YES(?, a + 1200) Initial complexity problem: 1: T: (1, 1) f0(a) -> f1(a) (?, 1) f1(a) -> f1(a - 1000) [ a >= 1201 ] start location: f0 leaf cost: 0 A polynomial rank function with Pol(f0) = V_1 - 1199 Pol(f1) = V_1 - 1199 orients all transitions weakly and the transition f1(a) -> f1(a - 1000) [ a >= 1201 ] strictly and produces the following problem: 2: T: (1, 1) f0(a) -> f1(a) (a + 1199, 1) f1(a) -> f1(a - 1000) [ a >= 1201 ] start location: f0 leaf cost: 0 Complexity upper bound a + 1200 Time: 0.068 sec (SMT: 0.065 sec)