15.67/15.61	YES
15.67/15.61	
15.67/15.61	DP problem for innermost termination.
15.67/15.61	P =
15.67/15.61	  init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
15.67/15.61	  f4#(I0, I1, I2, I3) -> f4#(I0 - 1, I1, I4, I5) [0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1]
15.67/15.61	  f6#(I6, I7, I8, I9) -> f4#(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	  f4#(I13, I14, I15, I16) -> f6#(I13, I14, I13 - 1, I17) [0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1]
15.67/15.61	  f7#(I18, I19, I20, I21) -> f6#(I19, I18, I19 - 1, I22) [0 <= I19 - 1]
15.67/15.61	  f4#(I23, I24, I25, I26) -> f6#(I23, I24, I23 - 1, I27) [I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1]
15.67/15.61	  f4#(I28, I29, I30, I31) -> f4#(I28, I29 - I28, I32, I33) [0 <= I28 - 1 /\ I28 <= I29 /\ 0 <= I29 - 1]
15.67/15.61	  f4#(I34, I35, I36, I37) -> f4#(I35, I35, I38, I39) [1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1]
15.67/15.61	  f3#(I40, I41, I42, I43) -> f3#(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  f5#(I45, I46, I47, I48) -> f3#(I49, I46, I47 + 1, I48) [0 <= I49 - 1 /\ 0 <= I45 - 1 /\ -1 <= I48 - 1 /\ I49 <= I45]
15.67/15.61	  f3#(I50, I51, I52, I53) -> f3#(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  f3#(I55, I56, I57, I58) -> f3#(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  f3#(I60, I61, I62, I63) -> f4#(I62, I61, I64, I65) [0 <= I60 - 1 /\ I62 <= I63 /\ I61 <= I63]
15.67/15.61	  f3#(I66, I67, I68, I69) -> f2#(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	  f2#(I72, I73, I74, I75) -> f3#(I76, I73, 0, I74) [0 <= I76 - 1 /\ 0 <= I72 - 1 /\ I76 <= I72 /\ -1 <= I74 - 1 /\ I73 <= I74]
15.67/15.61	  f1#(I77, I78, I79, I80) -> f2#(I81, 0, I78, I82) [0 <= I81 - 1 /\ 0 <= I77 - 1 /\ -1 <= I78 - 1 /\ I81 <= I77]
15.67/15.61	R = 
15.67/15.61	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
15.67/15.61	  f4(I0, I1, I2, I3) -> f4(I0 - 1, I1, I4, I5) [0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1]
15.67/15.61	  f6(I6, I7, I8, I9) -> f4(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	  f4(I13, I14, I15, I16) -> f6(I13, I14, I13 - 1, I17) [0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1]
15.67/15.61	  f7(I18, I19, I20, I21) -> f6(I19, I18, I19 - 1, I22) [0 <= I19 - 1]
15.67/15.61	  f4(I23, I24, I25, I26) -> f6(I23, I24, I23 - 1, I27) [I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1]
15.67/15.61	  f4(I28, I29, I30, I31) -> f4(I28, I29 - I28, I32, I33) [0 <= I28 - 1 /\ I28 <= I29 /\ 0 <= I29 - 1]
15.67/15.61	  f4(I34, I35, I36, I37) -> f4(I35, I35, I38, I39) [1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1]
15.67/15.61	  f3(I40, I41, I42, I43) -> f3(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  f5(I45, I46, I47, I48) -> f3(I49, I46, I47 + 1, I48) [0 <= I49 - 1 /\ 0 <= I45 - 1 /\ -1 <= I48 - 1 /\ I49 <= I45]
