1.08/1.49	MAYBE
1.08/1.49	
1.08/1.49	DP problem for innermost termination.
1.08/1.49	P =
1.08/1.49	  init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
1.08/1.49	  f4#(I0, I1, I2, I3) -> f4#(I0, I4, I2 + 1, I3) [I2 <= I3 - 1 /\ I0 <= I3 - 1 /\ y2 <= y1 - 1 /\ I4 <= I1 /\ 0 <= I1 - 1 /\ 0 <= I4 - 1]
1.08/1.49	  f4#(I5, I6, I7, I8) -> f4#(I5, I9, I7 + 1, I8) [I7 <= I8 - 1 /\ I5 <= I8 - 1 /\ I10 <= I11 /\ I9 <= I6 /\ 0 <= I6 - 1 /\ 0 <= I9 - 1]
1.08/1.49	  f5#(I12, I13, I14, I15) -> f5#(I16, I13 + 1, I15 - 1, I15) [0 <= I16 - 1 /\ 0 <= I12 - 1 /\ I16 <= I12 /\ I13 <= I14 - 1 /\ -1 <= I15 - 1]
1.08/1.49	  f3#(I17, I18, I19, I20) -> f5#(I21, 0, I20 - 1, I20) [0 <= I21 - 1 /\ 0 <= I17 - 1 /\ I21 <= I17 /\ -1 <= I20 - 1 /\ I19 <= I18]
1.08/1.49	  f4#(I22, I23, I24, I25) -> f3#(I26, I22 + 1, I25 - 1, I25) [0 <= I26 - 1 /\ 0 <= I23 - 1 /\ I26 <= I23 /\ I25 <= I24 /\ -1 <= I25 - 1]
1.08/1.49	  f3#(I27, I28, I29, I30) -> f4#(I28, I31, I28 + 1, I30) [0 <= I31 - 1 /\ 0 <= I27 - 1 /\ I31 <= I27 /\ I28 <= I29 - 1 /\ -1 <= I28 - 1]
1.08/1.49	  f2#(I32, I33, I34, I35) -> f3#(I36, 0, I35 - 1, I35) [0 <= I36 - 1 /\ 0 <= I32 - 1 /\ I36 <= I32 /\ -1 <= I35 - 1 /\ I34 <= I33]
1.08/1.49	  f2#(I37, I38, I39, I40) -> f2#(I41, I38 + 1, I40 - 1, I40) [0 <= I41 - 1 /\ 0 <= I37 - 1 /\ I41 <= I37 /\ -1 <= I40 - 1 /\ I38 <= I40 - 1 /\ I38 <= I39 - 1]
1.08/1.49	  f1#(I42, I43, I44, I45) -> f2#(I46, 0, I43 - 1, I43) [0 <= I46 - 1 /\ 0 <= I42 - 1 /\ -1 <= I43 - 1 /\ I46 <= I42]
1.08/1.49	R = 
1.08/1.49	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
1.08/1.49	  f4(I0, I1, I2, I3) -> f4(I0, I4, I2 + 1, I3) [I2 <= I3 - 1 /\ I0 <= I3 - 1 /\ y2 <= y1 - 1 /\ I4 <= I1 /\ 0 <= I1 - 1 /\ 0 <= I4 - 1]
1.08/1.49	  f4(I5, I6, I7, I8) -> f4(I5, I9, I7 + 1, I8) [I7 <= I8 - 1 /\ I5 <= I8 - 1 /\ I10 <= I11 /\ I9 <= I6 /\ 0 <= I6 - 1 /\ 0 <= I9 - 1]
1.08/1.49	  f5(I12, I13, I14, I15) -> f5(I16, I13 + 1, I15 - 1, I15) [0 <= I16 - 1 /\ 0 <= I12 - 1 /\ I16 <= I12 /\ I13 <= I14 - 1 /\ -1 <= I15 - 1]
1.08/1.49	  f3(I17, I18, I19, I20) -> f5(I21, 0, I20 - 1, I20) [0 <= I21 - 1 /\ 0 <= I17 - 1 /\ I21 <= I17 /\ -1 <= I20 - 1 /\ I19 <= I18]
1.08/1.49	  f4(I22, I23, I24, I25) -> f3(I26, I22 + 1, I25 - 1, I25) [0 <= I26 - 1 /\ 0 <= I23 - 1 /\ I26 <= I23 /\ I25 <= I24 /\ -1 <= I25 - 1]
