0.00/0.23 MAYBE 0.00/0.23 0.00/0.23 DP problem for innermost termination. 0.00/0.23 P = 0.00/0.23 round#(x) -> if#(x % 2 = 0, x, x + 1) 0.00/0.23 minusNat#(true, I2, y) -> minus#(I2, round(I2)) 0.00/0.23 minusNat#(true, I2, y) -> round#(I2) 0.00/0.23 minus#(I3, I4) -> minusNat#(I4 >= 0 && I3 = I4 + 1, I3, I4) 0.00/0.23 R = 0.00/0.23 if(false, u, v) -> v 0.00/0.23 if(true, I0, I1) -> I0 0.00/0.23 round(x) -> if(x % 2 = 0, x, x + 1) 0.00/0.23 minusNat(true, I2, y) -> minus(I2, round(I2)) 0.00/0.23 minus(I3, I4) -> minusNat(I4 >= 0 && I3 = I4 + 1, I3, I4) 0.00/0.23 0.00/0.23 This problem is converted using chaining, where edges between chained DPs are removed. 0.00/0.23 0.00/0.23 DP problem for innermost termination. 0.00/0.23 P = 0.00/0.23 round#(x) -> if#(x % 2 = 0, x, x + 1) 0.00/0.23 minusNat#(true, I2, y) -> minus#(I2, round(I2)) 0.00/0.23 minusNat#(true, I2, y) -> round#(I2) 0.00/0.23 minus#(I3, I4) -> minusNat#(I4 >= 0 && I3 = I4 + 1, I3, I4) 0.00/0.23 minus#(I3, I4) -> minus#(I3, round(I3)) [I4 >= 0 && I3 = I4 + 1] 0.00/0.23 minus#(I3, I4) -> round#(I3) [I4 >= 0 && I3 = I4 + 1] 0.00/0.23 R = 0.00/0.23 if(false, u, v) -> v 0.00/0.23 if(true, I0, I1) -> I0 0.00/0.23 round(x) -> if(x % 2 = 0, x, x + 1) 0.00/0.23 minusNat(true, I2, y) -> minus(I2, round(I2)) 0.00/0.23 minus(I3, I4) -> minusNat(I4 >= 0 && I3 = I4 + 1, I3, I4) 0.00/0.23 0.00/0.23 The dependency graph for this problem is: 0.00/0.23 0 -> 0.00/0.23 1 -> 5, 4, 3 0.00/0.23 2 -> 0 0.00/0.23 3 -> 0.00/0.23 4 -> 5, 4, 3 0.00/0.23 5 -> 0 0.00/0.23 Where: 0.00/0.23 0) round#(x) -> if#(x % 2 = 0, x, x + 1) 0.00/0.23 1) minusNat#(true, I2, y) -> minus#(I2, round(I2)) 0.00/0.23 2) minusNat#(true, I2, y) -> round#(I2) 0.00/0.23 3) minus#(I3, I4) -> minusNat#(I4 >= 0 && I3 = I4 + 1, I3, I4) 0.00/0.23 4) minus#(I3, I4) -> minus#(I3, round(I3)) [I4 >= 0 && I3 = I4 + 1] 0.00/0.23 5) minus#(I3, I4) -> round#(I3) [I4 >= 0 && I3 = I4 + 1] 0.00/0.23 0.00/0.23 We have the following SCCs. 0.00/0.23 { 4 } 0.00/0.23 0.00/0.23 DP problem for innermost termination. 0.00/0.23 P = 0.00/0.23 minus#(I3, I4) -> minus#(I3, round(I3)) [I4 >= 0 && I3 = I4 + 1] 0.00/0.23 R = 0.00/0.23 if(false, u, v) -> v 0.00/0.23 if(true, I0, I1) -> I0 0.00/0.23 round(x) -> if(x % 2 = 0, x, x + 1) 0.00/0.23 minusNat(true, I2, y) -> minus(I2, round(I2)) 0.00/0.23 minus(I3, I4) -> minusNat(I4 >= 0 && I3 = I4 + 1, I3, I4) 0.00/0.23 0.00/3.21 EOF