YES(?, a + b + 2) Initial complexity problem: 1: T: (1, 1) eval0(a, b, c) -> eval1(a, b, c) [ a >= 1 ] (?, 1) eval1(a, b, c) -> eval1(a, b + a, c) [ a >= b + 1 /\ c >= a + 1 /\ a >= 1 ] (?, 1) eval1(a, b, c) -> eval1(a, b, b - a) [ a >= b + 1 /\ c >= a + 1 /\ a >= 1 ] start location: eval0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) eval0(a, b, c) -> eval1(a, b, c) [ a >= 1 ] (?, 1) eval1(a, b, c) -> eval1(a, b + a, c) [ a >= b + 1 /\ c >= a + 1 /\ a >= 1 ] start location: eval0 leaf cost: 1 A polynomial rank function with Pol(eval0) = V_1 - V_2 Pol(eval1) = V_1 - V_2 orients all transitions weakly and the transition eval1(a, b, c) -> eval1(a, b + a, c) [ a >= b + 1 /\ c >= a + 1 /\ a >= 1 ] strictly and produces the following problem: 3: T: (1, 1) eval0(a, b, c) -> eval1(a, b, c) [ a >= 1 ] (a + b, 1) eval1(a, b, c) -> eval1(a, b + a, c) [ a >= b + 1 /\ c >= a + 1 /\ a >= 1 ] start location: eval0 leaf cost: 1 Complexity upper bound a + b + 2 Time: 0.122 sec (SMT: 0.117 sec)