1.36/1.47	YES
1.36/1.47	
1.36/1.47	DP problem for innermost termination.
1.36/1.47	P =
1.36/1.47	  init#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f3#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) 
1.36/1.47	  f4#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f4#(I20, I1 - 1, I2, I3, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I15 + 1, I16 + 1, I32, I33, I19 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I15 - 1 /\ I15 <= y1 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I14 - 1 /\ -1 <= y2 - 1 /\ 0 <= I8 - 1 /\ 0 <= I11 - 1 /\ 0 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I10 - 1 /\ 0 <= I7 - 1 /\ -1 <= I19 - 1 /\ -1 <= I16 - 1 /\ 11 <= I0 - 1 /\ 11 <= I20 - 1 /\ I16 + 5 <= I0 /\ I17 + 11 <= I0 /\ I19 + 3 <= I0 /\ I18 + 9 <= I0]
1.36/1.47	  f2#(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f4#(I54, I34, I37, I38, I44, I43, I36, I39, I40, I41, I42, I45, I46, I47, I48, I50, I51, I55, I56, I52) [I52 + 3 <= I35 /\ I51 + 5 <= I35 /\ 11 <= I54 - 1 /\ 11 <= I35 - 1]
1.36/1.47	  f3#(I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f1#(I77, I78, I79, I80, 1, 0, 0, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93) [7 <= I78 - 1 /\ 0 <= I57 - 1 /\ I78 - 7 <= I57 /\ 0 <= I58 - 1 /\ -1 <= I77 - 1]
1.36/1.47	  f1#(I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113) -> f2#(I94, I114, 0, 0, I96, I115, 0, 0, 0, I116, I117, I118, I96, I97, I97, I119, I98, I99, I100, I120) [I100 + 3 <= I95 /\ I99 + 5 <= I95 /\ 9 <= I114 - 1 /\ 9 <= I95 - 1 /\ I114 <= I95]
1.36/1.47	R = 
1.36/1.47	  init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f3(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) 
1.36/1.47	  f4(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f4(I20, I1 - 1, I2, I3, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I15 + 1, I16 + 1, I32, I33, I19 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I15 - 1 /\ I15 <= y1 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I14 - 1 /\ -1 <= y2 - 1 /\ 0 <= I8 - 1 /\ 0 <= I11 - 1 /\ 0 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I10 - 1 /\ 0 <= I7 - 1 /\ -1 <= I19 - 1 /\ -1 <= I16 - 1 /\ 11 <= I0 - 1 /\ 11 <= I20 - 1 /\ I16 + 5 <= I0 /\ I17 + 11 <= I0 /\ I19 + 3 <= I0 /\ I18 + 9 <= I0]
1.36/1.47	  f2(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f4(I54, I34, I37, I38, I44, I43, I36, I39, I40, I41, I42, I45, I46, I47, I48, I50, I51, I55, I56, I52) [I52 + 3 <= I35 /\ I51 + 5 <= I35 /\ 11 <= I54 - 1 /\ 11 <= I35 - 1]
1.36/1.47	  f3(I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f1(I77, I78, I79, I80, 1, 0, 0, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93) [7 <= I78 - 1 /\ 0 <= I57 - 1 /\ I78 - 7 <= I57 /\ 0 <= I58 - 1 /\ -1 <= I77 - 1]
1.36/1.47	  f1(I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113) -> f2(I94, I114, 0, 0, I96, I115, 0, 0, 0, I116, I117, I118, I96, I97, I97, I119, I98, I99, I100, I120) [I100 + 3 <= I95 /\ I99 + 5 <= I95 /\ 9 <= I114 - 1 /\ 9 <= I95 - 1 /\ I114 <= I95]
1.36/1.47	
1.36/1.47	The dependency graph for this problem is:
1.36/1.47	  0 -> 3
1.36/1.47	  1 -> 1
1.36/1.47	  2 -> 1
1.36/1.47	  3 -> 4
1.36/1.47	  4 -> 2
1.36/1.47	Where:
1.36/1.47	  0) init#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f3#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) 
1.36/1.47	  1) f4#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f4#(I20, I1 - 1, I2, I3, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I15 + 1, I16 + 1, I32, I33, I19 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I15 - 1 /\ I15 <= y1 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I14 - 1 /\ -1 <= y2 - 1 /\ 0 <= I8 - 1 /\ 0 <= I11 - 1 /\ 0 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I10 - 1 /\ 0 <= I7 - 1 /\ -1 <= I19 - 1 /\ -1 <= I16 - 1 /\ 11 <= I0 - 1 /\ 11 <= I20 - 1 /\ I16 + 5 <= I0 /\ I17 + 11 <= I0 /\ I19 + 3 <= I0 /\ I18 + 9 <= I0]
1.36/1.47	  2) f2#(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f4#(I54, I34, I37, I38, I44, I43, I36, I39, I40, I41, I42, I45, I46, I47, I48, I50, I51, I55, I56, I52) [I52 + 3 <= I35 /\ I51 + 5 <= I35 /\ 11 <= I54 - 1 /\ 11 <= I35 - 1]
1.36/1.47	  3) f3#(I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f1#(I77, I78, I79, I80, 1, 0, 0, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93) [7 <= I78 - 1 /\ 0 <= I57 - 1 /\ I78 - 7 <= I57 /\ 0 <= I58 - 1 /\ -1 <= I77 - 1]
1.36/1.47	  4) f1#(I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113) -> f2#(I94, I114, 0, 0, I96, I115, 0, 0, 0, I116, I117, I118, I96, I97, I97, I119, I98, I99, I100, I120) [I100 + 3 <= I95 /\ I99 + 5 <= I95 /\ 9 <= I114 - 1 /\ 9 <= I95 - 1 /\ I114 <= I95]
1.36/1.47	
1.36/1.47	We have the following SCCs.
