YES(?, a + 2) Initial complexity problem: 1: T: (?, 1) f2(a, b) -> f3(a, 1) [ 0 >= a ] (1, 1) f0(a, b) -> f2(a, 0) (?, 1) f2(a, b) -> f2(a - 1, b) [ a >= 1 ] 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) -> f2(a, 0) (?, 1) f2(a, b) -> f2(a - 1, b) [ a >= 1 ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f0) = V_1 Pol(f2) = V_1 orients all transitions weakly and the transition f2(a, b) -> f2(a - 1, b) [ a >= 1 ] strictly and produces the following problem: 3: T: (1, 1) f0(a, b) -> f2(a, 0) (a, 1) f2(a, b) -> f2(a - 1, b) [ a >= 1 ] start location: f0 leaf cost: 1 Complexity upper bound a + 2 Time: 0.087 sec (SMT: 0.084 sec)