, I4, I5) 
14.42/14.21	  f3(I6, I7, I8) -> f13(I6, I7, I8) 
14.42/14.21	  f3(I9, I10, I11) -> f17(I9, I10, I11) 
14.42/14.21	  f17(I12, I13, I14) -> f16(I12, I13, I14) 
14.42/14.21	  f16(I15, I16, I17) -> f15(I15, I16, I17) 
14.42/14.21	  f16(I18, I19, I20) -> f14(I18, I19, I20) 
14.42/14.21	  f16(I21, I22, I23) -> f14(I21, I22, I23) 
14.42/14.21	  f15(I24, I25, I26) -> f13(I24, I25, I26) 
14.42/14.21	  f14(I27, I28, I29) -> f15(I27, I28, I29) 
14.42/14.21	  f2(I30, I31, I32) -> f11(I30, I31, I32) 
14.42/14.21	  f13(I33, I34, I35) -> f7(I33, 1 + I34, I35) 
14.42/14.21	  f11(I36, I37, I38) -> f10(I36, I37, I38) [1 + I37 <= 1000]
14.42/14.21	  f11(I39, I40, I41) -> f12(I39, I40, I41) [1000 <= I40]
14.42/14.21	  f10(I42, I43, I44) -> f9(I42, I43, I44) 
14.42/14.21	  f10(I45, I46, I47) -> f4(I45, I46, I47) 
14.42/14.21	  f10(I48, I49, I50) -> f9(I48, I49, I50) 
14.42/14.21	  f9(I51, I52, I53) -> f8(I51, I52, rnd3) [rnd3 = rnd3]
14.42/14.21	  f8(I54, I55, I56) -> f6(I54, I55, I56) 
14.42/14.21	  f8(I57, I58, I59) -> f5(I57, I58, I59) 
14.42/14.21	  f8(I60, I61, I62) -> f5(I60, I61, I62) 
14.42/14.21	  f7(I63, I64, I65) -> f1(I63, I64, I65) 
14.42/14.21	  f6(I66, I67, I68) -> f4(I66, I67, I68) 
14.42/14.21	  f5(I69, I70, I71) -> f6(I69, I70, I71) 
14.42/14.21	  f4(I72, I73, I74) -> f2(I72, 1 + I73, I74) 
14.42/14.21	  f1(I75, I76, I77) -> f3(I76, I76, I77) [1 + I76 <= 1000]
14.42/14.21	  f1(I78, I79, I80) -> f2(I78, 0, I80) [1000 <= I79]
14.42/14.21	
14.42/14.21	We use the extended value criterion with the projection function NU:
14.42/14.21	  NU[f5#(x0,x1,x2)] = -x1 + 998
14.42/14.21	  NU[f6#(x0,x1,x2)] = -x1 + 998
14.42/14.21	  NU[f8#(x0,x1,x2)] = -x1 + 998
14.42/14.21	  NU[f4#(x0,x1,x2)] = -x1 + 998
14.42/14.21	  NU[f9#(x0,x1,x2)] = -x1 + 998
14.42/14.21	  NU[f10#(x0,x1,x2)] = -x1 + 998
14.42/14.21	  NU[f11#(x0,x1,x2)] = -x1 + 999
14.42/14.21	  NU[f2#(x0,x1,x2)] = -x1 + 999
14.42/14.21	
14.42/14.21	This gives the following inequalities:
14.42/14.21	    ==>  -I31 + 999 >= -I31 + 999
14.42/14.21	  1 + I37 <= 1000  ==>  -I37 + 999 > -I37 + 998  with  -I37 + 999 >= 0
14.42/14.21	    ==>  -I43 + 998 >= -I43 + 998
14.42/14.21	    ==>  -I46 + 998 >= -I46 + 998
14.42/14.21	    ==>  -I49 + 998 >= -I49 + 998
14.42/14.21	  rnd3 = rnd3  ==>  -I52 + 998 >= -I52 + 998
14.42/14.21	    ==>  -I55 + 998 >= -I55 + 998
14.42/14.21	    ==>  -I58 + 998 >= -I58 + 998
14.42/14.21	    ==>  -I61 + 998 >= -I61 + 998
14.42/14.21	    ==>  -I67 + 998 >= -I67 + 998
14.42/14.21	    ==>  -I70 + 998 >= -I70 + 998
14.42/14.21	    ==>  -I73 + 998 >= -(1 + I73) + 999
14.42/14.21	
14.42/14.21	We remove all the strictly oriented dependency pairs.
