YES(?, 2*a + 2*b + 2*c + 1) Initial complexity problem: 1: T: (?, 1) f(a, b, c) -> f(a, b + 1, c) [ a >= b + c + 1 ] (?, 1) f(a, b, c) -> f(a, b, c + 1) [ a >= b + 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) = V_1 - V_2 - V_3 Pol(start) = V_1 - V_2 - V_3 orients all transitions weakly and the transitions f(a, b, c) -> f(a, b + 1, c) [ a >= b + c + 1 ] f(a, b, c) -> f(a, b, c + 1) [ a >= b + c + 1 ] strictly and produces the following problem: 2: T: (a + b + c, 1) f(a, b, c) -> f(a, b + 1, c) [ a >= b + c + 1 ] (a + b + c, 1) f(a, b, c) -> f(a, b, c + 1) [ a >= b + c + 1 ] (1, 1) start(a, b, c) -> f(a, b, c) start location: start leaf cost: 0 Complexity upper bound 2*a + 2*b + 2*c + 1 Time: 0.095 sec (SMT: 0.091 sec)