YES(?, 4*a + 2*b + 2*c + 3) Initial complexity problem: 1: T: (?, 1) f(a, b, c) -> f(a, b + 1, c) [ a >= b + 1 /\ a >= c + 1 ] (?, 1) f(a, b, c) -> f(a, b, c + 1) [ a >= b + 1 /\ a >= c + 1 ] (1, 1) start(a, b, c) -> f(a, b, c) start location: start leaf cost: 0 A polynomial rank function with Pol(f) = 2*V_1 - V_2 - V_3 - 1 Pol(start) = 2*V_1 - V_2 - V_3 - 1 orients all transitions weakly and the transitions f(a, b, c) -> f(a, b + 1, c) [ a >= b + 1 /\ a >= c + 1 ] f(a, b, c) -> f(a, b, c + 1) [ a >= b + 1 /\ a >= c + 1 ] strictly and produces the following problem: 2: T: (2*a + b + c + 1, 1) f(a, b, c) -> f(a, b + 1, c) [ a >= b + 1 /\ a >= c + 1 ] (2*a + b + c + 1, 1) f(a, b, c) -> f(a, b, c + 1) [ a >= b + 1 /\ a >= c + 1 ] (1, 1) start(a, b, c) -> f(a, b, c) start location: start leaf cost: 0 Complexity upper bound 4*a + 2*b + 2*c + 3 Time: 0.093 sec (SMT: 0.089 sec)