YES(?, 20) Initial complexity problem: 1: T: (1, 1) f0(a, b) -> f5(2, 4) (?, 1) f5(a, b) -> f5(a + 2, a + 4) [ 19 >= a ] (?, 1) f5(a, b) -> f8(a, b) [ a >= 20 ] 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) -> f5(2, 4) (?, 1) f5(a, b) -> f5(a + 2, a + 4) [ 19 >= a ] start location: f0 leaf cost: 1 A polynomial rank function with Pol(f0) = 18 Pol(f5) = -V_1 + 20 orients all transitions weakly and the transition f5(a, b) -> f5(a + 2, a + 4) [ 19 >= a ] strictly and produces the following problem: 3: T: (1, 1) f0(a, b) -> f5(2, 4) (18, 1) f5(a, b) -> f5(a + 2, a + 4) [ 19 >= a ] start location: f0 leaf cost: 1 Complexity upper bound 20 Time: 0.122 sec (SMT: 0.118 sec)