1.08/1.49	  f3(I27, I28, I29, I30) -> f4(I28, I31, I28 + 1, I30) [0 <= I31 - 1 /\ 0 <= I27 - 1 /\ I31 <= I27 /\ I28 <= I29 - 1 /\ -1 <= I28 - 1]
1.08/1.49	  f2(I32, I33, I34, I35) -> f3(I36, 0, I35 - 1, I35) [0 <= I36 - 1 /\ 0 <= I32 - 1 /\ I36 <= I32 /\ -1 <= I35 - 1 /\ I34 <= I33]
1.08/1.49	  f2(I37, I38, I39, I40) -> f2(I41, I38 + 1, I40 - 1, I40) [0 <= I41 - 1 /\ 0 <= I37 - 1 /\ I41 <= I37 /\ -1 <= I40 - 1 /\ I38 <= I40 - 1 /\ I38 <= I39 - 1]
1.08/1.49	  f1(I42, I43, I44, I45) -> f2(I46, 0, I43 - 1, I43) [0 <= I46 - 1 /\ 0 <= I42 - 1 /\ -1 <= I43 - 1 /\ I46 <= I42]
1.08/1.49	
1.08/1.49	The dependency graph for this problem is:
1.08/1.49	  0 -> 9
1.08/1.49	  1 -> 1, 2, 5
1.08/1.49	  2 -> 1, 2, 5
1.08/1.49	  3 -> 3
1.08/1.49	  4 -> 3
1.08/1.49	  5 -> 4, 6
1.08/1.49	  6 -> 1, 2, 5
1.08/1.49	  7 -> 4, 6
1.08/1.49	  8 -> 7, 8
1.08/1.49	  9 -> 7, 8
1.08/1.49	Where:
1.08/1.49	  0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
1.08/1.49	  1) f4#(I0, I1, I2, I3) -> f4#(I0, I4, I2 + 1, I3) [I2 <= I3 - 1 /\ I0 <= I3 - 1 /\ y2 <= y1 - 1 /\ I4 <= I1 /\ 0 <= I1 - 1 /\ 0 <= I4 - 1]
1.08/1.49	  2) f4#(I5, I6, I7, I8) -> f4#(I5, I9, I7 + 1, I8) [I7 <= I8 - 1 /\ I5 <= I8 - 1 /\ I10 <= I11 /\ I9 <= I6 /\ 0 <= I6 - 1 /\ 0 <= I9 - 1]
1.08/1.49	  3) f5#(I12, I13, I14, I15) -> f5#(I16, I13 + 1, I15 - 1, I15) [0 <= I16 - 1 /\ 0 <= I12 - 1 /\ I16 <= I12 /\ I13 <= I14 - 1 /\ -1 <= I15 - 1]
1.08/1.49	  4) f3#(I17, I18, I19, I20) -> f5#(I21, 0, I20 - 1, I20) [0 <= I21 - 1 /\ 0 <= I17 - 1 /\ I21 <= I17 /\ -1 <= I20 - 1 /\ I19 <= I18]
1.08/1.49	  5) f4#(I22, I23, I24, I25) -> f3#(I26, I22 + 1, I25 - 1, I25) [0 <= I26 - 1 /\ 0 <= I23 - 1 /\ I26 <= I23 /\ I25 <= I24 /\ -1 <= I25 - 1]
1.08/1.49	  6) f3#(I27, I28, I29, I30) -> f4#(I28, I31, I28 + 1, I30) [0 <= I31 - 1 /\ 0 <= I27 - 1 /\ I31 <= I27 /\ I28 <= I29 - 1 /\ -1 <= I28 - 1]
1.08/1.49	  7) f2#(I32, I33, I34, I35) -> f3#(I36, 0, I35 - 1, I35) [0 <= I36 - 1 /\ 0 <= I32 - 1 /\ I36 <= I32 /\ -1 <= I35 - 1 /\ I34 <= I33]
1.08/1.49	  8) f2#(I37, I38, I39, I40) -> f2#(I41, I38 + 1, I40 - 1, I40) [0 <= I41 - 1 /\ 0 <= I37 - 1 /\ I41 <= I37 /\ -1 <= I40 - 1 /\ I38 <= I40 - 1 /\ I38 <= I39 - 1]
1.08/1.49	  9) f1#(I42, I43, I44, I45) -> f2#(I46, 0, I43 - 1, I43) [0 <= I46 - 1 /\ 0 <= I42 - 1 /\ -1 <= I43 - 1 /\ I46 <= I42]
1.08/1.49	
1.08/1.49	We have the following SCCs.
