YES(?, 13) Initial complexity problem: 1: T: (1, 1) f0(a, b, c) -> f8(0, 10, 0) (?, 1) f8(a, b, c) -> f8(a + 2, b, c + 1) [ b >= c + 1 ] (?, 1) f8(a, b, c) -> f6(a, b, c) [ 2*b >= a + 1 /\ c >= b ] (?, 1) f8(a, b, c) -> f6(a, b, c) [ a >= 2*b /\ c >= b ] start location: f0 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (1, 1) f0(a, b, c) -> f8(0, 10, 0) (?, 1) f8(a, b, c) -> f8(a + 2, b, c + 1) [ b >= c + 1 ] start location: f0 leaf cost: 2 A polynomial rank function with Pol(f0) = 10 Pol(f8) = V_2 - V_3 orients all transitions weakly and the transition f8(a, b, c) -> f8(a + 2, b, c + 1) [ b >= c + 1 ] strictly and produces the following problem: 3: T: (1, 1) f0(a, b, c) -> f8(0, 10, 0) (10, 1) f8(a, b, c) -> f8(a + 2, b, c + 1) [ b >= c + 1 ] start location: f0 leaf cost: 2 Complexity upper bound 13 Time: 0.074 sec (SMT: 0.071 sec)