1.69/1.72	MAYBE
1.69/1.72	
1.69/1.72	DP problem for innermost termination.
1.69/1.72	P =
1.69/1.72	  init#(x1, x2, x3, x4) -> f3#(rnd1, rnd2, rnd3, rnd4) 
1.69/1.72	  f5#(I0, I1, I2, I3) -> f5#(I0, I1, I2 - 1, I3) [0 <= I2 - 1]
1.69/1.72	  f5#(I4, I5, I6, I7) -> f4#(I5 + 1, I4, I7, I8) [0 = I6]
1.69/1.72	  f4#(I9, I10, I11, I12) -> f5#(I10, I9, I13, I11 + 1) [0 <= I11 - 1 /\ I9 <= I10 - 1 /\ -1 <= I13 - 1]
1.69/1.72	  f3#(I14, I15, I16, I17) -> f4#(0, I18, 1, I19) [0 <= I14 - 1 /\ -1 <= I18 - 1 /\ -1 <= I15 - 1]
1.69/1.72	  f2#(I20, I21, I22, I23) -> f2#(I24, I25, I26, I27) [0 <= I24 - 1 /\ 2 <= I20 - 1 /\ I24 <= I20]
1.69/1.72	  f2#(I28, I29, I30, I31) -> f2#(I32, I33, I34, I35) [-1 <= I32 - 1 /\ 1 <= I28 - 1 /\ I32 + 2 <= I28]
1.69/1.72	  f2#(I36, I37, I38, I39) -> f2#(I40, I41, I42, I43) [-1 <= I40 - 1 /\ 2 <= I36 - 1 /\ I40 + 2 <= I36]
1.69/1.72	  f3#(I44, I45, I46, I47) -> f2#(I48, I49, I50, I51) [-1 <= I48 - 1 /\ 0 <= I44 - 1]
1.69/1.72	  f1#(I52, I53, I54, I55) -> f2#(I56, I57, I58, I59) [-1 <= I56 - 1 /\ -1 <= I52 - 1 /\ I56 <= I52]
1.69/1.72	R = 
1.69/1.72	  init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) 
1.69/1.72	  f5(I0, I1, I2, I3) -> f5(I0, I1, I2 - 1, I3) [0 <= I2 - 1]
1.69/1.72	  f5(I4, I5, I6, I7) -> f4(I5 + 1, I4, I7, I8) [0 = I6]
1.69/1.72	  f4(I9, I10, I11, I12) -> f5(I10, I9, I13, I11 + 1) [0 <= I11 - 1 /\ I9 <= I10 - 1 /\ -1 <= I13 - 1]
1.69/1.72	  f3(I14, I15, I16, I17) -> f4(0, I18, 1, I19) [0 <= I14 - 1 /\ -1 <= I18 - 1 /\ -1 <= I15 - 1]
1.69/1.72	  f2(I20, I21, I22, I23) -> f2(I24, I25, I26, I27) [0 <= I24 - 1 /\ 2 <= I20 - 1 /\ I24 <= I20]
1.69/1.72	  f2(I28, I29, I30, I31) -> f2(I32, I33, I34, I35) [-1 <= I32 - 1 /\ 1 <= I28 - 1 /\ I32 + 2 <= I28]
1.69/1.72	  f2(I36, I37, I38, I39) -> f2(I40, I41, I42, I43) [-1 <= I40 - 1 /\ 2 <= I36 - 1 /\ I40 + 2 <= I36]
1.69/1.72	  f3(I44, I45, I46, I47) -> f2(I48, I49, I50, I51) [-1 <= I48 - 1 /\ 0 <= I44 - 1]
1.69/1.72	  f1(I52, I53, I54, I55) -> f2(I56, I57, I58, I59) [-1 <= I56 - 1 /\ -1 <= I52 - 1 /\ I56 <= I52]
1.69/1.72	
1.69/1.72	The dependency graph for this problem is:
1.69/1.72	  0 -> 4, 8
1.69/1.72	  1 -> 1, 2
1.69/1.72	  2 -> 3
