14.56/14.38	YES
14.56/14.38	
14.56/14.38	DP problem for innermost termination.
14.56/14.38	P =
14.56/14.38	  f19#(x1, x2, x3) -> f18#(x1, x2, x3) 
14.56/14.38	  f18#(I0, I1, I2) -> f7#(I0, 0, I2) [y1 = 0]
14.56/14.38	  f3#(I3, I4, I5) -> f17#(I3, I4, I5) 
14.56/14.38	  f3#(I6, I7, I8) -> f13#(I6, I7, I8) 
14.56/14.38	  f3#(I9, I10, I11) -> f17#(I9, I10, I11) 
14.56/14.38	  f17#(I12, I13, I14) -> f16#(I12, I13, I14) 
14.56/14.38	  f16#(I15, I16, I17) -> f15#(I15, I16, I17) 
14.56/14.38	  f16#(I18, I19, I20) -> f14#(I18, I19, I20) 
14.56/14.38	  f16#(I21, I22, I23) -> f14#(I21, I22, I23) 
14.56/14.38	  f15#(I24, I25, I26) -> f13#(I24, I25, I26) 
14.56/14.38	  f14#(I27, I28, I29) -> f15#(I27, I28, I29) 
14.56/14.38	  f2#(I30, I31, I32) -> f11#(I30, I31, I32) 
14.56/14.38	  f13#(I33, I34, I35) -> f7#(I33, 1 + I34, I35) 
14.56/14.38	  f11#(I36, I37, I38) -> f10#(I36, I37, I38) [1 + I37 <= 100]
14.56/14.38	  f10#(I42, I43, I44) -> f9#(I42, I43, I44) 
14.56/14.38	  f10#(I45, I46, I47) -> f4#(I45, I46, I47) 
14.56/14.38	  f10#(I48, I49, I50) -> f9#(I48, I49, I50) 
14.56/14.38	  f9#(I51, I52, I53) -> f8#(I51, I52, rnd3) [rnd3 = rnd3]
14.56/14.38	  f8#(I54, I55, I56) -> f6#(I54, I55, I56) 
14.56/14.38	  f8#(I57, I58, I59) -> f5#(I57, I58, I59) 
14.56/14.38	  f8#(I60, I61, I62) -> f5#(I60, I61, I62) 
14.56/14.38	  f7#(I63, I64, I65) -> f1#(I63, I64, I65) 
14.56/14.38	  f6#(I66, I67, I68) -> f4#(I66, I67, I68) 
14.56/14.38	  f5#(I69, I70, I71) -> f6#(I69, I70, I71) 
14.56/14.38	  f4#(I72, I73, I74) -> f2#(I72, 1 + I73, I74) 
14.56/14.38	  f1#(I75, I76, I77) -> f3#(I76, I76, I77) [1 + I76 <= 100]
14.56/14.38	  f1#(I78, I79, I80) -> f2#(I78, 0, I80) [100 <= I79]
14.56/14.38	R = 
14.56/14.38	  f19(x1, x2, x3) -> f18(x1, x2, x3) 
14.56/14.38	  f18(I0, I1, I2) -> f7(I0, 0, I2) [y1 = 0]
14.56/14.38	  f3(I3, I4, I5) -> f17(I3, I4, I5) 
14.56/14.38	  f3(I6, I7, I8) -> f13(I6, I7, I8) 
14.56/14.38	  f3(I9, I10, I11) -> f17(I9, I10, I11) 
14.56/14.38	  f17(I12, I13, I14) -> f16(I12, I13, I14) 
14.56/14.38	  f16(I15, I16, I17) -> f15(I15, I16, I17) 
14.56/14.38	  f16(I18, I19, I20) -> f14(I18, I19, I20) 
14.56/14.38	  f16(I21, I22, I23) -> f14(I21, I22, I23) 
14.56/14.38	  f15(I24, I25, I26) -> f13(I24, I25, I26) 
14.56/14.38	  f14(I27, I28, I29) -> f15(I27, I28, I29) 
14.56/14.38	  f2(I30, I31, I32) -> f11(I30, I31, I32) 
14.56/14.38	  f13(I33, I34, I35) -> f7(I33, 1 + I34, I35) 
