WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_2, Ar_1 - 1, Ar_0 + 1)) [ 100 >= Ar_0 /\ Ar_1 >= Ar_2 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_2, Ar_1 - 1, Ar_0 + 1)) [ 100 >= Ar_0 /\ Ar_1 >= Ar_2 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval) = -V_1 + V_2 - V_3 + 101 Pol(start) = -V_1 + V_2 - V_3 + 101 Pol(koat_start) = -V_1 + V_2 - V_3 + 101 orients all transitions weakly and the transition eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_2, Ar_1 - 1, Ar_0 + 1)) [ 100 >= Ar_0 /\ Ar_1 >= Ar_2 ] strictly and produces the following problem: 3: T: (Comp: Ar_0 + Ar_1 + Ar_2 + 101, Cost: 1) eval(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_2, Ar_1 - 1, Ar_0 + 1)) [ 100 >= Ar_0 /\ Ar_1 >= Ar_2 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2) -> Com_1(eval(Ar_0, Ar_1, Ar_2)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound Ar_0 + Ar_1 + Ar_2 + 102 Time: 0.386 sec (SMT: 0.375 sec)