1.69/1.72	  3 -> 1, 2
1.69/1.72	  4 -> 3
1.69/1.72	  5 -> 5, 6, 7
1.69/1.72	  6 -> 5, 6, 7
1.69/1.72	  7 -> 5, 6, 7
1.69/1.72	  8 -> 5, 6, 7
1.69/1.72	  9 -> 5, 6, 7
1.69/1.72	Where:
1.69/1.72	  0) init#(x1, x2, x3, x4) -> f3#(rnd1, rnd2, rnd3, rnd4) 
1.69/1.72	  1) f5#(I0, I1, I2, I3) -> f5#(I0, I1, I2 - 1, I3) [0 <= I2 - 1]
1.69/1.72	  2) f5#(I4, I5, I6, I7) -> f4#(I5 + 1, I4, I7, I8) [0 = I6]
1.69/1.72	  3) f4#(I9, I10, I11, I12) -> f5#(I10, I9, I13, I11 + 1) [0 <= I11 - 1 /\ I9 <= I10 - 1 /\ -1 <= I13 - 1]
1.69/1.72	  4) f3#(I14, I15, I16, I17) -> f4#(0, I18, 1, I19) [0 <= I14 - 1 /\ -1 <= I18 - 1 /\ -1 <= I15 - 1]
1.69/1.72	  5) f2#(I20, I21, I22, I23) -> f2#(I24, I25, I26, I27) [0 <= I24 - 1 /\ 2 <= I20 - 1 /\ I24 <= I20]
1.69/1.72	  6) f2#(I28, I29, I30, I31) -> f2#(I32, I33, I34, I35) [-1 <= I32 - 1 /\ 1 <= I28 - 1 /\ I32 + 2 <= I28]
1.69/1.72	  7) f2#(I36, I37, I38, I39) -> f2#(I40, I41, I42, I43) [-1 <= I40 - 1 /\ 2 <= I36 - 1 /\ I40 + 2 <= I36]
1.69/1.72	  8) f3#(I44, I45, I46, I47) -> f2#(I48, I49, I50, I51) [-1 <= I48 - 1 /\ 0 <= I44 - 1]
1.69/1.72	  9) f1#(I52, I53, I54, I55) -> f2#(I56, I57, I58, I59) [-1 <= I56 - 1 /\ -1 <= I52 - 1 /\ I56 <= I52]
1.69/1.72	
1.69/1.72	We have the following SCCs.
1.69/1.72	  { 1, 2, 3 }
1.69/1.72	  { 5, 6, 7 }
1.69/1.72	
1.69/1.72	DP problem for innermost termination.
1.69/1.72	P =
1.69/1.72	  f2#(I20, I21, I22, I23) -> f2#(I24, I25, I26, I27) [0 <= I24 - 1 /\ 2 <= I20 - 1 /\ I24 <= I20]
1.69/1.72	  f2#(I28, I29, I30, I31) -> f2#(I32, I33, I34, I35) [-1 <= I32 - 1 /\ 1 <= I28 - 1 /\ I32 + 2 <= I28]
1.69/1.72	  f2#(I36, I37, I38, I39) -> f2#(I40, I41, I42, I43) [-1 <= I40 - 1 /\ 2 <= I36 - 1 /\ I40 + 2 <= I36]
1.69/1.72	R = 
1.69/1.72	  init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) 
1.69/1.72	  f5(I0, I1, I2, I3) -> f5(I0, I1, I2 - 1, I3) [0 <= I2 - 1]
1.69/1.72	  f5(I4, I5, I6, I7) -> f4(I5 + 1, I4, I7, I8) [0 = I6]
1.69/1.72	  f4(I9, I10, I11, I12) -> f5(I10, I9, I13, I11 + 1) [0 <= I11 - 1 /\ I9 <= I10 - 1 /\ -1 <= I13 - 1]
1.69/1.72	  f3(I14, I15, I16, I17) -> f4(0, I18, 1, I19) [0 <= I14 - 1 /\ -1 <= I18 - 1 /\ -1 <= I15 - 1]