14.56/14.38	  f11(I36, I37, I38) -> f10(I36, I37, I38) [1 + I37 <= 100]
14.56/14.38	  f11(I39, I40, I41) -> f12(I39, I40, I41) [100 <= I40]
14.56/14.38	  f10(I42, I43, I44) -> f9(I42, I43, I44) 
14.56/14.38	  f10(I45, I46, I47) -> f4(I45, I46, I47) 
14.56/14.38	  f10(I48, I49, I50) -> f9(I48, I49, I50) 
14.56/14.38	  f9(I51, I52, I53) -> f8(I51, I52, rnd3) [rnd3 = rnd3]
14.56/14.38	  f8(I54, I55, I56) -> f6(I54, I55, I56) 
14.56/14.38	  f8(I57, I58, I59) -> f5(I57, I58, I59) 
14.56/14.38	  f8(I60, I61, I62) -> f5(I60, I61, I62) 
14.56/14.38	  f7(I63, I64, I65) -> f1(I63, I64, I65) 
14.56/14.38	  f6(I66, I67, I68) -> f4(I66, I67, I68) 
14.56/14.38	  f5(I69, I70, I71) -> f6(I69, I70, I71) 
14.56/14.38	  f4(I72, I73, I74) -> f2(I72, 1 + I73, I74) 
14.56/14.38	  f1(I75, I76, I77) -> f3(I76, I76, I77) [1 + I76 <= 100]
14.56/14.38	  f1(I78, I79, I80) -> f2(I78, 0, I80) [100 <= I79]
14.56/14.38	
14.56/14.38	The dependency graph for this problem is:
14.56/14.38	  0 -> 1
14.56/14.38	  1 -> 21
14.56/14.38	  2 -> 5
14.56/14.38	  3 -> 12
14.56/14.38	  4 -> 5
14.56/14.38	  5 -> 6, 7, 8
14.56/14.38	  6 -> 9
14.56/14.38	  7 -> 10
14.56/14.38	  8 -> 10
14.56/14.38	  9 -> 12
14.56/14.38	  10 -> 9
14.56/14.38	  11 -> 13
14.56/14.38	  12 -> 21
14.56/14.38	  13 -> 14, 15, 16
14.56/14.38	  14 -> 17
14.56/14.38	  15 -> 24
14.56/14.38	  16 -> 17
14.56/14.38	  17 -> 18, 19, 20
14.56/14.38	  18 -> 22
14.56/14.38	  19 -> 23
14.56/14.38	  20 -> 23
14.56/14.38	  21 -> 25, 26
14.56/14.38	  22 -> 24
14.56/14.38	  23 -> 22
14.56/14.38	  24 -> 11
14.56/14.38	  25 -> 2, 3, 4
14.56/14.38	  26 -> 11
14.56/14.38	Where:
14.56/14.38	  0) f19#(x1, x2, x3) -> f18#(x1, x2, x3) 
14.56/14.38	  1) f18#(I0, I1, I2) -> f7#(I0, 0, I2) [y1 = 0]
14.56/14.38	  2) f3#(I3, I4, I5) -> f17#(I3, I4, I5) 
14.56/14.38	  3) f3#(I6, I7, I8) -> f13#(I6, I7, I8) 
14.56/14.38	  4) f3#(I9, I10, I11) -> f17#(I9, I10, I11) 
14.56/14.38	  5) f17#(I12, I13, I14) -> f16#(I12, I13, I14) 
14.56/14.38	  6) f16#(I15, I16, I17) -> f15#(I15, I16, I17) 
14.56/14.38	  7) f16#(I18, I19, I20) -> f14#(I18, I19, I20) 
14.56/14.38	  8) f16#(I21, I22, I23) -> f14#(I21, I22, I23) 
14.56/14.38	  9) f15#(I24, I25, I26) -> f13#(I24, I25, I26) 
14.56/14.38	  10) f14#(I27, I28, I29) -> f15#(I27, I28, I29) 
14.56/14.38	  11) f2#(I30, I31, I32) -> f11#(I30, I31, I32) 
14.56/14.38	  12) f13#(I33, I34, I35) -> f7#(I33, 1 + I34, I35) 