15.67/15.61	  f3(I50, I51, I52, I53) -> f3(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  f3(I55, I56, I57, I58) -> f3(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  f3(I60, I61, I62, I63) -> f4(I62, I61, I64, I65) [0 <= I60 - 1 /\ I62 <= I63 /\ I61 <= I63]
15.67/15.61	  f3(I66, I67, I68, I69) -> f2(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	  f2(I72, I73, I74, I75) -> f3(I76, I73, 0, I74) [0 <= I76 - 1 /\ 0 <= I72 - 1 /\ I76 <= I72 /\ -1 <= I74 - 1 /\ I73 <= I74]
15.67/15.61	  f1(I77, I78, I79, I80) -> f2(I81, 0, I78, I82) [0 <= I81 - 1 /\ 0 <= I77 - 1 /\ -1 <= I78 - 1 /\ I81 <= I77]
15.67/15.61	
15.67/15.61	The dependency graph for this problem is:
15.67/15.61	  0 -> 15
15.67/15.61	  1 -> 1, 3, 6
15.67/15.61	  2 -> 1, 3, 5, 6, 7
15.67/15.61	  3 -> 2
15.67/15.61	  4 -> 2
15.67/15.61	  5 -> 2
15.67/15.61	  6 -> 1, 3, 5, 6, 7
15.67/15.61	  7 -> 1, 3, 5, 6
15.67/15.61	  8 -> 8, 10, 11, 12, 13
15.67/15.61	  9 -> 8, 10, 11, 12, 13
15.67/15.61	  10 -> 8, 11, 12, 13
15.67/15.61	  11 -> 8, 10, 11, 12, 13
15.67/15.61	  12 -> 1, 3, 5, 6, 7
15.67/15.61	  13 -> 14
15.67/15.61	  14 -> 8, 10, 11, 12
15.67/15.61	  15 -> 14
15.67/15.61	Where:
15.67/15.61	  0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
15.67/15.61	  1) f4#(I0, I1, I2, I3) -> f4#(I0 - 1, I1, I4, I5) [0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1]
15.67/15.61	  2) f6#(I6, I7, I8, I9) -> f4#(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	  3) f4#(I13, I14, I15, I16) -> f6#(I13, I14, I13 - 1, I17) [0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1]
15.67/15.61	  4) f7#(I18, I19, I20, I21) -> f6#(I19, I18, I19 - 1, I22) [0 <= I19 - 1]
15.67/15.61	  5) f4#(I23, I24, I25, I26) -> f6#(I23, I24, I23 - 1, I27) [I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1]
15.67/15.61	  6) f4#(I28, I29, I30, I31) -> f4#(I28, I29 - I28, I32, I33) [0 <= I28 - 1 /\ I28 <= I29 /\ 0 <= I29 - 1]
15.67/15.61	  7) f4#(I34, I35, I36, I37) -> f4#(I35, I35, I38, I39) [1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1]
15.67/15.61	  8) f3#(I40, I41, I42, I43) -> f3#(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  9) f5#(I45, I46, I47, I48) -> f3#(I49, I46, I47 + 1, I48) [0 <= I49 - 1 /\ 0 <= I45 - 1 /\ -1 <= I48 - 1 /\ I49 <= I45]
15.67/15.61	  10) f3#(I50, I51, I52, I53) -> f3#(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  11) f3#(I55, I56, I57, I58) -> f3#(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  12) f3#(I60, I61, I62, I63) -> f4#(I62, I61, I64, I65) [0 <= I60 - 1 /\ I62 <= I63 /\ I61 <= I63]
15.67/15.61	  13) f3#(I66, I67, I68, I69) -> f2#(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	  14) f2#(I72, I73, I74, I75) -> f3#(I76, I73, 0, I74) [0 <= I76 - 1 /\ 0 <= I72 - 1 /\ I76 <= I72 /\ -1 <= I74 - 1 /\ I73 <= I74]
15.67/15.61	  15) f1#(I77, I78, I79, I80) -> f2#(I81, 0, I78, I82) [0 <= I81 - 1 /\ 0 <= I77 - 1 /\ -1 <= I78 - 1 /\ I81 <= I77]
15.67/15.61	
15.67/15.61	We have the following SCCs.
15.67/15.61	  { 8, 10, 11, 13, 14 }
15.67/15.61	  { 1, 2, 3, 5, 6, 7 }
15.67/15.61	
15.67/15.61	DP problem for innermost termination.
