WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_1 >= Ar_0 /\ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= Ar_2 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_1 >= Ar_0 /\ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= Ar_2 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval) = 2*V_1 - 2*V_2 - 1 Pol(start) = 2*V_1 - 2*V_2 Pol(koat_start) = 2*V_1 - 2*V_2 orients all transitions weakly and the transitions eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= Ar_2 ] eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] strictly and produces the following problem: 3: T: (Comp: 2*Ar_0 + 2*Ar_1, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_1 >= Ar_0 /\ Ar_2 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 2*Ar_1, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= Ar_2 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval) = 2*V_1 - 2*V_2 + V_3 - V_4 - 2 Pol(start) = 2*V_1 - 2*V_2 + V_3 - V_4 Pol(koat_start) = 2*V_1 - 2*V_2 + V_3 - V_4 orients all transitions weakly and the transition eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] strictly and produces the following problem: 4: T: (Comp: 2*Ar_0 + 2*Ar_1, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 2*Ar_1 + Ar_2 + Ar_3, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_1 >= Ar_0 /\ Ar_2 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 2*Ar_1, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= Ar_2 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval) = V_3 - V_4 Pol(start) = V_3 - V_4 Pol(koat_start) = V_3 - V_4 orients all transitions weakly and the transition eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_1 >= Ar_0 /\ Ar_2 >= Ar_3 + 1 ] strictly and produces the following problem: 5: T: (Comp: 2*Ar_0 + 2*Ar_1, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 2*Ar_1 + Ar_2 + Ar_3, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_2 >= Ar_3 + 1 ] (Comp: Ar_2 + Ar_3, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + 1)) [ Ar_1 >= Ar_0 /\ Ar_2 >= Ar_3 + 1 ] (Comp: 2*Ar_0 + 2*Ar_1, Cost: 1) eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= Ar_2 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(eval(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 6*Ar_0 + 6*Ar_1 + 2*Ar_2 + 2*Ar_3 + 1 Time: 1.208 sec (SMT: 1.165 sec)