14.56/14.38	  13) f11#(I36, I37, I38) -> f10#(I36, I37, I38) [1 + I37 <= 100]
14.56/14.38	  14) f10#(I42, I43, I44) -> f9#(I42, I43, I44) 
14.56/14.38	  15) f10#(I45, I46, I47) -> f4#(I45, I46, I47) 
14.56/14.38	  16) f10#(I48, I49, I50) -> f9#(I48, I49, I50) 
14.56/14.38	  17) f9#(I51, I52, I53) -> f8#(I51, I52, rnd3) [rnd3 = rnd3]
14.56/14.38	  18) f8#(I54, I55, I56) -> f6#(I54, I55, I56) 
14.56/14.38	  19) f8#(I57, I58, I59) -> f5#(I57, I58, I59) 
14.56/14.38	  20) f8#(I60, I61, I62) -> f5#(I60, I61, I62) 
14.56/14.38	  21) f7#(I63, I64, I65) -> f1#(I63, I64, I65) 
14.56/14.38	  22) f6#(I66, I67, I68) -> f4#(I66, I67, I68) 
14.56/14.38	  23) f5#(I69, I70, I71) -> f6#(I69, I70, I71) 
14.56/14.38	  24) f4#(I72, I73, I74) -> f2#(I72, 1 + I73, I74) 
14.56/14.38	  25) f1#(I75, I76, I77) -> f3#(I76, I76, I77) [1 + I76 <= 100]
14.56/14.38	  26) f1#(I78, I79, I80) -> f2#(I78, 0, I80) [100 <= I79]
14.56/14.38	
14.56/14.38	We have the following SCCs.
14.56/14.38	  { 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 21, 25 }
14.56/14.38	  { 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24 }
14.56/14.38	
14.56/14.38	DP problem for innermost termination.
14.56/14.38	P =
14.56/14.38	  f2#(I30, I31, I32) -> f11#(I30, I31, I32) 
14.56/14.38	  f11#(I36, I37, I38) -> f10#(I36, I37, I38) [1 + I37 <= 100]
14.56/14.38	  f10#(I42, I43, I44) -> f9#(I42, I43, I44) 
14.56/14.38	  f10#(I45, I46, I47) -> f4#(I45, I46, I47) 
14.56/14.38	  f10#(I48, I49, I50) -> f9#(I48, I49, I50) 
14.56/14.38	  f9#(I51, I52, I53) -> f8#(I51, I52, rnd3) [rnd3 = rnd3]
14.56/14.38	  f8#(I54, I55, I56) -> f6#(I54, I55, I56) 
14.56/14.38	  f8#(I57, I58, I59) -> f5#(I57, I58, I59) 
14.56/14.38	  f8#(I60, I61, I62) -> f5#(I60, I61, I62) 
14.56/14.38	  f6#(I66, I67, I68) -> f4#(I66, I67, I68) 
14.56/14.38	  f5#(I69, I70, I71) -> f6#(I69, I70, I71) 
14.56/14.38	  f4#(I72, I73, I74) -> f2#(I72, 1 + I73, I74) 
14.56/14.38	R = 
14.56/14.38	  f19(x1, x2, x3) -> f18(x1, x2, x3) 
14.56/14.38	  f18(I0, I1, I2) -> f7(I0, 0, I2) [y1 = 0]
14.56/14.38	  f3(I3, I4, I5) -> f17(I3, I4, I5) 
14.56/14.38	  f3(I6, I7, I8) -> f13(I6, I7, I8) 
14.56/14.38	  f3(I9, I10, I11) -> f17(I9, I10, I11) 
14.56/14.38	  f17(I12, I13, I14) -> f16(I12, I13, I14) 
14.56/14.38	  f16(I15, I16, I17) -> f15(I15, I16, I17) 
14.56/14.38	  f16(I18, I19, I20) -> f14(I18, I19, I20) 
