YES(?, 22) Initial complexity problem: 1: T: (1, 1) f0(a) -> f5(b) [ b >= 1 ] (?, 1) f5(a) -> f5(a + 1) [ 19 >= a ] (1, 1) f0(a) -> f12(b) [ 0 >= b ] (?, 1) f5(a) -> f12(a) [ 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) -> f5(b) [ b >= 1 ] (?, 1) f5(a) -> f5(a + 1) [ 19 >= a ] start location: f0 leaf cost: 2 A polynomial rank function with Pol(f0) = 19 Pol(f5) = -V_1 + 20 orients all transitions weakly and the transition f5(a) -> f5(a + 1) [ 19 >= a ] strictly and produces the following problem: 3: T: (1, 1) f0(a) -> f5(b) [ b >= 1 ] (19, 1) f5(a) -> f5(a + 1) [ 19 >= a ] start location: f0 leaf cost: 2 Complexity upper bound 22 Time: 0.077 sec (SMT: 0.074 sec)