YES(?, a + b + 2) Initial complexity problem: 1: T: (?, 1) f300(a, b, c) -> f300(a + 1, b, c) [ b >= a + 1 ] (?, 1) f300(a, b, c) -> f1(a, b, d) [ a >= b ] (1, 1) f2(a, b, c) -> f300(a, b, c) start location: f2 leaf cost: 0 Repeatedly removing leaves of the complexity graph in problem 1 produces the following problem: 2: T: (?, 1) f300(a, b, c) -> f300(a + 1, b, c) [ b >= a + 1 ] (1, 1) f2(a, b, c) -> f300(a, b, c) start location: f2 leaf cost: 1 A polynomial rank function with Pol(f300) = -V_1 + V_2 Pol(f2) = -V_1 + V_2 orients all transitions weakly and the transition f300(a, b, c) -> f300(a + 1, b, c) [ b >= a + 1 ] strictly and produces the following problem: 3: T: (a + b, 1) f300(a, b, c) -> f300(a + 1, b, c) [ b >= a + 1 ] (1, 1) f2(a, b, c) -> f300(a, b, c) start location: f2 leaf cost: 1 Complexity upper bound a + b + 2 Time: 0.061 sec (SMT: 0.059 sec)