14.56/14.38	  f16(I21, I22, I23) -> f14(I21, I22, I23) 
14.56/14.38	  f15(I24, I25, I26) -> f13(I24, I25, I26) 
14.56/14.38	  f14(I27, I28, I29) -> f15(I27, I28, I29) 
14.56/14.38	  f2(I30, I31, I32) -> f11(I30, I31, I32) 
14.56/14.38	  f13(I33, I34, I35) -> f7(I33, 1 + I34, I35) 
14.56/14.38	  f11(I36, I37, I38) -> f10(I36, I37, I38) [1 + I37 <= 100]
14.56/14.38	  f11(I39, I40, I41) -> f12(I39, I40, I41) [100 <= I40]
14.56/14.38	  f10(I42, I43, I44) -> f9(I42, I43, I44) 
14.56/14.38	  f10(I45, I46, I47) -> f4(I45, I46, I47) 
14.56/14.38	  f10(I48, I49, I50) -> f9(I48, I49, I50) 
14.56/14.38	  f9(I51, I52, I53) -> f8(I51, I52, rnd3) [rnd3 = rnd3]
14.56/14.38	  f8(I54, I55, I56) -> f6(I54, I55, I56) 
14.56/14.38	  f8(I57, I58, I59) -> f5(I57, I58, I59) 
14.56/14.38	  f8(I60, I61, I62) -> f5(I60, I61, I62) 
14.56/14.38	  f7(I63, I64, I65) -> f1(I63, I64, I65) 
14.56/14.38	  f6(I66, I67, I68) -> f4(I66, I67, I68) 
14.56/14.38	  f5(I69, I70, I71) -> f6(I69, I70, I71) 
14.56/14.38	  f4(I72, I73, I74) -> f2(I72, 1 + I73, I74) 
14.56/14.38	  f1(I75, I76, I77) -> f3(I76, I76, I77) [1 + I76 <= 100]
14.56/14.38	  f1(I78, I79, I80) -> f2(I78, 0, I80) [100 <= I79]
14.56/14.38	
14.56/14.38	We use the extended value criterion with the projection function NU:
14.56/14.38	  NU[f5#(x0,x1,x2)] = -x1 + 98
14.56/14.38	  NU[f6#(x0,x1,x2)] = -x1 + 98
14.56/14.38	  NU[f8#(x0,x1,x2)] = -x1 + 98
14.56/14.38	  NU[f4#(x0,x1,x2)] = -x1 + 98
14.56/14.38	  NU[f9#(x0,x1,x2)] = -x1 + 98
14.56/14.38	  NU[f10#(x0,x1,x2)] = -x1 + 98
14.56/14.38	  NU[f11#(x0,x1,x2)] = -x1 + 99
14.56/14.38	  NU[f2#(x0,x1,x2)] = -x1 + 99
14.56/14.38	
14.56/14.38	This gives the following inequalities:
14.56/14.38	    ==>  -I31 + 99 >= -I31 + 99
14.56/14.38	  1 + I37 <= 100  ==>  -I37 + 99 > -I37 + 98  with  -I37 + 99 >= 0
14.56/14.38	    ==>  -I43 + 98 >= -I43 + 98
14.56/14.38	    ==>  -I46 + 98 >= -I46 + 98
14.56/14.38	    ==>  -I49 + 98 >= -I49 + 98
14.56/14.38	  rnd3 = rnd3  ==>  -I52 + 98 >= -I52 + 98
14.56/14.38	    ==>  -I55 + 98 >= -I55 + 98
14.56/14.38	    ==>  -I58 + 98 >= -I58 + 98
14.56/14.38	    ==>  -I61 + 98 >= -I61 + 98
14.56/14.38	    ==>  -I67 + 98 >= -I67 + 98
14.56/14.38	    ==>  -I70 + 98 >= -I70 + 98
14.56/14.38	    ==>  -I73 + 98 >= -(1 + I73) + 99
14.56/14.38	
14.56/14.38	We remove all the strictly oriented dependency pairs.
14.56/14.38	
14.56/14.38	DP problem for innermost termination.
