7.80/7.71	MAYBE
7.80/7.71	
7.80/7.71	DP problem for innermost termination.
7.80/7.71	P =
7.80/7.71	  f8#(x1, x2, x3) -> f1#(x1, x2, x3) 
7.80/7.71	  f7#(I0, I1, I2) -> f2#(I0, I1, I2) 
7.80/7.71	  f6#(I3, I4, I5) -> f7#(I3, I4, -1 + I5) 
7.80/7.71	  f5#(I6, I7, I8) -> f6#(I6, I7, I8) [1 <= I7]
7.80/7.71	  f5#(I9, I10, I11) -> f6#(I9, I10, I11) [1 + I10 <= 0]
7.80/7.71	  f2#(I12, I13, I14) -> f5#(I12, rnd2, I14) [rnd2 = rnd2 /\ -1 * I14 <= 0]
7.80/7.71	  f4#(I15, I16, I17) -> f2#(I15, I16, I17) 
7.80/7.71	  f2#(I18, I19, I20) -> f4#(I18, I21, I20) [0 <= I21 /\ I21 <= 0 /\ I21 = I21 /\ -1 * I20 <= 0]
7.80/7.71	  f1#(I25, I26, I27) -> f2#(I25, I26, I27) 
7.80/7.71	R = 
7.80/7.71	  f8(x1, x2, x3) -> f1(x1, x2, x3) 
7.80/7.71	  f7(I0, I1, I2) -> f2(I0, I1, I2) 
7.80/7.71	  f6(I3, I4, I5) -> f7(I3, I4, -1 + I5) 
7.80/7.71	  f5(I6, I7, I8) -> f6(I6, I7, I8) [1 <= I7]
7.80/7.71	  f5(I9, I10, I11) -> f6(I9, I10, I11) [1 + I10 <= 0]
7.80/7.71	  f2(I12, I13, I14) -> f5(I12, rnd2, I14) [rnd2 = rnd2 /\ -1 * I14 <= 0]
7.80/7.71	  f4(I15, I16, I17) -> f2(I15, I16, I17) 
7.80/7.71	  f2(I18, I19, I20) -> f4(I18, I21, I20) [0 <= I21 /\ I21 <= 0 /\ I21 = I21 /\ -1 * I20 <= 0]
7.80/7.71	  f2(I22, I23, I24) -> f3(rnd1, I23, I24) [rnd1 = rnd1 /\ 0 <= -1 - I24]
7.80/7.72	  f1(I25, I26, I27) -> f2(I25, I26, I27) 
7.80/7.72	
7.80/7.72	The dependency graph for this problem is:
7.80/7.72	  0 -> 8
7.80/7.72	  1 -> 5, 7
7.80/7.72	  2 -> 1
7.80/7.72	  3 -> 2
7.80/7.72	  4 -> 2
7.80/7.72	  5 -> 3, 4
7.80/7.72	  6 -> 5, 7
7.80/7.72	  7 -> 6
7.80/7.72	  8 -> 5, 7
7.80/7.72	Where:
7.80/7.72	  0) f8#(x1, x2, x3) -> f1#(x1, x2, x3) 
7.80/7.72	  1) f7#(I0, I1, I2) -> f2#(I0, I1, I2) 
7.80/7.72	  2) f6#(I3, I4, I5) -> f7#(I3, I4, -1 + I5) 
7.80/7.72	  3) f5#(I6, I7, I8) -> f6#(I6, I7, I8) [1 <= I7]
7.80/7.72	  4) f5#(I9, I10, I11) -> f6#(I9, I10, I11) [1 + I10 <= 0]
7.80/7.72	  5) f2#(I12, I13, I14) -> f5#(I12, rnd2, I14) [rnd2 = rnd2 /\ -1 * I14 <= 0]
7.80/7.72	  6) f4#(I15, I16, I17) -> f2#(I15, I16, I17) 
7.80/7.72	  7) f2#(I18, I19, I20) -> f4#(I18, I21, I20) [0 <= I21 /\ I21 <= 0 /\ I21 = I21 /\ -1 * I20 <= 0]
7.80/7.72	  8) f1#(I25, I26, I27) -> f2#(I25, I26, I27) 
7.80/7.72	
7.80/7.72	We have the following SCCs.
7.80/7.72	  { 1, 2, 3, 4, 5, 6, 7 }
7.80/7.72	
7.80/7.72	DP problem for innermost termination.
