0.76/0.79 MAYBE 0.76/0.79 0.76/0.79 DP problem for innermost termination. 0.76/0.79 P = 0.76/0.79 cond2#(false, x) -> f#(3 * x + 1) 0.76/0.79 cond2#(true, I0) -> f#(I0 / 2) 0.76/0.79 cond1#(true, I2) -> cond2#(I2 % 2 = 0, I2) 0.76/0.79 f#(I3) -> cond1#(I3 > 1, I3) 0.76/0.79 R = 0.76/0.79 cond2(false, x) -> f(3 * x + 1) 0.76/0.79 cond2(true, I0) -> f(I0 / 2) 0.76/0.79 cond1(false, I1) -> I1 0.76/0.79 cond1(true, I2) -> cond2(I2 % 2 = 0, I2) 0.76/0.79 f(I3) -> cond1(I3 > 1, I3) 0.76/0.79 0.76/0.79 This problem is converted using chaining, where edges between chained DPs are removed. 0.76/0.79 0.76/0.79 DP problem for innermost termination. 0.76/0.79 P = 0.76/0.79 cond2#(false, x) -> f#(3 * x + 1) 0.76/0.79 cond2#(true, I0) -> f#(I0 / 2) 0.76/0.79 cond1#(true, I2) -> cond2#(I2 % 2 = 0, I2) 0.76/0.79 f#(I3) -> cond1#(I3 > 1, I3) 0.76/0.79 f#(I3) -> cond2#(I3 % 2 = 0, I3) [I3 > 1] 0.76/0.79 f#(I3) -> f#(I3 / 2) [I3 > 1, I3 % 2 = 0] 0.76/0.79 f#(I3) -> f#(3 * I3 + 1) [I3 > 1, not(I3 % 2 = 0)] 0.76/0.79 cond1#(true, I2) -> f#(3 * I2 + 1) [not(I2 % 2 = 0)] 0.76/0.79 cond1#(true, I2) -> f#(I2 / 2) [I2 % 2 = 0] 0.76/0.79 R = 0.76/0.79 cond2(false, x) -> f(3 * x + 1) 0.76/0.79 cond2(true, I0) -> f(I0 / 2) 0.76/0.79 cond1(false, I1) -> I1 0.76/0.79 cond1(true, I2) -> cond2(I2 % 2 = 0, I2) 0.76/0.80 f(I3) -> cond1(I3 > 1, I3) 0.76/0.80 0.76/0.80 The dependency graph for this problem is: 0.76/0.80 0 -> 6, 5, 4, 3 0.76/0.80 1 -> 6, 5, 4, 3 0.76/0.80 2 -> 0.76/0.80 3 -> 0.76/0.80 4 -> 0.76/0.80 5 -> 6, 5, 3, 4 0.76/0.80 6 -> 3, 4, 5 0.76/0.80 7 -> 3, 4, 5 0.76/0.80 8 -> 3, 4, 5, 6 0.76/0.80 Where: 0.76/0.80 0) cond2#(false, x) -> f#(3 * x + 1) 0.76/0.80 1) cond2#(true, I0) -> f#(I0 / 2) 0.76/0.80 2) cond1#(true, I2) -> cond2#(I2 % 2 = 0, I2) 0.76/0.80 3) f#(I3) -> cond1#(I3 > 1, I3) 0.76/0.80 4) f#(I3) -> cond2#(I3 % 2 = 0, I3) [I3 > 1] 0.76/0.80 5) f#(I3) -> f#(I3 / 2) [I3 > 1, I3 % 2 = 0] 0.76/0.80 6) f#(I3) -> f#(3 * I3 + 1) [I3 > 1, not(I3 % 2 = 0)] 0.76/0.80 7) cond1#(true, I2) -> f#(3 * I2 + 1) [not(I2 % 2 = 0)] 0.76/0.80 8) cond1#(true, I2) -> f#(I2 / 2) [I2 % 2 = 0] 0.76/0.80 0.76/0.80 We have the following SCCs. 0.76/0.80 { 5, 6 } 0.76/0.80 0.76/0.80 DP problem for innermost termination. 0.76/0.80 P = 0.76/0.80 f#(I3) -> f#(I3 / 2) [I3 > 1, I3 % 2 = 0] 0.76/0.80 f#(I3) -> f#(3 * I3 + 1) [I3 > 1, not(I3 % 2 = 0)] 0.76/0.80 R = 0.76/0.80 cond2(false, x) -> f(3 * x + 1) 0.76/0.80 cond2(true, I0) -> f(I0 / 2) 0.76/0.80 cond1(false, I1) -> I1 0.76/0.80 cond1(true, I2) -> cond2(I2 % 2 = 0, I2) 0.76/0.80 f(I3) -> cond1(I3 > 1, I3) 0.76/0.80 0.76/3.78 EOF