14.56/14.38	P =
14.56/14.38	  f2#(I30, I31, I32) -> f11#(I30, I31, I32) 
14.56/14.38	  f10#(I42, I43, I44) -> f9#(I42, I43, I44) 
14.56/14.38	  f10#(I45, I46, I47) -> f4#(I45, I46, I47) 
14.56/14.38	  f10#(I48, I49, I50) -> f9#(I48, I49, I50) 
14.56/14.38	  f9#(I51, I52, I53) -> f8#(I51, I52, rnd3) [rnd3 = rnd3]
14.56/14.38	  f8#(I54, I55, I56) -> f6#(I54, I55, I56) 
14.56/14.38	  f8#(I57, I58, I59) -> f5#(I57, I58, I59) 
14.56/14.38	  f8#(I60, I61, I62) -> f5#(I60, I61, I62) 
14.56/14.38	  f6#(I66, I67, I68) -> f4#(I66, I67, I68) 
14.56/14.38	  f5#(I69, I70, I71) -> f6#(I69, I70, I71) 
14.56/14.38	  f4#(I72, I73, I74) -> f2#(I72, 1 + I73, I74) 
14.56/14.38	R = 
14.56/14.38	  f19(x1, x2, x3) -> f18(x1, x2, x3) 
14.56/14.38	  f18(I0, I1, I2) -> f7(I0, 0, I2) [y1 = 0]
14.56/14.38	  f3(I3, I4, I5) -> f17(I3, I4, I5) 
14.56/14.38	  f3(I6, I7, I8) -> f13(I6, I7, I8) 
14.56/14.38	  f3(I9, I10, I11) -> f17(I9, I10, I11) 
14.56/14.38	  f17(I12, I13, I14) -> f16(I12, I13, I14) 
14.56/14.38	  f16(I15, I16, I17) -> f15(I15, I16, I17) 
14.56/14.38	  f16(I18, I19, I20) -> f14(I18, I19, I20) 
14.56/14.38	  f16(I21, I22, I23) -> f14(I21, I22, I23) 
14.56/14.38	  f15(I24, I25, I26) -> f13(I24, I25, I26) 
14.56/14.38	  f14(I27, I28, I29) -> f15(I27, I28, I29) 
14.56/14.38	  f2(I30, I31, I32) -> f11(I30, I31, I32) 
14.56/14.38	  f13(I33, I34, I35) -> f7(I33, 1 + I34, I35) 
14.56/14.38	  f11(I36, I37, I38) -> f10(I36, I37, I38) [1 + I37 <= 100]
14.56/14.38	  f11(I39, I40, I41) -> f12(I39, I40, I41) [100 <= I40]
14.56/14.38	  f10(I42, I43, I44) -> f9(I42, I43, I44) 
14.56/14.38	  f10(I45, I46, I47) -> f4(I45, I46, I47) 
14.56/14.38	  f10(I48, I49, I50) -> f9(I48, I49, I50) 
14.56/14.38	  f9(I51, I52, I53) -> f8(I51, I52, rnd3) [rnd3 = rnd3]
14.56/14.38	  f8(I54, I55, I56) -> f6(I54, I55, I56) 
14.56/14.38	  f8(I57, I58, I59) -> f5(I57, I58, I59) 
14.56/14.38	  f8(I60, I61, I62) -> f5(I60, I61, I62) 
14.56/14.38	  f7(I63, I64, I65) -> f1(I63, I64, I65) 
14.56/14.38	  f6(I66, I67, I68) -> f4(I66, I67, I68) 
14.56/14.38	  f5(I69, I70, I71) -> f6(I69, I70, I71) 
14.56/14.38	  f4(I72, I73, I74) -> f2(I72, 1 + I73, I74) 
14.56/14.38	  f1(I75, I76, I77) -> f3(I76, I76, I77) [1 + I76 <= 100]
14.56/14.38	  f1(I78, I79, I80) -> f2(I78, 0, I80) [100 <= I79]
14.56/14.38	
14.56/14.38	The dependency graph for this problem is:
14.56/14.38	  11 -> 
14.56/14.38	  14 -> 17
14.56/14.38	  15 -> 24
14.56/14.38	  16 -> 17
14.56/14.38	  17 -> 18, 19, 20
14.56/14.38	  18 -> 22
14.56/14.38	  19 -> 23
14.56/14.38	  20 -> 23
14.56/14.38	  22 -> 24
14.56/14.38	  23 -> 22
14.56/14.38	  24 -> 11
14.56/14.38	Where:
14.56/14.38	  11) f2#(I30, I31, I32) -> f11#(I30, I31, I32) 
14.56/14.38	  14) f10#(I42, I43, I44) -> f9#(I42, I43, I44) 
14.56/14.38	  15) f10#(I45, I46, I47) -> f4#(I45, I46, I47) 
14.56/14.38	  16) f10#(I48, I49, I50) -> f9#(I48, I49, I50) 
14.56/14.38	  17) f9#(I51, I52, I53) -> f8#(I51, I52, rnd3) [rnd3 = rnd3]
14.56/14.38	  18) f8#(I54, I55, I56) -> f6#(I54, I55, I56) 
14.56/14.38	  19) f8#(I57, I58, I59) -> f5#(I57, I58, I59) 
14.56/14.38	  20) f8#(I60, I61, I62) -> f5#(I60, I61, I62) 
14.56/14.38	  22) f6#(I66, I67, I68) -> f4#(I66, I67, I68) 
14.56/14.38	  23) f5#(I69, I70, I71) -> f6#(I69, I70, I71) 
14.56/14.38	  24) f4#(I72, I73, I74) -> f2#(I72, 1 + I73, I74) 
14.56/14.38	
14.56/14.38	We have the following SCCs.