1.36/1.47	  { 1 }
1.36/1.47	
1.36/1.47	DP problem for innermost termination.
1.36/1.47	P =
1.36/1.47	  f4#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f4#(I20, I1 - 1, I2, I3, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I15 + 1, I16 + 1, I32, I33, I19 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I15 - 1 /\ I15 <= y1 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I14 - 1 /\ -1 <= y2 - 1 /\ 0 <= I8 - 1 /\ 0 <= I11 - 1 /\ 0 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I10 - 1 /\ 0 <= I7 - 1 /\ -1 <= I19 - 1 /\ -1 <= I16 - 1 /\ 11 <= I0 - 1 /\ 11 <= I20 - 1 /\ I16 + 5 <= I0 /\ I17 + 11 <= I0 /\ I19 + 3 <= I0 /\ I18 + 9 <= I0]
1.36/1.47	R = 
1.36/1.47	  init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> f3(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20) 
1.36/1.47	  f4(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f4(I20, I1 - 1, I2, I3, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I15 + 1, I16 + 1, I32, I33, I19 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I15 - 1 /\ I15 <= y1 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I14 - 1 /\ -1 <= y2 - 1 /\ 0 <= I8 - 1 /\ 0 <= I11 - 1 /\ 0 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I10 - 1 /\ 0 <= I7 - 1 /\ -1 <= I19 - 1 /\ -1 <= I16 - 1 /\ 11 <= I0 - 1 /\ 11 <= I20 - 1 /\ I16 + 5 <= I0 /\ I17 + 11 <= I0 /\ I19 + 3 <= I0 /\ I18 + 9 <= I0]
1.36/1.47	  f2(I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f4(I54, I34, I37, I38, I44, I43, I36, I39, I40, I41, I42, I45, I46, I47, I48, I50, I51, I55, I56, I52) [I52 + 3 <= I35 /\ I51 + 5 <= I35 /\ 11 <= I54 - 1 /\ 11 <= I35 - 1]
1.36/1.47	  f3(I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75, I76) -> f1(I77, I78, I79, I80, 1, 0, 0, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93) [7 <= I78 - 1 /\ 0 <= I57 - 1 /\ I78 - 7 <= I57 /\ 0 <= I58 - 1 /\ -1 <= I77 - 1]
1.36/1.47	  f1(I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110, I111, I112, I113) -> f2(I94, I114, 0, 0, I96, I115, 0, 0, 0, I116, I117, I118, I96, I97, I97, I119, I98, I99, I100, I120) [I100 + 3 <= I95 /\ I99 + 5 <= I95 /\ 9 <= I114 - 1 /\ 9 <= I95 - 1 /\ I114 <= I95]
1.36/1.47	
1.36/1.47	We use the basic value criterion with the projection function NU:
1.36/1.47	  NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20)] = z2
1.36/1.47	
1.36/1.47	This gives the following inequalities:
1.36/1.47	  0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I15 - 1 /\ I15 <= y1 - 1 /\ 0 <= I3 - 1 /\ 0 <= I2 - 1 /\ 0 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I14 - 1 /\ -1 <= y2 - 1 /\ 0 <= I8 - 1 /\ 0 <= I11 - 1 /\ 0 <= I9 - 1 /\ 0 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I10 - 1 /\ 0 <= I7 - 1 /\ -1 <= I19 - 1 /\ -1 <= I16 - 1 /\ 11 <= I0 - 1 /\ 11 <= I20 - 1 /\ I16 + 5 <= I0 /\ I17 + 11 <= I0 /\ I19 + 3 <= I0 /\ I18 + 9 <= I0  ==>  I1 >! I1 - 1
1.36/1.47	
1.36/1.47	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
1.36/4.45	EOF