15.67/15.61	P =
15.67/15.61	  f4#(I0, I1, I2, I3) -> f4#(I0 - 1, I1, I4, I5) [0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1]
15.67/15.61	  f6#(I6, I7, I8, I9) -> f4#(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	  f4#(I13, I14, I15, I16) -> f6#(I13, I14, I13 - 1, I17) [0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1]
15.67/15.61	  f4#(I23, I24, I25, I26) -> f6#(I23, I24, I23 - 1, I27) [I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1]
15.67/15.61	  f4#(I28, I29, I30, I31) -> f4#(I28, I29 - I28, I32, I33) [0 <= I28 - 1 /\ I28 <= I29 /\ 0 <= I29 - 1]
15.67/15.61	  f4#(I34, I35, I36, I37) -> f4#(I35, I35, I38, I39) [1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1]
15.67/15.61	R = 
15.67/15.61	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
15.67/15.61	  f4(I0, I1, I2, I3) -> f4(I0 - 1, I1, I4, I5) [0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1]
15.67/15.61	  f6(I6, I7, I8, I9) -> f4(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	  f4(I13, I14, I15, I16) -> f6(I13, I14, I13 - 1, I17) [0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1]
15.67/15.61	  f7(I18, I19, I20, I21) -> f6(I19, I18, I19 - 1, I22) [0 <= I19 - 1]
15.67/15.61	  f4(I23, I24, I25, I26) -> f6(I23, I24, I23 - 1, I27) [I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1]
15.67/15.61	  f4(I28, I29, I30, I31) -> f4(I28, I29 - I28, I32, I33) [0 <= I28 - 1 /\ I28 <= I29 /\ 0 <= I29 - 1]
15.67/15.61	  f4(I34, I35, I36, I37) -> f4(I35, I35, I38, I39) [1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1]
15.67/15.61	  f3(I40, I41, I42, I43) -> f3(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  f5(I45, I46, I47, I48) -> f3(I49, I46, I47 + 1, I48) [0 <= I49 - 1 /\ 0 <= I45 - 1 /\ -1 <= I48 - 1 /\ I49 <= I45]
15.67/15.61	  f3(I50, I51, I52, I53) -> f3(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  f3(I55, I56, I57, I58) -> f3(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  f3(I60, I61, I62, I63) -> f4(I62, I61, I64, I65) [0 <= I60 - 1 /\ I62 <= I63 /\ I61 <= I63]
15.67/15.61	  f3(I66, I67, I68, I69) -> f2(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	  f2(I72, I73, I74, I75) -> f3(I76, I73, 0, I74) [0 <= I76 - 1 /\ 0 <= I72 - 1 /\ I76 <= I72 /\ -1 <= I74 - 1 /\ I73 <= I74]
15.67/15.61	  f1(I77, I78, I79, I80) -> f2(I81, 0, I78, I82) [0 <= I81 - 1 /\ 0 <= I77 - 1 /\ -1 <= I78 - 1 /\ I81 <= I77]
15.67/15.61	
15.67/15.61	We use the basic value criterion with the projection function NU:
15.67/15.61	  NU[f6#(z1,z2,z3,z4)] = z2
15.67/15.61	  NU[f4#(z1,z2,z3,z4)] = z2
15.67/15.61	
15.67/15.61	This gives the following inequalities:
15.67/15.61	  0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1  ==>  I1 (>! \union =) I1
15.67/15.61	  0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1  ==>  I7 (>! \union =) I7
15.67/15.61	  0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1  ==>  I14 (>! \union =) I14
15.67/15.61	  I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1  ==>  I24 (>! \union =) I24
15.67/15.61	  0 <= I28 - 1 /\ I28 <= I29 /\ 0 <= I29 - 1  ==>  I29 >! I29 - I28
15.67/15.61	  1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1  ==>  I35 (>! \union =) I35
15.67/15.61	
15.67/15.61	We remove all the strictly oriented dependency pairs.
15.67/15.61	
15.67/15.61	DP problem for innermost termination.