14.42/14.21	
14.42/14.21	DP problem for innermost termination.
14.42/14.21	P =
14.42/14.21	  f2#(I30, I31, I32) -> f11#(I30, I31, I32) 
14.42/14.21	  f10#(I42, I43, I44) -> f9#(I42, I43, I44) 
14.42/14.21	  f10#(I45, I46, I47) -> f4#(I45, I46, I47) 
14.42/14.21	  f10#(I48, I49, I50) -> f9#(I48, I49, I50) 
14.42/14.21	  f9#(I51, I52, I53) -> f8#(I51, I52, rnd3) [rnd3 = rnd3]
14.42/14.21	  f8#(I54, I55, I56) -> f6#(I54, I55, I56) 
14.42/14.21	  f8#(I57, I58, I59) -> f5#(I57, I58, I59) 
14.42/14.21	  f8#(I60, I61, I62) -> f5#(I60, I61, I62) 
14.42/14.21	  f6#(I66, I67, I68) -> f4#(I66, I67, I68) 
14.42/14.21	  f5#(I69, I70, I71) -> f6#(I69, I70, I71) 
14.42/14.21	  f4#(I72, I73, I74) -> f2#(I72, 1 + I73, I74) 
14.42/14.21	R = 
14.42/14.21	  f19(x1, x2, x3) -> f18(x1, x2, x3) 
14.42/14.21	  f18(I0, I1, I2) -> f7(I0, 0, I2) [y1 = 0]
14.42/14.21	  f3(I3, I4, I5) -> f17(I3, I4, I5) 
14.42/14.21	  f3(I6, I7, I8) -> f13(I6, I7, I8) 
14.42/14.21	  f3(I9, I10, I11) -> f17(I9, I10, I11) 
14.42/14.21	  f17(I12, I13, I14) -> f16(I12, I13, I14) 
14.42/14.21	  f16(I15, I16, I17) -> f15(I15, I16, I17) 
14.42/14.21	  f16(I18, I19, I20) -> f14(I18, I19, I20) 
14.42/14.21	  f16(I21, I22, I23) -> f14(I21, I22, I23) 
14.42/14.21	  f15(I24, I25, I26) -> f13(I24, I25, I26) 
14.42/14.21	  f14(I27, I28, I29) -> f15(I27, I28, I29) 
14.42/14.21	  f2(I30, I31, I32) -> f11(I30, I31, I32) 
14.42/14.21	  f13(I33, I34, I35) -> f7(I33, 1 + I34, I35) 
14.42/14.21	  f11(I36, I37, I38) -> f10(I36, I37, I38) [1 + I37 <= 1000]
14.42/14.21	  f11(I39, I40, I41) -> f12(I39, I40, I41) [1000 <= I40]
14.42/14.21	  f10(I42, I43, I44) -> f9(I42, I43, I44) 
14.42/14.21	  f10(I45, I46, I47) -> f4(I45, I46, I47) 
14.42/14.21	  f10(I48, I49, I50) -> f9(I48, I49, I50) 
14.42/14.21	  f9(I51, I52, I53) -> f8(I51, I52, rnd3) [rnd3 = rnd3]
14.42/14.21	  f8(I54, I55, I56) -> f6(I54, I55, I56) 
14.42/14.21	  f8(I57, I58, I59) -> f5(I57, I58, I59) 
14.42/14.21	  f8(I60, I61, I62) -> f5(I60, I61, I62) 
14.42/14.21	  f7(I63, I64, I65) -> f1(I63, I64, I65) 
14.42/14.21	  f6(I66, I67, I68) -> f4(I66, I67, I68) 
14.42/14.21	  f5(I69, I70, I71) -> f6(I69, I70, I71) 
14.42/14.21	  f4(I72, I73, I74) -> f2(I72, 1 + I73, I74) 
14.42/14.21	  f1(I75, I76, I77) -> f3(I76, I76, I77) [1 + I76 <= 1000]
14.42/14.21	  f1(I78, I79, I80) -> f2(I78, 0, I80) [1000 <= I79]
14.42/14.21	
