YES(?, 13) Initial complexity problem: 1: T: (1, 1) f0(a) -> f3(0) (?, 1) f3(a) -> f3(a + 1) [ 9 >= a ] (?, 1) f3(a) -> f11(a) [ a >= 10 /\ 0 >= b + 1 ] (?, 1) f3(a) -> f11(a) [ a >= 10 ] 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) -> f3(0) (?, 1) f3(a) -> f3(a + 1) [ 9 >= a ] start location: f0 leaf cost: 2 A polynomial rank function with Pol(f0) = 10 Pol(f3) = -V_1 + 10 orients all transitions weakly and the transition f3(a) -> f3(a + 1) [ 9 >= a ] strictly and produces the following problem: 3: T: (1, 1) f0(a) -> f3(0) (10, 1) f3(a) -> f3(a + 1) [ 9 >= a ] start location: f0 leaf cost: 2 Complexity upper bound 13 Time: 0.077 sec (SMT: 0.074 sec)