WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 /\ Ar_1 = 0 /\ Ar_4 + Ar_2 = Ar_5 + Ar_3 /\ Ar_0 + Ar_2 = Ar_3 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 + Ar_2 >= Ar_3 + 1 /\ Ar_3 >= Ar_2 + 1 /\ Ar_0 + Ar_2 >= Ar_3 /\ Ar_4 + Ar_2 = Ar_3 + Ar_5 /\ Ar_1 + Ar_3 = Ar_0 + Ar_2 ] (Comp: ?, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_0, Ar_3, Ar_3, Ar_5, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 /\ Ar_1 = 0 /\ Ar_4 + Ar_2 = Ar_5 + Ar_3 /\ Ar_0 + Ar_2 = Ar_3 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 + Ar_2 >= Ar_3 + 1 /\ Ar_3 >= Ar_2 + 1 /\ Ar_0 + Ar_2 >= Ar_3 /\ Ar_4 + Ar_2 = Ar_3 + Ar_5 /\ Ar_1 + Ar_3 = Ar_0 + Ar_2 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_0, Ar_3, Ar_3, Ar_5, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(start) = 1 Pol(stop) = 0 Pol(lbl71) = 1 Pol(start0) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 /\ Ar_1 = 0 /\ Ar_4 + Ar_2 = Ar_5 + Ar_3 /\ Ar_0 + Ar_2 = Ar_3 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: 1, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 /\ Ar_1 = 0 /\ Ar_4 + Ar_2 = Ar_5 + Ar_3 /\ Ar_0 + Ar_2 = Ar_3 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 + Ar_2 >= Ar_3 + 1 /\ Ar_3 >= Ar_2 + 1 /\ Ar_0 + Ar_2 >= Ar_3 /\ Ar_4 + Ar_2 = Ar_3 + Ar_5 /\ Ar_1 + Ar_3 = Ar_0 + Ar_2 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_0, Ar_3, Ar_3, Ar_5, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(start) = V_1 + V_3 - V_4 Pol(stop) = V_1 + V_3 - V_4 Pol(lbl71) = V_1 + V_3 - V_4 Pol(start0) = V_1 Pol(koat_start) = V_1 orients all transitions weakly and the transition lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 + Ar_2 >= Ar_3 + 1 /\ Ar_3 >= Ar_2 + 1 /\ Ar_0 + Ar_2 >= Ar_3 /\ Ar_4 + Ar_2 = Ar_3 + Ar_5 /\ Ar_1 + Ar_3 = Ar_0 + Ar_2 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_0 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: 1, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_2 + 1 /\ Ar_1 = 0 /\ Ar_4 + Ar_2 = Ar_5 + Ar_3 /\ Ar_0 + Ar_2 = Ar_3 ] (Comp: Ar_0, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1 - 1, Ar_2 - 1, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 + Ar_2 >= Ar_3 + 1 /\ Ar_3 >= Ar_2 + 1 /\ Ar_0 + Ar_2 >= Ar_3 /\ Ar_4 + Ar_2 = Ar_3 + Ar_5 /\ Ar_1 + Ar_3 = Ar_0 + Ar_2 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_0, Ar_3, Ar_3, Ar_5, Ar_5)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound Ar_0 + 4 Time: 1.484 sec (SMT: 1.434 sec)