YES(?, a + b + 1) Initial complexity problem: 1: T: (?, 1) eval(a, b, c) -> eval(a, b + 1, c + 1) [ a >= b + 1 /\ a >= c + 1 ] (1, 1) start(a, b, c) -> eval(a, b, c) start location: start leaf cost: 0 A polynomial rank function with Pol(eval) = V_1 - V_2 Pol(start) = V_1 - V_2 orients all transitions weakly and the transition eval(a, b, c) -> eval(a, b + 1, c + 1) [ a >= b + 1 /\ a >= c + 1 ] strictly and produces the following problem: 2: T: (a + b, 1) eval(a, b, c) -> eval(a, b + 1, c + 1) [ a >= b + 1 /\ a >= c + 1 ] (1, 1) start(a, b, c) -> eval(a, b, c) start location: start leaf cost: 0 Complexity upper bound a + b + 1 Time: 0.071 sec (SMT: 0.068 sec)