YES(?, a + b + 2) Initial complexity problem: 1: T: (?, 1) eval(a, b, c) -> eval(a, b + c, c) [ a >= b /\ 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 + 1 Pol(start) = V_1 - V_2 + 1 orients all transitions weakly and the transition eval(a, b, c) -> eval(a, b + c, c) [ a >= b /\ c >= 1 ] strictly and produces the following problem: 2: T: (a + b + 1, 1) eval(a, b, c) -> eval(a, b + c, c) [ a >= b /\ c >= 1 ] (1, 1) start(a, b, c) -> eval(a, b, c) start location: start leaf cost: 0 Complexity upper bound a + b + 2 Time: 0.105 sec (SMT: 0.101 sec)