MAYBE Initial complexity problem: 1: T: (?, 1) f2(a, b) -> f1(c, d) [ 0 >= c + 1 /\ a = 14 ] (?, 1) f2(a, b) -> f2(c, b) [ c >= 0 /\ a = 14 ] (?, 1) f2(a, b) -> f1(a - 1, c) [ a >= 15 /\ 0 >= a ] (?, 1) f2(a, b) -> f1(a - 1, c) [ 13 >= a /\ 0 >= a ] (?, 1) f2(a, b) -> f2(a - 1, b) [ a >= 15 /\ a >= 1 ] (?, 1) f2(a, b) -> f2(a - 1, b) [ 13 >= a /\ a >= 1 ] (1, 1) f300(a, b) -> f2(a, b) start location: f300 leaf cost: 0 Testing for unsatisfiable constraints removes the following transition from problem 1: f2(a, b) -> f1(a - 1, c) [ a >= 15 /\ 0 >= a ] We thus obtain the following problem: 2: T: (?, 1) f2(a, b) -> f1(c, d) [ 0 >= c + 1 /\ a = 14 ] (?, 1) f2(a, b) -> f2(c, b) [ c >= 0 /\ a = 14 ] (?, 1) f2(a, b) -> f1(a - 1, c) [ 13 >= a /\ 0 >= a ] (?, 1) f2(a, b) -> f2(a - 1, b) [ a >= 15 /\ a >= 1 ] (?, 1) f2(a, b) -> f2(a - 1, b) [ 13 >= a /\ a >= 1 ] (1, 1) f300(a, b) -> f2(a, b) start location: f300 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 2 produces the following problem: 3: T: (?, 1) f2(a, b) -> f2(c, b) [ c >= 0 /\ a = 14 ] (?, 1) f2(a, b) -> f2(a - 1, b) [ a >= 15 /\ a >= 1 ] (?, 1) f2(a, b) -> f2(a - 1, b) [ 13 >= a /\ a >= 1 ] (1, 1) f300(a, b) -> f2(a, b) start location: f300 leaf cost: 2 Complexity upper bound ? Time: 0.272 sec (SMT: 0.257 sec)