YES(?, a + 2) Initial complexity problem: 1: T: (?, 1) eval(a, b) -> eval(a - 1, b) [ a >= 1 /\ b >= a ] (?, 1) eval(a, b) -> eval(b, b) [ a >= 1 /\ a >= b + 1 ] (1, 1) start(a, b) -> eval(a, b) start location: start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (?, 1) eval(a, b) -> eval(a - 1, b) [ a >= 1 /\ b >= a ] (1, 1) eval(a, b) -> eval(b, b) [ a >= 1 /\ a >= b + 1 ] (1, 1) start(a, b) -> eval(a, b) start location: start leaf cost: 0 A polynomial rank function with Pol(eval) = V_1 Pol(start) = V_1 orients all transitions weakly and the transition eval(a, b) -> eval(a - 1, b) [ a >= 1 /\ b >= a ] strictly and produces the following problem: 3: T: (a, 1) eval(a, b) -> eval(a - 1, b) [ a >= 1 /\ b >= a ] (1, 1) eval(a, b) -> eval(b, b) [ a >= 1 /\ a >= b + 1 ] (1, 1) start(a, b) -> eval(a, b) start location: start leaf cost: 0 Complexity upper bound a + 2 Time: 0.090 sec (SMT: 0.086 sec)