14.56/14.38	  
14.56/14.38	
14.56/14.38	DP problem for innermost termination.
14.56/14.38	P =
14.56/14.38	  f3#(I3, I4, I5) -> f17#(I3, I4, I5) 
14.56/14.38	  f3#(I6, I7, I8) -> f13#(I6, I7, I8) 
14.56/14.38	  f3#(I9, I10, I11) -> f17#(I9, I10, I11) 
14.56/14.38	  f17#(I12, I13, I14) -> f16#(I12, I13, I14) 
14.56/14.38	  f16#(I15, I16, I17) -> f15#(I15, I16, I17) 
14.56/14.38	  f16#(I18, I19, I20) -> f14#(I18, I19, I20) 
14.56/14.38	  f16#(I21, I22, I23) -> f14#(I21, I22, I23) 
14.56/14.38	  f15#(I24, I25, I26) -> f13#(I24, I25, I26) 
14.56/14.38	  f14#(I27, I28, I29) -> f15#(I27, I28, I29) 
14.56/14.38	  f13#(I33, I34, I35) -> f7#(I33, 1 + I34, I35) 
14.56/14.38	  f7#(I63, I64, I65) -> f1#(I63, I64, I65) 
14.56/14.38	  f1#(I75, I76, I77) -> f3#(I76, I76, I77) [1 + I76 <= 100]
14.56/14.38	R = 
14.56/14.38	  f19(x1, x2, x3) -> f18(x1, x2, x3) 
14.56/14.38	  f18(I0, I1, I2) -> f7(I0, 0, I2) [y1 = 0]
14.56/14.38	  f3(I3, I4, I5) -> f17(I3, I4, I5) 
14.56/14.38	  f3(I6, I7, I8) -> f13(I6, I7, I8) 
14.56/14.38	  f3(I9, I10, I11) -> f17(I9, I10, I11) 
14.56/14.38	  f17(I12, I13, I14) -> f16(I12, I13, I14) 
14.56/14.38	  f16(I15, I16, I17) -> f15(I15, I16, I17) 
14.56/14.38	  f16(I18, I19, I20) -> f14(I18, I19, I20) 
14.56/14.38	  f16(I21, I22, I23) -> f14(I21, I22, I23) 
14.56/14.38	  f15(I24, I25, I26) -> f13(I24, I25, I26) 
14.56/14.38	  f14(I27, I28, I29) -> f15(I27, I28, I29) 
14.56/14.38	  f2(I30, I31, I32) -> f11(I30, I31, I32) 
14.56/14.38	  f13(I33, I34, I35) -> f7(I33, 1 + I34, I35) 
14.56/14.38	  f11(I36, I37, I38) -> f10(I36, I37, I38) [1 + I37 <= 100]
14.56/14.38	  f11(I39, I40, I41) -> f12(I39, I40, I41) [100 <= I40]
14.56/14.38	  f10(I42, I43, I44) -> f9(I42, I43, I44) 
14.56/14.38	  f10(I45, I46, I47) -> f4(I45, I46, I47) 
14.56/14.38	  f10(I48, I49, I50) -> f9(I48, I49, I50) 
14.56/14.38	  f9(I51, I52, I53) -> f8(I51, I52, rnd3) [rnd3 = rnd3]
14.56/14.38	  f8(I54, I55, I56) -> f6(I54, I55, I56) 
14.56/14.38	  f8(I57, I58, I59) -> f5(I57, I58, I59) 
14.56/14.38	  f8(I60, I61, I62) -> f5(I60, I61, I62) 
14.56/14.38	  f7(I63, I64, I65) -> f1(I63, I64, I65) 
14.56/14.38	  f6(I66, I67, I68) -> f4(I66, I67, I68) 
14.56/14.38	  f5(I69, I70, I71) -> f6(I69, I70, I71) 
14.56/14.38	  f4(I72, I73, I74) -> f2(I72, 1 + I73, I74) 
14.56/14.38	  f1(I75, I76, I77) -> f3(I76, I76, I77) [1 + I76 <= 100]