14.42/14.21	The dependency graph for this problem is:
14.42/14.21	  11 -> 
14.42/14.21	  14 -> 17
14.42/14.21	  15 -> 24
14.42/14.21	  16 -> 17
14.42/14.21	  17 -> 18, 19, 20
14.42/14.21	  18 -> 22
14.42/14.21	  19 -> 23
14.42/14.21	  20 -> 23
14.42/14.21	  22 -> 24
14.42/14.21	  23 -> 22
14.42/14.21	  24 -> 11
14.42/14.21	Where:
14.42/14.21	  11) f2#(I30, I31, I32) -> f11#(I30, I31, I32) 
14.42/14.21	  14) f10#(I42, I43, I44) -> f9#(I42, I43, I44) 
14.42/14.21	  15) f10#(I45, I46, I47) -> f4#(I45, I46, I47) 
14.42/14.21	  16) f10#(I48, I49, I50) -> f9#(I48, I49, I50) 
14.42/14.21	  17) f9#(I51, I52, I53) -> f8#(I51, I52, rnd3) [rnd3 = rnd3]
14.42/14.21	  18) f8#(I54, I55, I56) -> f6#(I54, I55, I56) 
14.42/14.21	  19) f8#(I57, I58, I59) -> f5#(I57, I58, I59) 
14.42/14.21	  20) f8#(I60, I61, I62) -> f5#(I60, I61, I62) 
14.42/14.21	  22) f6#(I66, I67, I68) -> f4#(I66, I67, I68) 
14.42/14.21	  23) f5#(I69, I70, I71) -> f6#(I69, I70, I71) 
14.42/14.21	  24) f4#(I72, I73, I74) -> f2#(I72, 1 + I73, I74) 
14.42/14.21	
14.42/14.21	We have the following SCCs.
14.42/14.21	  
14.42/14.21	
14.42/14.21	DP problem for innermost termination.
14.42/14.21	P =
14.42/14.21	  f3#(I3, I4, I5) -> f17#(I3, I4, I5) 
14.42/14.21	  f3#(I6, I7, I8) -> f13#(I6, I7, I8) 
14.42/14.21	  f3#(I9, I10, I11) -> f17#(I9, I10, I11) 
14.42/14.21	  f17#(I12, I13, I14) -> f16#(I12, I13, I14) 
14.42/14.21	  f16#(I15, I16, I17) -> f15#(I15, I16, I17) 
14.42/14.21	  f16#(I18, I19, I20) -> f14#(I18, I19, I20) 
14.42/14.21	  f16#(I21, I22, I23) -> f14#(I21, I22, I23) 
14.42/14.21	  f15#(I24, I25, I26) -> f13#(I24, I25, I26) 
14.42/14.21	  f14#(I27, I28, I29) -> f15#(I27, I28, I29) 
14.42/14.21	  f13#(I33, I34, I35) -> f7#(I33, 1 + I34, I35) 
14.42/14.21	  f7#(I63, I64, I65) -> f1#(I63, I64, I65) 
14.42/14.21	  f1#(I75, I76, I77) -> f3#(I76, I76, I77) [1 + I76 <= 1000]
14.42/14.21	R = 
14.42/14.21	  f19(x1, x2, x3) -> f18(x1, x2, x3) 
14.42/14.21	  f18(I0, I1, I2) -> f7(I0, 0, I2) [y1 = 0]
14.42/14.21	  f3(I3, I4, I5) -> f17(I3, I4, I5) 
14.42/14.21	  f3(I6, I7, I8) -> f13(I6, I7, I8) 
14.42/14.21	  f3(I9, I10, I11) -> f17(I9, I10, I11) 
14.42/14.21	  f17(I12, I13, I14) -> f16(I12, I13, I14) 
14.42/14.21	  f16(I15, I16, I17) -> f15(I15, I16, I17) 
14.42/14.21	  f16(I18, I19, I20) -> f14(I18, I19, I20) 
14.42/14.21	  f16(I21, I22, I23) -> f14(I21, I22, I23) 
