YES(?, 5) Initial complexity problem: 1: T: (1, 1) f0(a) -> f5(0) (?, 1) f5(a) -> f5(a + 1) [ 1 >= a ] (?, 1) f5(a) -> f13(a) [ a >= 2 /\ 0 >= b + 1 ] (?, 1) f5(a) -> f13(a) [ a >= 2 ] 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) -> f5(0) (?, 1) f5(a) -> f5(a + 1) [ 1 >= a ] start location: f0 leaf cost: 2 A polynomial rank function with Pol(f0) = 2 Pol(f5) = -V_1 + 2 orients all transitions weakly and the transition f5(a) -> f5(a + 1) [ 1 >= a ] strictly and produces the following problem: 3: T: (1, 1) f0(a) -> f5(0) (2, 1) f5(a) -> f5(a + 1) [ 1 >= a ] start location: f0 leaf cost: 2 Complexity upper bound 5 Time: 0.073 sec (SMT: 0.070 sec)