15.67/15.61	P =
15.67/15.61	  f4#(I0, I1, I2, I3) -> f4#(I0 - 1, I1, I4, I5) [0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1]
15.67/15.61	  f6#(I6, I7, I8, I9) -> f4#(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	  f4#(I13, I14, I15, I16) -> f6#(I13, I14, I13 - 1, I17) [0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1]
15.67/15.61	  f4#(I23, I24, I25, I26) -> f6#(I23, I24, I23 - 1, I27) [I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1]
15.67/15.61	  f4#(I34, I35, I36, I37) -> f4#(I35, I35, I38, I39) [1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1]
15.67/15.61	R = 
15.67/15.61	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
15.67/15.61	  f4(I0, I1, I2, I3) -> f4(I0 - 1, I1, I4, I5) [0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1]
15.67/15.61	  f6(I6, I7, I8, I9) -> f4(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	  f4(I13, I14, I15, I16) -> f6(I13, I14, I13 - 1, I17) [0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1]
15.67/15.61	  f7(I18, I19, I20, I21) -> f6(I19, I18, I19 - 1, I22) [0 <= I19 - 1]
15.67/15.61	  f4(I23, I24, I25, I26) -> f6(I23, I24, I23 - 1, I27) [I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1]
15.67/15.61	  f4(I28, I29, I30, I31) -> f4(I28, I29 - I28, I32, I33) [0 <= I28 - 1 /\ I28 <= I29 /\ 0 <= I29 - 1]
15.67/15.61	  f4(I34, I35, I36, I37) -> f4(I35, I35, I38, I39) [1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1]
15.67/15.61	  f3(I40, I41, I42, I43) -> f3(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  f5(I45, I46, I47, I48) -> f3(I49, I46, I47 + 1, I48) [0 <= I49 - 1 /\ 0 <= I45 - 1 /\ -1 <= I48 - 1 /\ I49 <= I45]
15.67/15.61	  f3(I50, I51, I52, I53) -> f3(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  f3(I55, I56, I57, I58) -> f3(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  f3(I60, I61, I62, I63) -> f4(I62, I61, I64, I65) [0 <= I60 - 1 /\ I62 <= I63 /\ I61 <= I63]
15.67/15.61	  f3(I66, I67, I68, I69) -> f2(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	  f2(I72, I73, I74, I75) -> f3(I76, I73, 0, I74) [0 <= I76 - 1 /\ 0 <= I72 - 1 /\ I76 <= I72 /\ -1 <= I74 - 1 /\ I73 <= I74]
15.67/15.61	  f1(I77, I78, I79, I80) -> f2(I81, 0, I78, I82) [0 <= I81 - 1 /\ 0 <= I77 - 1 /\ -1 <= I78 - 1 /\ I81 <= I77]
15.67/15.61	
15.67/15.61	We use the basic value criterion with the projection function NU:
15.67/15.61	  NU[f6#(z1,z2,z3,z4)] = z3
15.67/15.61	  NU[f4#(z1,z2,z3,z4)] = z1
15.67/15.61	
15.67/15.61	This gives the following inequalities:
15.67/15.61	  0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1  ==>  I0 >! I0 - 1
15.67/15.61	  0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1  ==>  I8 (>! \union =) I8
15.67/15.61	  0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1  ==>  I13 >! I13 - 1
15.67/15.61	  I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1  ==>  I23 >! I23 - 1
15.67/15.61	  1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1  ==>  I34 >! I35
15.67/15.61	
15.67/15.61	We remove all the strictly oriented dependency pairs.
15.67/15.61	
15.67/15.61	DP problem for innermost termination.
15.67/15.61	P =
15.67/15.61	  f6#(I6, I7, I8, I9) -> f4#(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	R = 
15.67/15.61	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
15.67/15.61	  f4(I0, I1, I2, I3) -> f4(I0 - 1, I1, I4, I5) [0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1]
15.67/15.61	  f6(I6, I7, I8, I9) -> f4(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	  f4(I13, I14, I15, I16) -> f6(I13, I14, I13 - 1, I17) [0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1]
15.67/15.61	  f7(I18, I19, I20, I21) -> f6(I19, I18, I19 - 1, I22) [0 <= I19 - 1]
15.67/15.61	  f4(I23, I24, I25, I26) -> f6(I23, I24, I23 - 1, I27) [I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1]
15.67/15.61	  f4(I28, I29, I30, I31) -> f4(I28, I29 - I28, I32, I33) [0 <= I28 - 1 /\ I28 <= I29 /\ 0 <= I29 - 1]
15.67/15.61	  f4(I34, I35, I36, I37) -> f4(I35, I35, I38, I39) [1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1]
15.67/15.61	  f3(I40, I41, I42, I43) -> f3(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  f5(I45, I46, I47, I48) -> f3(I49, I46, I47 + 1, I48) [0 <= I49 - 1 /\ 0 <= I45 - 1 /\ -1 <= I48 - 1 /\ I49 <= I45]
15.67/15.61	  f3(I50, I51, I52, I53) -> f3(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  f3(I55, I56, I57, I58) -> f3(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  f3(I60, I61, I62, I63) -> f4(I62, I61, I64, I65) [0 <= I60 - 1 /\ I62 <= I63 /\ I61 <= I63]
15.67/15.61	  f3(I66, I67, I68, I69) -> f2(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	  f2(I72, I73, I74, I75) -> f3(I76, I73, 0, I74) [0 <= I76 - 1 /\ 0 <= I72 - 1 /\ I76 <= I72 /\ -1 <= I74 - 1 /\ I73 <= I74]
15.67/15.61	  f1(I77, I78, I79, I80) -> f2(I81, 0, I78, I82) [0 <= I81 - 1 /\ 0 <= I77 - 1 /\ -1 <= I78 - 1 /\ I81 <= I77]
15.67/15.61	
15.67/15.61	The dependency graph for this problem is:
15.67/15.61	  2 -> 
15.67/15.61	Where:
15.67/15.61	  2) f6#(I6, I7, I8, I9) -> f4#(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	
15.67/15.61	We have the following SCCs.