14.56/14.38	  f1(I78, I79, I80) -> f2(I78, 0, I80) [100 <= I79]
14.56/14.38	
14.56/14.38	We use the extended value criterion with the projection function NU:
14.56/14.38	  NU[f1#(x0,x1,x2)] = -x1 + 99
14.56/14.38	  NU[f7#(x0,x1,x2)] = -x1 + 99
14.56/14.38	  NU[f14#(x0,x1,x2)] = -x1 + 98
14.56/14.38	  NU[f15#(x0,x1,x2)] = -x1 + 98
14.56/14.38	  NU[f16#(x0,x1,x2)] = -x1 + 98
14.56/14.38	  NU[f13#(x0,x1,x2)] = -x1 + 98
14.56/14.38	  NU[f17#(x0,x1,x2)] = -x1 + 98
14.56/14.38	  NU[f3#(x0,x1,x2)] = -x1 + 98
14.56/14.38	
14.56/14.38	This gives the following inequalities:
14.56/14.38	    ==>  -I4 + 98 >= -I4 + 98
14.56/14.38	    ==>  -I7 + 98 >= -I7 + 98
14.56/14.38	    ==>  -I10 + 98 >= -I10 + 98
14.56/14.38	    ==>  -I13 + 98 >= -I13 + 98
14.56/14.38	    ==>  -I16 + 98 >= -I16 + 98
14.56/14.38	    ==>  -I19 + 98 >= -I19 + 98
14.56/14.38	    ==>  -I22 + 98 >= -I22 + 98
14.56/14.38	    ==>  -I25 + 98 >= -I25 + 98
14.56/14.38	    ==>  -I28 + 98 >= -I28 + 98
14.56/14.38	    ==>  -I34 + 98 >= -(1 + I34) + 99
14.56/14.38	    ==>  -I64 + 99 >= -I64 + 99
14.56/14.38	  1 + I76 <= 100  ==>  -I76 + 99 > -I76 + 98  with  -I76 + 99 >= 0
14.56/14.38	
14.56/14.38	We remove all the strictly oriented dependency pairs.
14.56/14.38	
14.56/14.38	DP problem for innermost termination.
14.56/14.38	P =
14.56/14.38	  f3#(I3, I4, I5) -> f17#(I3, I4, I5) 
14.56/14.38	  f3#(I6, I7, I8) -> f13#(I6, I7, I8) 
14.56/14.38	  f3#(I9, I10, I11) -> f17#(I9, I10, I11) 
14.56/14.38	  f17#(I12, I13, I14) -> f16#(I12, I13, I14) 
14.56/14.38	  f16#(I15, I16, I17) -> f15#(I15, I16, I17) 
14.56/14.38	  f16#(I18, I19, I20) -> f14#(I18, I19, I20) 
14.56/14.38	  f16#(I21, I22, I23) -> f14#(I21, I22, I23) 
14.56/14.38	  f15#(I24, I25, I26) -> f13#(I24, I25, I26) 
14.56/14.38	  f14#(I27, I28, I29) -> f15#(I27, I28, I29) 
14.56/14.38	  f13#(I33, I34, I35) -> f7#(I33, 1 + I34, I35) 
14.56/14.38	  f7#(I63, I64, I65) -> f1#(I63, I64, I65) 
14.56/14.38	R = 
14.56/14.38	  f19(x1, x2, x3) -> f18(x1, x2, x3) 
14.56/14.38	  f18(I0, I1, I2) -> f7(I0, 0, I2) [y1 = 0]
14.56/14.38	  f3(I3, I4, I5) -> f17(I3, I4, I5) 
14.56/14.38	  f3(I6, I7, I8) -> f13(I6, I7, I8) 
14.56/14.38	  f3(I9, I10, I11) -> f17(I9, I10, I11) 
14.56/14.38	  f17(I12, I13, I14) -> f16(I12, I13, I14) 
14.56/14.38	  f16(I15, I16, I17) -> f15(I15, I16, I17) 
