1.17/1.19 MAYBE 1.17/1.19 1.17/1.19 DP problem for innermost termination. 1.17/1.19 P = 1.17/1.19 f4#(x1, x2) -> f3#(x1, x2) 1.17/1.19 f3#(I0, I1) -> f1#(I0, 3000) 1.17/1.19 f2#(I2, I3) -> f1#(I2, I3) 1.17/1.19 f1#(I4, I5) -> f2#(1000 + I4, I5) [111 <= 1000 + I4 /\ 1 + I5 <= 4000] 1.17/1.19 R = 1.17/1.19 f4(x1, x2) -> f3(x1, x2) 1.17/1.19 f3(I0, I1) -> f1(I0, 3000) 1.17/1.19 f2(I2, I3) -> f1(I2, I3) 1.17/1.19 f1(I4, I5) -> f2(1000 + I4, I5) [111 <= 1000 + I4 /\ 1 + I5 <= 4000] 1.17/1.19 1.17/1.19 The dependency graph for this problem is: 1.17/1.19 0 -> 1 1.17/1.19 1 -> 3 1.17/1.19 2 -> 3 1.17/1.19 3 -> 2 1.17/1.19 Where: 1.17/1.19 0) f4#(x1, x2) -> f3#(x1, x2) 1.17/1.19 1) f3#(I0, I1) -> f1#(I0, 3000) 1.17/1.19 2) f2#(I2, I3) -> f1#(I2, I3) 1.17/1.19 3) f1#(I4, I5) -> f2#(1000 + I4, I5) [111 <= 1000 + I4 /\ 1 + I5 <= 4000] 1.17/1.19 1.17/1.19 We have the following SCCs. 1.17/1.19 { 2, 3 } 1.17/1.19 1.17/1.19 DP problem for innermost termination. 1.17/1.19 P = 1.17/1.19 f2#(I2, I3) -> f1#(I2, I3) 1.17/1.19 f1#(I4, I5) -> f2#(1000 + I4, I5) [111 <= 1000 + I4 /\ 1 + I5 <= 4000] 1.17/1.19 R = 1.17/1.19 f4(x1, x2) -> f3(x1, x2) 1.17/1.19 f3(I0, I1) -> f1(I0, 3000) 1.17/1.19 f2(I2, I3) -> f1(I2, I3) 1.17/1.19 f1(I4, I5) -> f2(1000 + I4, I5) [111 <= 1000 + I4 /\ 1 + I5 <= 4000] 1.17/1.19 1.17/4.17 EOF