15.67/15.61	  
15.67/15.61	
15.67/15.61	DP problem for innermost termination.
15.67/15.61	P =
15.67/15.61	  f3#(I40, I41, I42, I43) -> f3#(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  f3#(I50, I51, I52, I53) -> f3#(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  f3#(I55, I56, I57, I58) -> f3#(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  f3#(I66, I67, I68, I69) -> f2#(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	  f2#(I72, I73, I74, I75) -> f3#(I76, I73, 0, I74) [0 <= I76 - 1 /\ 0 <= I72 - 1 /\ I76 <= I72 /\ -1 <= I74 - 1 /\ I73 <= I74]
15.67/15.61	R = 
15.67/15.61	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
15.67/15.61	  f4(I0, I1, I2, I3) -> f4(I0 - 1, I1, I4, I5) [0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1]
15.67/15.61	  f6(I6, I7, I8, I9) -> f4(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	  f4(I13, I14, I15, I16) -> f6(I13, I14, I13 - 1, I17) [0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1]
15.67/15.61	  f7(I18, I19, I20, I21) -> f6(I19, I18, I19 - 1, I22) [0 <= I19 - 1]
15.67/15.61	  f4(I23, I24, I25, I26) -> f6(I23, I24, I23 - 1, I27) [I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1]
15.67/15.61	  f4(I28, I29, I30, I31) -> f4(I28, I29 - I28, I32, I33) [0 <= I28 - 1 /\ I28 <= I29 /\ 0 <= I29 - 1]
15.67/15.61	  f4(I34, I35, I36, I37) -> f4(I35, I35, I38, I39) [1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1]
15.67/15.61	  f3(I40, I41, I42, I43) -> f3(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  f5(I45, I46, I47, I48) -> f3(I49, I46, I47 + 1, I48) [0 <= I49 - 1 /\ 0 <= I45 - 1 /\ -1 <= I48 - 1 /\ I49 <= I45]
15.67/15.61	  f3(I50, I51, I52, I53) -> f3(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  f3(I55, I56, I57, I58) -> f3(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  f3(I60, I61, I62, I63) -> f4(I62, I61, I64, I65) [0 <= I60 - 1 /\ I62 <= I63 /\ I61 <= I63]
15.67/15.61	  f3(I66, I67, I68, I69) -> f2(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	  f2(I72, I73, I74, I75) -> f3(I76, I73, 0, I74) [0 <= I76 - 1 /\ 0 <= I72 - 1 /\ I76 <= I72 /\ -1 <= I74 - 1 /\ I73 <= I74]
15.67/15.61	  f1(I77, I78, I79, I80) -> f2(I81, 0, I78, I82) [0 <= I81 - 1 /\ 0 <= I77 - 1 /\ -1 <= I78 - 1 /\ I81 <= I77]
15.67/15.61	
15.67/15.61	We use the reverse value criterion with the projection function NU:
15.67/15.61	  NU[f2#(z1,z2,z3,z4)] = z3 + -1 * z2
15.67/15.61	  NU[f3#(z1,z2,z3,z4)] = z4 + -1 * (z2 + 1)
15.67/15.61	
15.67/15.61	This gives the following inequalities:
15.67/15.61	  0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43  ==>  I43 + -1 * (I41 + 1) >= I43 + -1 * (I41 + 1)
15.67/15.61	  0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53  ==>  I53 + -1 * (I51 + 1) >= I53 + -1 * (I51 + 1)
15.67/15.61	  0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1  ==>  I58 + -1 * (I56 + 1) >= I58 + -1 * (0 + 1)
15.67/15.61	  0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1  ==>  I69 + -1 * (I67 + 1) >= I69 + -1 * (I67 + 1)
15.67/15.61	  0 <= I76 - 1 /\ 0 <= I72 - 1 /\ I76 <= I72 /\ -1 <= I74 - 1 /\ I73 <= I74  ==>  I74 + -1 * I73 > I74 + -1 * (I73 + 1)  with  I74 + -1 * I73 >= 0
15.67/15.61	
15.67/15.61	We remove all the strictly oriented dependency pairs.