7.80/7.72	P =
7.80/7.72	  f7#(I0, I1, I2) -> f2#(I0, I1, I2) 
7.80/7.72	  f6#(I3, I4, I5) -> f7#(I3, I4, -1 + I5) 
7.80/7.72	  f5#(I6, I7, I8) -> f6#(I6, I7, I8) [1 <= I7]
7.80/7.72	  f5#(I9, I10, I11) -> f6#(I9, I10, I11) [1 + I10 <= 0]
7.80/7.72	  f2#(I12, I13, I14) -> f5#(I12, rnd2, I14) [rnd2 = rnd2 /\ -1 * I14 <= 0]
7.80/7.72	  f4#(I15, I16, I17) -> f2#(I15, I16, I17) 
7.80/7.72	  f2#(I18, I19, I20) -> f4#(I18, I21, I20) [0 <= I21 /\ I21 <= 0 /\ I21 = I21 /\ -1 * I20 <= 0]
7.80/7.72	R = 
7.80/7.72	  f8(x1, x2, x3) -> f1(x1, x2, x3) 
7.80/7.72	  f7(I0, I1, I2) -> f2(I0, I1, I2) 
7.80/7.72	  f6(I3, I4, I5) -> f7(I3, I4, -1 + I5) 
7.80/7.72	  f5(I6, I7, I8) -> f6(I6, I7, I8) [1 <= I7]
7.80/7.72	  f5(I9, I10, I11) -> f6(I9, I10, I11) [1 + I10 <= 0]
7.80/7.72	  f2(I12, I13, I14) -> f5(I12, rnd2, I14) [rnd2 = rnd2 /\ -1 * I14 <= 0]
7.80/7.72	  f4(I15, I16, I17) -> f2(I15, I16, I17) 
7.80/7.72	  f2(I18, I19, I20) -> f4(I18, I21, I20) [0 <= I21 /\ I21 <= 0 /\ I21 = I21 /\ -1 * I20 <= 0]
7.80/7.72	  f2(I22, I23, I24) -> f3(rnd1, I23, I24) [rnd1 = rnd1 /\ 0 <= -1 - I24]
7.80/7.72	  f1(I25, I26, I27) -> f2(I25, I26, I27) 
7.80/7.72	
7.80/7.72	We use the extended value criterion with the projection function NU:
7.80/7.72	  NU[f4#(x0,x1,x2)] = x2
7.80/7.72	  NU[f5#(x0,x1,x2)] = x2 - 1
7.80/7.72	  NU[f6#(x0,x1,x2)] = x2 - 1
7.80/7.72	  NU[f2#(x0,x1,x2)] = x2
7.80/7.72	  NU[f7#(x0,x1,x2)] = x2
7.80/7.72	
7.80/7.72	This gives the following inequalities:
7.80/7.72	    ==>  I2 >= I2
7.80/7.72	    ==>  I5 - 1 >= (-1 + I5)
7.80/7.72	  1 <= I7  ==>  I8 - 1 >= I8 - 1
7.80/7.72	  1 + I10 <= 0  ==>  I11 - 1 >= I11 - 1
7.80/7.72	  rnd2 = rnd2 /\ -1 * I14 <= 0  ==>  I14 > I14 - 1  with  I14 >= 0
7.80/7.72	    ==>  I17 >= I17
7.80/7.72	  0 <= I21 /\ I21 <= 0 /\ I21 = I21 /\ -1 * I20 <= 0  ==>  I20 >= I20
7.80/7.72	
7.80/7.72	We remove all the strictly oriented dependency pairs.
7.80/7.72	
7.80/7.72	DP problem for innermost termination.