14.42/14.21	  f15(I24, I25, I26) -> f13(I24, I25, I26) 
14.42/14.21	  f14(I27, I28, I29) -> f15(I27, I28, I29) 
14.42/14.21	  f2(I30, I31, I32) -> f11(I30, I31, I32) 
14.42/14.21	  f13(I33, I34, I35) -> f7(I33, 1 + I34, I35) 
14.42/14.21	  f11(I36, I37, I38) -> f10(I36, I37, I38) [1 + I37 <= 1000]
14.42/14.21	  f11(I39, I40, I41) -> f12(I39, I40, I41) [1000 <= I40]
14.42/14.21	  f10(I42, I43, I44) -> f9(I42, I43, I44) 
14.42/14.21	  f10(I45, I46, I47) -> f4(I45, I46, I47) 
14.42/14.21	  f10(I48, I49, I50) -> f9(I48, I49, I50) 
14.42/14.21	  f9(I51, I52, I53) -> f8(I51, I52, rnd3) [rnd3 = rnd3]
14.42/14.21	  f8(I54, I55, I56) -> f6(I54, I55, I56) 
14.42/14.21	  f8(I57, I58, I59) -> f5(I57, I58, I59) 
14.42/14.21	  f8(I60, I61, I62) -> f5(I60, I61, I62) 
14.42/14.21	  f7(I63, I64, I65) -> f1(I63, I64, I65) 
14.42/14.21	  f6(I66, I67, I68) -> f4(I66, I67, I68) 
14.42/14.21	  f5(I69, I70, I71) -> f6(I69, I70, I71) 
14.42/14.21	  f4(I72, I73, I74) -> f2(I72, 1 + I73, I74) 
14.42/14.21	  f1(I75, I76, I77) -> f3(I76, I76, I77) [1 + I76 <= 1000]
14.42/14.21	  f1(I78, I79, I80) -> f2(I78, 0, I80) [1000 <= I79]
14.42/14.21	
14.42/14.21	We use the extended value criterion with the projection function NU:
14.42/14.21	  NU[f1#(x0,x1,x2)] = -x1 + 999
14.42/14.21	  NU[f7#(x0,x1,x2)] = -x1 + 999
14.42/14.21	  NU[f14#(x0,x1,x2)] = -x1 + 998
14.42/14.21	  NU[f15#(x0,x1,x2)] = -x1 + 998
14.42/14.21	  NU[f16#(x0,x1,x2)] = -x1 + 998
14.42/14.21	  NU[f13#(x0,x1,x2)] = -x1 + 998
14.42/14.21	  NU[f17#(x0,x1,x2)] = -x1 + 998
14.42/14.21	  NU[f3#(x0,x1,x2)] = -x1 + 998
14.42/14.21	
14.42/14.21	This gives the following inequalities:
14.42/14.21	    ==>  -I4 + 998 >= -I4 + 998
14.42/14.21	    ==>  -I7 + 998 >= -I7 + 998
14.42/14.21	    ==>  -I10 + 998 >= -I10 + 998
14.42/14.21	    ==>  -I13 + 998 >= -I13 + 998
14.42/14.21	    ==>  -I16 + 998 >= -I16 + 998
14.42/14.21	    ==>  -I19 + 998 >= -I19 + 998
14.42/14.21	    ==>  -I22 + 998 >= -I22 + 998
14.42/14.21	    ==>  -I25 + 998 >= -I25 + 998
14.42/14.21	    ==>  -I28 + 998 >= -I28 + 998
14.42/14.21	    ==>  -I34 + 998 >= -(1 + I34) + 999
14.42/14.21	    ==>  -I64 + 999 >= -I64 + 999
14.42/14.21	  1 + I76 <= 1000  ==>  -I76 + 999 > -I76 + 998  with  -I76 + 999 >= 0
14.42/14.21	
14.42/14.21	We remove all the strictly oriented dependency pairs.
14.42/14.21	
14.42/14.21	DP problem for innermost termination.