15.67/15.61	
15.67/15.61	DP problem for innermost termination.
15.67/15.61	P =
15.67/15.61	  f3#(I40, I41, I42, I43) -> f3#(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  f3#(I50, I51, I52, I53) -> f3#(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  f3#(I55, I56, I57, I58) -> f3#(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  f3#(I66, I67, I68, I69) -> f2#(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	R = 
15.67/15.61	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
15.67/15.61	  f4(I0, I1, I2, I3) -> f4(I0 - 1, I1, I4, I5) [0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1]
15.67/15.61	  f6(I6, I7, I8, I9) -> f4(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	  f4(I13, I14, I15, I16) -> f6(I13, I14, I13 - 1, I17) [0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1]
15.67/15.61	  f7(I18, I19, I20, I21) -> f6(I19, I18, I19 - 1, I22) [0 <= I19 - 1]
15.67/15.61	  f4(I23, I24, I25, I26) -> f6(I23, I24, I23 - 1, I27) [I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1]
15.67/15.61	  f4(I28, I29, I30, I31) -> f4(I28, I29 - I28, I32, I33) [0 <= I28 - 1 /\ I28 <= I29 /\ 0 <= I29 - 1]
15.67/15.61	  f4(I34, I35, I36, I37) -> f4(I35, I35, I38, I39) [1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1]
15.67/15.61	  f3(I40, I41, I42, I43) -> f3(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  f5(I45, I46, I47, I48) -> f3(I49, I46, I47 + 1, I48) [0 <= I49 - 1 /\ 0 <= I45 - 1 /\ -1 <= I48 - 1 /\ I49 <= I45]
15.67/15.61	  f3(I50, I51, I52, I53) -> f3(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  f3(I55, I56, I57, I58) -> f3(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  f3(I60, I61, I62, I63) -> f4(I62, I61, I64, I65) [0 <= I60 - 1 /\ I62 <= I63 /\ I61 <= I63]
15.67/15.61	  f3(I66, I67, I68, I69) -> f2(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	  f2(I72, I73, I74, I75) -> f3(I76, I73, 0, I74) [0 <= I76 - 1 /\ 0 <= I72 - 1 /\ I76 <= I72 /\ -1 <= I74 - 1 /\ I73 <= I74]
15.67/15.61	  f1(I77, I78, I79, I80) -> f2(I81, 0, I78, I82) [0 <= I81 - 1 /\ 0 <= I77 - 1 /\ -1 <= I78 - 1 /\ I81 <= I77]
15.67/15.61	
15.67/15.61	The dependency graph for this problem is:
15.67/15.61	  8 -> 8, 10, 11, 13
15.67/15.61	  10 -> 8, 11, 13
15.67/15.61	  11 -> 8, 10, 11, 13
15.67/15.61	  13 -> 
15.67/15.61	Where:
15.67/15.61	  8) f3#(I40, I41, I42, I43) -> f3#(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  10) f3#(I50, I51, I52, I53) -> f3#(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  11) f3#(I55, I56, I57, I58) -> f3#(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  13) f3#(I66, I67, I68, I69) -> f2#(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	
15.67/15.61	We have the following SCCs.
15.67/15.61	  { 8, 10, 11 }
15.67/15.61	
15.67/15.61	DP problem for innermost termination.