7.80/7.72	P =
7.80/7.72	  f7#(I0, I1, I2) -> f2#(I0, I1, I2) 
7.80/7.72	  f6#(I3, I4, I5) -> f7#(I3, I4, -1 + I5) 
7.80/7.72	  f5#(I6, I7, I8) -> f6#(I6, I7, I8) [1 <= I7]
7.80/7.72	  f5#(I9, I10, I11) -> f6#(I9, I10, I11) [1 + I10 <= 0]
7.80/7.72	  f4#(I15, I16, I17) -> f2#(I15, I16, I17) 
7.80/7.72	  f2#(I18, I19, I20) -> f4#(I18, I21, I20) [0 <= I21 /\ I21 <= 0 /\ I21 = I21 /\ -1 * I20 <= 0]
7.80/7.72	R = 
7.80/7.72	  f8(x1, x2, x3) -> f1(x1, x2, x3) 
7.80/7.72	  f7(I0, I1, I2) -> f2(I0, I1, I2) 
7.80/7.72	  f6(I3, I4, I5) -> f7(I3, I4, -1 + I5) 
7.80/7.72	  f5(I6, I7, I8) -> f6(I6, I7, I8) [1 <= I7]
7.80/7.72	  f5(I9, I10, I11) -> f6(I9, I10, I11) [1 + I10 <= 0]
7.80/7.72	  f2(I12, I13, I14) -> f5(I12, rnd2, I14) [rnd2 = rnd2 /\ -1 * I14 <= 0]
7.80/7.72	  f4(I15, I16, I17) -> f2(I15, I16, I17) 
7.80/7.72	  f2(I18, I19, I20) -> f4(I18, I21, I20) [0 <= I21 /\ I21 <= 0 /\ I21 = I21 /\ -1 * I20 <= 0]
7.80/7.72	  f2(I22, I23, I24) -> f3(rnd1, I23, I24) [rnd1 = rnd1 /\ 0 <= -1 - I24]
7.80/7.72	  f1(I25, I26, I27) -> f2(I25, I26, I27) 
7.80/7.72	
7.80/7.72	The dependency graph for this problem is:
7.80/7.72	  1 -> 7
7.80/7.72	  2 -> 1
7.80/7.72	  3 -> 2
7.80/7.72	  4 -> 2
7.80/7.72	  6 -> 7
7.80/7.72	  7 -> 6
7.80/7.72	Where:
7.80/7.72	  1) f7#(I0, I1, I2) -> f2#(I0, I1, I2) 
7.80/7.72	  2) f6#(I3, I4, I5) -> f7#(I3, I4, -1 + I5) 
7.80/7.72	  3) f5#(I6, I7, I8) -> f6#(I6, I7, I8) [1 <= I7]
7.80/7.72	  4) f5#(I9, I10, I11) -> f6#(I9, I10, I11) [1 + I10 <= 0]
7.80/7.72	  6) f4#(I15, I16, I17) -> f2#(I15, I16, I17) 
7.80/7.72	  7) f2#(I18, I19, I20) -> f4#(I18, I21, I20) [0 <= I21 /\ I21 <= 0 /\ I21 = I21 /\ -1 * I20 <= 0]
7.80/7.72	
7.80/7.72	We have the following SCCs.
7.80/7.72	  { 6, 7 }
7.80/7.72	
7.80/7.72	DP problem for innermost termination.
7.80/7.72	P =
7.80/7.72	  f4#(I15, I16, I17) -> f2#(I15, I16, I17) 
7.80/7.72	  f2#(I18, I19, I20) -> f4#(I18, I21, I20) [0 <= I21 /\ I21 <= 0 /\ I21 = I21 /\ -1 * I20 <= 0]
7.80/7.72	R = 
7.80/7.72	  f8(x1, x2, x3) -> f1(x1, x2, x3) 
7.80/7.72	  f7(I0, I1, I2) -> f2(I0, I1, I2) 
7.80/7.72	  f6(I3, I4, I5) -> f7(I3, I4, -1 + I5) 
7.80/7.72	  f5(I6, I7, I8) -> f6(I6, I7, I8) [1 <= I7]
7.80/7.72	  f5(I9, I10, I11) -> f6(I9, I10, I11) [1 + I10 <= 0]
7.80/7.72	  f2(I12, I13, I14) -> f5(I12, rnd2, I14) [rnd2 = rnd2 /\ -1 * I14 <= 0]
7.80/7.72	  f4(I15, I16, I17) -> f2(I15, I16, I17) 
7.80/7.72	  f2(I18, I19, I20) -> f4(I18, I21, I20) [0 <= I21 /\ I21 <= 0 /\ I21 = I21 /\ -1 * I20 <= 0]
7.80/7.72	  f2(I22, I23, I24) -> f3(rnd1, I23, I24) [rnd1 = rnd1 /\ 0 <= -1 - I24]
7.80/7.72	  f1(I25, I26, I27) -> f2(I25, I26, I27) 
7.80/7.72	
7.80/10.69	EOF