12.34/12.18	MAYBE
12.34/12.18	
12.34/12.18	DP problem for innermost termination.
12.34/12.18	P =
12.34/12.18	  f8#(x1, x2, x3, x4, x5) -> f7#(x1, x2, x3, x4, x5) 
12.34/12.18	  f7#(I0, I1, I2, I3, I4) -> f1#(I0, I1, I2, I3, I4) 
12.34/12.18	  f6#(I5, I6, I7, I8, I9) -> f1#(I5, I6, I7, I8, I9) 
12.34/12.18	  f5#(I10, I11, I12, I13, I14) -> f6#(I10, I11, I12, 1 + I13, I14) 
12.34/12.18	  f4#(I15, I16, I17, I18, I19) -> f5#(I15, I16, I17, I18, I19) [I16 = I16]
12.34/12.18	  f1#(I20, I21, I22, I23, I24) -> f4#(I20, I21, rnd3, I23, I24) [rnd3 = rnd3 /\ 0 <= -1 - I23 + I24]
12.34/12.18	  f3#(I25, I26, I27, I28, I29) -> f1#(I25, I26, I27, I28, I29) 
12.34/12.18	  f1#(I30, I31, I32, I33, I34) -> f3#(I30, I31, I35, I33, 1 + I34) [0 <= I35 /\ I35 <= 0 /\ I35 = I35 /\ 0 <= -1 - I33 + I34]
12.34/12.18	R = 
12.34/12.18	  f8(x1, x2, x3, x4, x5) -> f7(x1, x2, x3, x4, x5) 
12.34/12.18	  f7(I0, I1, I2, I3, I4) -> f1(I0, I1, I2, I3, I4) 
12.34/12.18	  f6(I5, I6, I7, I8, I9) -> f1(I5, I6, I7, I8, I9) 
12.34/12.18	  f5(I10, I11, I12, I13, I14) -> f6(I10, I11, I12, 1 + I13, I14) 
12.34/12.18	  f4(I15, I16, I17, I18, I19) -> f5(I15, I16, I17, I18, I19) [I16 = I16]
12.34/12.18	  f1(I20, I21, I22, I23, I24) -> f4(I20, I21, rnd3, I23, I24) [rnd3 = rnd3 /\ 0 <= -1 - I23 + I24]
12.34/12.18	  f3(I25, I26, I27, I28, I29) -> f1(I25, I26, I27, I28, I29) 
12.34/12.18	  f1(I30, I31, I32, I33, I34) -> f3(I30, I31, I35, I33, 1 + I34) [0 <= I35 /\ I35 <= 0 /\ I35 = I35 /\ 0 <= -1 - I33 + I34]
12.34/12.18	  f1(I36, I37, I38, I39, I40) -> f2(rnd1, I37, I38, I39, I40) [rnd1 = rnd1 /\ -1 * I39 + I40 <= 0]
12.34/12.18	
12.34/12.18	The dependency graph for this problem is:
12.34/12.18	  0 -> 1
12.34/12.18	  1 -> 5, 7
12.34/12.18	  2 -> 5, 7
12.34/12.18	  3 -> 2
12.34/12.18	  4 -> 3
12.34/12.18	  5 -> 4
12.34/12.18	  6 -> 5, 7
12.34/12.18	  7 -> 6
12.34/12.18	Where:
12.34/12.18	  0) f8#(x1, x2, x3, x4, x5) -> f7#(x1, x2, x3, x4, x5) 
12.34/12.18	  1) f7#(I0, I1, I2, I3, I4) -> f1#(I0, I1, I2, I3, I4) 
12.34/12.18	  2) f6#(I5, I6, I7, I8, I9) -> f1#(I5, I6, I7, I8, I9) 
12.34/12.18	  3) f5#(I10, I11, I12, I13, I14) -> f6#(I10, I11, I12, 1 + I13, I14) 
12.34/12.18	  4) f4#(I15, I16, I17, I18, I19) -> f5#(I15, I16, I17, I18, I19) [I16 = I16]
12.34/12.18	  5) f1#(I20, I21, I22, I23, I24) -> f4#(I20, I21, rnd3, I23, I24) [rnd3 = rnd3 /\ 0 <= -1 - I23 + I24]
12.34/12.18	  6) f3#(I25, I26, I27, I28, I29) -> f1#(I25, I26, I27, I28, I29) 
12.34/12.18	  7) f1#(I30, I31, I32, I33, I34) -> f3#(I30, I31, I35, I33, 1 + I34) [0 <= I35 /\ I35 <= 0 /\ I35 = I35 /\ 0 <= -1 - I33 + I34]
12.34/12.18	
12.34/12.18	We have the following SCCs.
12.34/12.18	  { 2, 3, 4, 5, 6, 7 }
12.34/12.18	
12.34/12.18	DP problem for innermost termination.
12.34/12.18	P =
12.34/12.18	  f6#(I5, I6, I7, I8, I9) -> f1#(I5, I6, I7, I8, I9) 
12.34/12.18	  f5#(I10, I11, I12, I13, I14) -> f6#(I10, I11, I12, 1 + I13, I14) 
12.34/12.18	  f4#(I15, I16, I17, I18, I19) -> f5#(I15, I16, I17, I18, I19) [I16 = I16]
12.34/12.18	  f1#(I20, I21, I22, I23, I24) -> f4#(I20, I21, rnd3, I23, I24) [rnd3 = rnd3 /\ 0 <= -1 - I23 + I24]
12.34/12.18	  f3#(I25, I26, I27, I28, I29) -> f1#(I25, I26, I27, I28, I29) 
12.34/12.18	  f1#(I30, I31, I32, I33, I34) -> f3#(I30, I31, I35, I33, 1 + I34) [0 <= I35 /\ I35 <= 0 /\ I35 = I35 /\ 0 <= -1 - I33 + I34]
12.34/12.18	R = 
12.34/12.18	  f8(x1, x2, x3, x4, x5) -> f7(x1, x2, x3, x4, x5) 
12.34/12.18	  f7(I0, I1, I2, I3, I4) -> f1(I0, I1, I2, I3, I4) 
12.34/12.18	  f6(I5, I6, I7, I8, I9) -> f1(I5, I6, I7, I8, I9) 
12.34/12.18	  f5(I10, I11, I12, I13, I14) -> f6(I10, I11, I12, 1 + I13, I14) 
12.34/12.18	  f4(I15, I16, I17, I18, I19) -> f5(I15, I16, I17, I18, I19) [I16 = I16]
12.34/12.18	  f1(I20, I21, I22, I23, I24) -> f4(I20, I21, rnd3, I23, I24) [rnd3 = rnd3 /\ 0 <= -1 - I23 + I24]
12.34/12.18	  f3(I25, I26, I27, I28, I29) -> f1(I25, I26, I27, I28, I29) 
12.34/12.18	  f1(I30, I31, I32, I33, I34) -> f3(I30, I31, I35, I33, 1 + I34) [0 <= I35 /\ I35 <= 0 /\ I35 = I35 /\ 0 <= -1 - I33 + I34]
12.34/12.18	  f1(I36, I37, I38, I39, I40) -> f2(rnd1, I37, I38, I39, I40) [rnd1 = rnd1 /\ -1 * I39 + I40 <= 0]
12.34/12.18	
12.34/15.16	EOF