15.67/15.61	P =
15.67/15.61	  f3#(I40, I41, I42, I43) -> f3#(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  f3#(I50, I51, I52, I53) -> f3#(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  f3#(I55, I56, I57, I58) -> f3#(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	R = 
15.67/15.61	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
15.67/15.61	  f4(I0, I1, I2, I3) -> f4(I0 - 1, I1, I4, I5) [0 <= I1 - 1 /\ 1 <= I0 - 1 /\ I0 <= I1 /\ I0 - 1 <= I0 - 1 /\ 0 <= y1 - 1]
15.67/15.61	  f6(I6, I7, I8, I9) -> f4(I8, I7, I10, I11) [0 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I12 - 1 /\ I8 <= I6 - 1]
15.67/15.61	  f4(I13, I14, I15, I16) -> f6(I13, I14, I13 - 1, I17) [0 <= I13 - 1 /\ I13 <= I14 /\ 0 <= I14 - 1]
15.67/15.61	  f7(I18, I19, I20, I21) -> f6(I19, I18, I19 - 1, I22) [0 <= I19 - 1]
15.67/15.61	  f4(I23, I24, I25, I26) -> f6(I23, I24, I23 - 1, I27) [I23 <= I24 /\ I24 - I23 = 0 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1]
15.67/15.61	  f4(I28, I29, I30, I31) -> f4(I28, I29 - I28, I32, I33) [0 <= I28 - 1 /\ I28 <= I29 /\ 0 <= I29 - 1]
15.67/15.61	  f4(I34, I35, I36, I37) -> f4(I35, I35, I38, I39) [1 <= I34 - 1 /\ I35 <= I34 - 1 /\ 0 <= I35 - 1]
15.67/15.61	  f3(I40, I41, I42, I43) -> f3(I44, I41, I42 + 1, I43) [0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43]
15.67/15.61	  f5(I45, I46, I47, I48) -> f3(I49, I46, I47 + 1, I48) [0 <= I49 - 1 /\ 0 <= I45 - 1 /\ -1 <= I48 - 1 /\ I49 <= I45]
15.67/15.61	  f3(I50, I51, I52, I53) -> f3(I54, I51, 1, I53) [0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53]
15.67/15.61	  f3(I55, I56, I57, I58) -> f3(I59, 0, I57 + 1, I58) [0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1]
15.67/15.61	  f3(I60, I61, I62, I63) -> f4(I62, I61, I64, I65) [0 <= I60 - 1 /\ I62 <= I63 /\ I61 <= I63]
15.67/15.61	  f3(I66, I67, I68, I69) -> f2(I70, I67 + 1, I69, I71) [0 <= I70 - 1 /\ 0 <= I66 - 1 /\ I70 <= I66 /\ -1 <= I69 - 1 /\ I69 <= I68 - 1]
15.67/15.61	  f2(I72, I73, I74, I75) -> f3(I76, I73, 0, I74) [0 <= I76 - 1 /\ 0 <= I72 - 1 /\ I76 <= I72 /\ -1 <= I74 - 1 /\ I73 <= I74]
15.67/15.61	  f1(I77, I78, I79, I80) -> f2(I81, 0, I78, I82) [0 <= I81 - 1 /\ 0 <= I77 - 1 /\ -1 <= I78 - 1 /\ I81 <= I77]
15.67/15.61	
15.67/15.61	We use the reverse value criterion with the projection function NU:
15.67/15.61	  NU[f3#(z1,z2,z3,z4)] = z4 + -1 * z3
15.67/15.61	
15.67/15.61	This gives the following inequalities:
15.67/15.61	  0 <= I44 - 1 /\ 0 <= I40 - 1 /\ I44 <= I40 /\ -1 <= I43 - 1 /\ I42 <= I43 /\ I41 <= I43  ==>  I43 + -1 * I42 > I43 + -1 * (I42 + 1)  with  I43 + -1 * I42 >= 0
15.67/15.61	  0 = I52 /\ 0 <= I54 - 1 /\ 0 <= I50 - 1 /\ I54 <= I50 /\ -1 <= I53 - 1 /\ I51 <= I53  ==>  I53 + -1 * I52 > I53 + -1 * 1  with  I53 + -1 * I52 >= 0
15.67/15.61	  0 = I56 /\ 0 <= I59 - 1 /\ 0 <= I55 - 1 /\ I59 <= I55 /\ I57 <= I58 /\ -1 <= I58 - 1  ==>  I58 + -1 * I57 > I58 + -1 * (I57 + 1)  with  I58 + -1 * I57 >= 0
15.67/15.61	
15.67/15.61	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
15.67/18.59	EOF