YES(?, a + 2) Initial complexity problem: 1: T: (1, 1) f1(a) -> f0(a) (?, 1) f0(a) -> f0(a - 1) [ a >= 0 ] start location: f1 leaf cost: 0 A polynomial rank function with Pol(f1) = V_1 + 1 Pol(f0) = V_1 + 1 orients all transitions weakly and the transition f0(a) -> f0(a - 1) [ a >= 0 ] strictly and produces the following problem: 2: T: (1, 1) f1(a) -> f0(a) (a + 1, 1) f0(a) -> f0(a - 1) [ a >= 0 ] start location: f1 leaf cost: 0 Complexity upper bound a + 2 Time: 0.064 sec (SMT: 0.062 sec)