1.69/1.72	  f2(I20, I21, I22, I23) -> f2(I24, I25, I26, I27) [0 <= I24 - 1 /\ 2 <= I20 - 1 /\ I24 <= I20]
1.69/1.72	  f2(I28, I29, I30, I31) -> f2(I32, I33, I34, I35) [-1 <= I32 - 1 /\ 1 <= I28 - 1 /\ I32 + 2 <= I28]
1.69/1.72	  f2(I36, I37, I38, I39) -> f2(I40, I41, I42, I43) [-1 <= I40 - 1 /\ 2 <= I36 - 1 /\ I40 + 2 <= I36]
1.69/1.72	  f3(I44, I45, I46, I47) -> f2(I48, I49, I50, I51) [-1 <= I48 - 1 /\ 0 <= I44 - 1]
1.69/1.72	  f1(I52, I53, I54, I55) -> f2(I56, I57, I58, I59) [-1 <= I56 - 1 /\ -1 <= I52 - 1 /\ I56 <= I52]
1.69/1.72	
1.69/1.72	We use the basic value criterion with the projection function NU:
1.69/1.72	  NU[f2#(z1,z2,z3,z4)] = z1
1.69/1.72	
1.69/1.72	This gives the following inequalities:
1.69/1.72	  0 <= I24 - 1 /\ 2 <= I20 - 1 /\ I24 <= I20  ==>  I20 (>! \union =) I24
1.69/1.72	  -1 <= I32 - 1 /\ 1 <= I28 - 1 /\ I32 + 2 <= I28  ==>  I28 >! I32
1.69/1.72	  -1 <= I40 - 1 /\ 2 <= I36 - 1 /\ I40 + 2 <= I36  ==>  I36 >! I40
1.69/1.72	
1.69/1.72	We remove all the strictly oriented dependency pairs.
1.69/1.72	
1.69/1.72	DP problem for innermost termination.
1.69/1.72	P =
1.69/1.72	  f2#(I20, I21, I22, I23) -> f2#(I24, I25, I26, I27) [0 <= I24 - 1 /\ 2 <= I20 - 1 /\ I24 <= I20]
1.69/1.72	R = 
1.69/1.72	  init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) 
1.69/1.72	  f5(I0, I1, I2, I3) -> f5(I0, I1, I2 - 1, I3) [0 <= I2 - 1]
1.69/1.72	  f5(I4, I5, I6, I7) -> f4(I5 + 1, I4, I7, I8) [0 = I6]
1.69/1.72	  f4(I9, I10, I11, I12) -> f5(I10, I9, I13, I11 + 1) [0 <= I11 - 1 /\ I9 <= I10 - 1 /\ -1 <= I13 - 1]
1.69/1.72	  f3(I14, I15, I16, I17) -> f4(0, I18, 1, I19) [0 <= I14 - 1 /\ -1 <= I18 - 1 /\ -1 <= I15 - 1]
1.69/1.72	  f2(I20, I21, I22, I23) -> f2(I24, I25, I26, I27) [0 <= I24 - 1 /\ 2 <= I20 - 1 /\ I24 <= I20]
1.69/1.72	  f2(I28, I29, I30, I31) -> f2(I32, I33, I34, I35) [-1 <= I32 - 1 /\ 1 <= I28 - 1 /\ I32 + 2 <= I28]
1.69/1.72	  f2(I36, I37, I38, I39) -> f2(I40, I41, I42, I43) [-1 <= I40 - 1 /\ 2 <= I36 - 1 /\ I40 + 2 <= I36]
1.69/1.72	  f3(I44, I45, I46, I47) -> f2(I48, I49, I50, I51) [-1 <= I48 - 1 /\ 0 <= I44 - 1]
1.69/1.72	  f1(I52, I53, I54, I55) -> f2(I56, I57, I58, I59) [-1 <= I56 - 1 /\ -1 <= I52 - 1 /\ I56 <= I52]
1.69/1.72	
1.69/4.68	EOF