14.56/14.38	  f16(I18, I19, I20) -> f14(I18, I19, I20) 
14.56/14.38	  f16(I21, I22, I23) -> f14(I21, I22, I23) 
14.56/14.38	  f15(I24, I25, I26) -> f13(I24, I25, I26) 
14.56/14.38	  f14(I27, I28, I29) -> f15(I27, I28, I29) 
14.56/14.38	  f2(I30, I31, I32) -> f11(I30, I31, I32) 
14.56/14.38	  f13(I33, I34, I35) -> f7(I33, 1 + I34, I35) 
14.56/14.38	  f11(I36, I37, I38) -> f10(I36, I37, I38) [1 + I37 <= 100]
14.56/14.38	  f11(I39, I40, I41) -> f12(I39, I40, I41) [100 <= I40]
14.56/14.38	  f10(I42, I43, I44) -> f9(I42, I43, I44) 
14.56/14.38	  f10(I45, I46, I47) -> f4(I45, I46, I47) 
14.56/14.38	  f10(I48, I49, I50) -> f9(I48, I49, I50) 
14.56/14.38	  f9(I51, I52, I53) -> f8(I51, I52, rnd3) [rnd3 = rnd3]
14.56/14.38	  f8(I54, I55, I56) -> f6(I54, I55, I56) 
14.56/14.38	  f8(I57, I58, I59) -> f5(I57, I58, I59) 
14.56/14.38	  f8(I60, I61, I62) -> f5(I60, I61, I62) 
14.56/14.38	  f7(I63, I64, I65) -> f1(I63, I64, I65) 
14.56/14.38	  f6(I66, I67, I68) -> f4(I66, I67, I68) 
14.56/14.38	  f5(I69, I70, I71) -> f6(I69, I70, I71) 
14.56/14.38	  f4(I72, I73, I74) -> f2(I72, 1 + I73, I74) 
14.56/14.38	  f1(I75, I76, I77) -> f3(I76, I76, I77) [1 + I76 <= 100]
14.56/14.38	  f1(I78, I79, I80) -> f2(I78, 0, I80) [100 <= I79]
14.56/14.38	
14.56/14.38	The dependency graph for this problem is:
14.56/14.38	  2 -> 5
14.56/14.38	  3 -> 12
14.56/14.38	  4 -> 5
14.56/14.38	  5 -> 6, 7, 8
14.56/14.38	  6 -> 9
14.56/14.38	  7 -> 10
14.56/14.38	  8 -> 10
14.56/14.38	  9 -> 12
14.56/14.38	  10 -> 9
14.56/14.38	  12 -> 21
14.56/14.38	  21 -> 
14.56/14.38	Where:
14.56/14.38	  2) f3#(I3, I4, I5) -> f17#(I3, I4, I5) 
14.56/14.38	  3) f3#(I6, I7, I8) -> f13#(I6, I7, I8) 
14.56/14.38	  4) f3#(I9, I10, I11) -> f17#(I9, I10, I11) 
14.56/14.38	  5) f17#(I12, I13, I14) -> f16#(I12, I13, I14) 
14.56/14.38	  6) f16#(I15, I16, I17) -> f15#(I15, I16, I17) 
14.56/14.38	  7) f16#(I18, I19, I20) -> f14#(I18, I19, I20) 
14.56/14.38	  8) f16#(I21, I22, I23) -> f14#(I21, I22, I23) 
14.56/14.38	  9) f15#(I24, I25, I26) -> f13#(I24, I25, I26) 
14.56/14.38	  10) f14#(I27, I28, I29) -> f15#(I27, I28, I29) 
14.56/14.38	  12) f13#(I33, I34, I35) -> f7#(I33, 1 + I34, I35) 
14.56/14.38	  21) f7#(I63, I64, I65) -> f1#(I63, I64, I65) 
14.56/14.38	
14.56/14.38	We have the following SCCs.
14.56/14.38	  
14.56/14.39	EOF