YES(?, b + 1) Initial complexity problem: 1: T: (?, 1) eval(a, b) -> eval(a - 1, b - 1) [ a >= 1 /\ b >= 1 ] (1, 1) start(a, b) -> eval(a, b) start location: start leaf cost: 0 A polynomial rank function with Pol(eval) = V_2 Pol(start) = V_2 orients all transitions weakly and the transition eval(a, b) -> eval(a - 1, b - 1) [ a >= 1 /\ b >= 1 ] strictly and produces the following problem: 2: T: (b, 1) eval(a, b) -> eval(a - 1, b - 1) [ a >= 1 /\ b >= 1 ] (1, 1) start(a, b) -> eval(a, b) start location: start leaf cost: 0 Complexity upper bound b + 1 Time: 0.105 sec (SMT: 0.101 sec)