1.08/1.49	  { 8 }
1.08/1.49	  { 1, 2, 5, 6 }
1.08/1.49	  { 3 }
1.08/1.49	
1.08/1.49	DP problem for innermost termination.
1.08/1.49	P =
1.08/1.49	  f5#(I12, I13, I14, I15) -> f5#(I16, I13 + 1, I15 - 1, I15) [0 <= I16 - 1 /\ 0 <= I12 - 1 /\ I16 <= I12 /\ I13 <= I14 - 1 /\ -1 <= I15 - 1]
1.08/1.49	R = 
1.08/1.49	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
1.08/1.49	  f4(I0, I1, I2, I3) -> f4(I0, I4, I2 + 1, I3) [I2 <= I3 - 1 /\ I0 <= I3 - 1 /\ y2 <= y1 - 1 /\ I4 <= I1 /\ 0 <= I1 - 1 /\ 0 <= I4 - 1]
1.08/1.49	  f4(I5, I6, I7, I8) -> f4(I5, I9, I7 + 1, I8) [I7 <= I8 - 1 /\ I5 <= I8 - 1 /\ I10 <= I11 /\ I9 <= I6 /\ 0 <= I6 - 1 /\ 0 <= I9 - 1]
1.08/1.49	  f5(I12, I13, I14, I15) -> f5(I16, I13 + 1, I15 - 1, I15) [0 <= I16 - 1 /\ 0 <= I12 - 1 /\ I16 <= I12 /\ I13 <= I14 - 1 /\ -1 <= I15 - 1]
1.08/1.49	  f3(I17, I18, I19, I20) -> f5(I21, 0, I20 - 1, I20) [0 <= I21 - 1 /\ 0 <= I17 - 1 /\ I21 <= I17 /\ -1 <= I20 - 1 /\ I19 <= I18]
1.08/1.49	  f4(I22, I23, I24, I25) -> f3(I26, I22 + 1, I25 - 1, I25) [0 <= I26 - 1 /\ 0 <= I23 - 1 /\ I26 <= I23 /\ I25 <= I24 /\ -1 <= I25 - 1]
1.08/1.49	  f3(I27, I28, I29, I30) -> f4(I28, I31, I28 + 1, I30) [0 <= I31 - 1 /\ 0 <= I27 - 1 /\ I31 <= I27 /\ I28 <= I29 - 1 /\ -1 <= I28 - 1]
1.08/1.49	  f2(I32, I33, I34, I35) -> f3(I36, 0, I35 - 1, I35) [0 <= I36 - 1 /\ 0 <= I32 - 1 /\ I36 <= I32 /\ -1 <= I35 - 1 /\ I34 <= I33]
1.08/1.49	  f2(I37, I38, I39, I40) -> f2(I41, I38 + 1, I40 - 1, I40) [0 <= I41 - 1 /\ 0 <= I37 - 1 /\ I41 <= I37 /\ -1 <= I40 - 1 /\ I38 <= I40 - 1 /\ I38 <= I39 - 1]
1.08/1.49	  f1(I42, I43, I44, I45) -> f2(I46, 0, I43 - 1, I43) [0 <= I46 - 1 /\ 0 <= I42 - 1 /\ -1 <= I43 - 1 /\ I46 <= I42]
1.08/1.49	
1.08/4.47	EOF