14.42/14.21	P =
14.42/14.21	  f3#(I3, I4, I5) -> f17#(I3, I4, I5) 
14.42/14.21	  f3#(I6, I7, I8) -> f13#(I6, I7, I8) 
14.42/14.21	  f3#(I9, I10, I11) -> f17#(I9, I10, I11) 
14.42/14.21	  f17#(I12, I13, I14) -> f16#(I12, I13, I14) 
14.42/14.21	  f16#(I15, I16, I17) -> f15#(I15, I16, I17) 
14.42/14.21	  f16#(I18, I19, I20) -> f14#(I18, I19, I20) 
14.42/14.21	  f16#(I21, I22, I23) -> f14#(I21, I22, I23) 
14.42/14.21	  f15#(I24, I25, I26) -> f13#(I24, I25, I26) 
14.42/14.21	  f14#(I27, I28, I29) -> f15#(I27, I28, I29) 
14.42/14.21	  f13#(I33, I34, I35) -> f7#(I33, 1 + I34, I35) 
14.42/14.21	  f7#(I63, I64, I65) -> f1#(I63, I64, I65) 
14.42/14.21	R = 
14.42/14.21	  f19(x1, x2, x3) -> f18(x1, x2, x3) 
14.42/14.21	  f18(I0, I1, I2) -> f7(I0, 0, I2) [y1 = 0]
14.42/14.21	  f3(I3, I4, I5) -> f17(I3, I4, I5) 
14.42/14.21	  f3(I6, I7, I8) -> f13(I6, I7, I8) 
14.42/14.21	  f3(I9, I10, I11) -> f17(I9, I10, I11) 
14.42/14.21	  f17(I12, I13, I14) -> f16(I12, I13, I14) 
14.42/14.21	  f16(I15, I16, I17) -> f15(I15, I16, I17) 
14.42/14.22	  f16(I18, I19, I20) -> f14(I18, I19, I20) 
14.42/14.22	  f16(I21, I22, I23) -> f14(I21, I22, I23) 
14.42/14.22	  f15(I24, I25, I26) -> f13(I24, I25, I26) 
14.42/14.22	  f14(I27, I28, I29) -> f15(I27, I28, I29) 
14.42/14.22	  f2(I30, I31, I32) -> f11(I30, I31, I32) 
14.42/14.22	  f13(I33, I34, I35) -> f7(I33, 1 + I34, I35) 
14.42/14.22	  f11(I36, I37, I38) -> f10(I36, I37, I38) [1 + I37 <= 1000]
14.42/14.22	  f11(I39, I40, I41) -> f12(I39, I40, I41) [1000 <= I40]
14.42/14.22	  f10(I42, I43, I44) -> f9(I42, I43, I44) 
14.42/14.22	  f10(I45, I46, I47) -> f4(I45, I46, I47) 
14.42/14.22	  f10(I48, I49, I50) -> f9(I48, I49, I50) 
14.42/14.22	  f9(I51, I52, I53) -> f8(I51, I52, rnd3) [rnd3 = rnd3]
14.42/14.22	  f8(I54, I55, I56) -> f6(I54, I55, I56) 
14.42/14.22	  f8(I57, I58, I59) -> f5(I57, I58, I59) 
14.42/14.22	  f8(I60, I61, I62) -> f5(I60, I61, I62) 
14.42/14.22	  f7(I63, I64, I65) -> f1(I63, I64, I65) 
14.42/14.22	  f6(I66, I67, I68) -> f4(I66, I67, I68) 
14.42/14.22	  f5(I69, I70, I71) -> f6(I69, I70, I71) 
14.42/14.22	  f4(I72, I73, I74) -> f2(I72, 1 + I73, I74) 
14.42/14.22	  f1(I75, I76, I77) -> f3(I76, I76, I77) [1 + I76 <= 1000]
14.42/14.22	  f1(I78, I79, I80) -> f2(I78, 0, I80) [1000 <= I79]
14.42/14.22	
14.42/14.22	The dependency graph for this problem is:
14.42/14.22	  2 -> 5
14.42/14.22	  3 -> 12
14.42/14.22	  4 -> 5
14.42/14.22	  5 -> 6, 7, 8
14.42/14.22	  6 -> 9
14.42/14.22	  7 -> 10
14.42/14.22	  8 -> 10
14.42/14.22	  9 -> 12
14.42/14.22	  10 -> 9
14.42/14.22	  12 -> 21
14.42/14.22	  21 -> 
14.42/14.22	Where:
14.42/14.22	  2) f3#(I3, I4, I5) -> f17#(I3, I4, I5) 
14.42/14.22	  3) f3#(I6, I7, I8) -> f13#(I6, I7, I8) 
14.42/14.22	  4) f3#(I9, I10, I11) -> f17#(I9, I10, I11) 
14.42/14.22	  5) f17#(I12, I13, I14) -> f16#(I12, I13, I14) 
14.42/14.22	  6) f16#(I15, I16, I17) -> f15#(I15, I16, I17) 
14.42/14.22	  7) f16#(I18, I19, I20) -> f14#(I18, I19, I20) 
14.42/14.22	  8) f16#(I21, I22, I23) -> f14#(I21, I22, I23) 
14.42/14.22	  9) f15#(I24, I25, I26) -> f13#(I24, I25, I26) 
14.42/14.22	  10) f14#(I27, I28, I29) -> f15#(I27, I28, I29) 
14.42/14.22	  12) f13#(I33, I34, I35) -> f7#(I33, 1 + I34, I35) 
14.42/14.22	  21) f7#(I63, I64, I65) -> f1#(I63, I64, I65) 
14.42/14.22	
14.42/14.22	We have the following SCCs.
14.42/14.22	  
14.42/17.19	EOF