20.13/20.08	MAYBE
20.13/20.08	
20.13/20.08	DP problem for innermost termination.
20.13/20.08	P =
20.13/20.08	  f4#(x1, x2, x3) -> f3#(x1, x2, x3) 
20.13/20.08	  f3#(I0, I1, I2) -> f2#(I0, I1, 1 + I0) [0 <= 1 + I0 /\ 1 + I0 <= 1 + I1 /\ 1 <= I1 /\ 1 <= I0 /\ I0 <= I1]
20.13/20.08	  f2#(I3, I4, I5) -> f1#(I3, I4, I5) [1 + I5 <= I3]
20.13/20.08	  f2#(I6, I7, I8) -> f1#(I6, I7, I8) [1 + I6 <= I8]
20.13/20.08	  f1#(I9, I10, I11) -> f2#(I9, I10, 0) [0 <= 0 /\ 0 <= 1 + I10 /\ 1 <= I11 /\ 1 + I10 <= I11]
20.13/20.08	  f1#(I12, I13, I14) -> f2#(I12, I13, 1 + I14) [0 <= 1 + I14 /\ 1 + I14 <= 1 + I13 /\ I14 <= I13]
20.13/20.08	R = 
20.13/20.08	  f4(x1, x2, x3) -> f3(x1, x2, x3) 
20.13/20.08	  f3(I0, I1, I2) -> f2(I0, I1, 1 + I0) [0 <= 1 + I0 /\ 1 + I0 <= 1 + I1 /\ 1 <= I1 /\ 1 <= I0 /\ I0 <= I1]
20.13/20.08	  f2(I3, I4, I5) -> f1(I3, I4, I5) [1 + I5 <= I3]
20.13/20.08	  f2(I6, I7, I8) -> f1(I6, I7, I8) [1 + I6 <= I8]
20.13/20.08	  f1(I9, I10, I11) -> f2(I9, I10, 0) [0 <= 0 /\ 0 <= 1 + I10 /\ 1 <= I11 /\ 1 + I10 <= I11]
20.13/20.08	  f1(I12, I13, I14) -> f2(I12, I13, 1 + I14) [0 <= 1 + I14 /\ 1 + I14 <= 1 + I13 /\ I14 <= I13]
20.13/20.08	
20.13/20.08	The dependency graph for this problem is:
20.13/20.08	  0 -> 1
20.13/20.08	  1 -> 3
20.13/20.08	  2 -> 4, 5
20.13/20.08	  3 -> 4, 5
20.13/20.08	  4 -> 2, 3
20.13/20.08	  5 -> 2, 3
20.13/20.08	Where:
20.13/20.08	  0) f4#(x1, x2, x3) -> f3#(x1, x2, x3) 
20.13/20.08	  1) f3#(I0, I1, I2) -> f2#(I0, I1, 1 + I0) [0 <= 1 + I0 /\ 1 + I0 <= 1 + I1 /\ 1 <= I1 /\ 1 <= I0 /\ I0 <= I1]
20.13/20.08	  2) f2#(I3, I4, I5) -> f1#(I3, I4, I5) [1 + I5 <= I3]
20.13/20.08	  3) f2#(I6, I7, I8) -> f1#(I6, I7, I8) [1 + I6 <= I8]
20.13/20.08	  4) f1#(I9, I10, I11) -> f2#(I9, I10, 0) [0 <= 0 /\ 0 <= 1 + I10 /\ 1 <= I11 /\ 1 + I10 <= I11]
20.13/20.08	  5) f1#(I12, I13, I14) -> f2#(I12, I13, 1 + I14) [0 <= 1 + I14 /\ 1 + I14 <= 1 + I13 /\ I14 <= I13]
20.13/20.08	
20.13/20.08	We have the following SCCs.
20.13/20.08	  { 2, 3, 4, 5 }
20.13/20.08	
20.13/20.08	DP problem for innermost termination.
20.13/20.08	P =
20.13/20.08	  f2#(I3, I4, I5) -> f1#(I3, I4, I5) [1 + I5 <= I3]
20.13/20.08	  f2#(I6, I7, I8) -> f1#(I6, I7, I8) [1 + I6 <= I8]
20.13/20.08	  f1#(I9, I10, I11) -> f2#(I9, I10, 0) [0 <= 0 /\ 0 <= 1 + I10 /\ 1 <= I11 /\ 1 + I10 <= I11]
20.13/20.08	  f1#(I12, I13, I14) -> f2#(I12, I13, 1 + I14) [0 <= 1 + I14 /\ 1 + I14 <= 1 + I13 /\ I14 <= I13]
20.13/20.08	R = 
20.13/20.08	  f4(x1, x2, x3) -> f3(x1, x2, x3) 
20.13/20.08	  f3(I0, I1, I2) -> f2(I0, I1, 1 + I0) [0 <= 1 + I0 /\ 1 + I0 <= 1 + I1 /\ 1 <= I1 /\ 1 <= I0 /\ I0 <= I1]
20.13/20.08	  f2(I3, I4, I5) -> f1(I3, I4, I5) [1 + I5 <= I3]
20.13/20.08	  f2(I6, I7, I8) -> f1(I6, I7, I8) [1 + I6 <= I8]
20.13/20.08	  f1(I9, I10, I11) -> f2(I9, I10, 0) [0 <= 0 /\ 0 <= 1 + I10 /\ 1 <= I11 /\ 1 + I10 <= I11]
20.13/20.08	  f1(I12, I13, I14) -> f2(I12, I13, 1 + I14) [0 <= 1 + I14 /\ 1 + I14 <= 1 + I13 /\ I14 <= I13]
20.13/20.08	
20.13/23.06	EOF