YES(?, b + 2) Initial complexity problem: 1: T: (1, 1) f0(a, b) -> f1(a, b) [ a >= 1 ] (?, 1) f1(a, b) -> f1(a, b - a) [ a >= 1 /\ b >= 0 ] start location: f0 leaf cost: 0 A polynomial rank function with Pol(f0) = V_2 + 1 Pol(f1) = V_2 + 1 orients all transitions weakly and the transition f1(a, b) -> f1(a, b - a) [ a >= 1 /\ b >= 0 ] strictly and produces the following problem: 2: T: (1, 1) f0(a, b) -> f1(a, b) [ a >= 1 ] (b + 1, 1) f1(a, b) -> f1(a, b - a) [ a >= 1 /\ b >= 0 ] start location: f0 leaf cost: 0 Complexity upper bound b + 2 Time: 0.087 sec (SMT: 0.083 sec)