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(lbl91(Ar_0, Ar_1, 100, Ar_3, 1, Ar_5)) [ Ar_0 = 0 /\ Ar_1 = 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(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ Ar_0 = Ar_1 /\ 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(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 = Ar_1 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: ?, Cost: 1) lbl91(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_4 = 40 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] (Comp: ?, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_0 = 0 /\ Ar_2 = 100 /\ Ar_1 = 0 ] (Comp: ?, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] (Comp: ?, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] (Comp: ?, Cost: 1) lbl111(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_4 >= 40 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_0 = 0 /\ Ar_2 = 100 /\ Ar_1 = 0 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ Ar_1 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_1, Ar_1, 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 Testing for reachability in the complexity graph removes the following transitions from problem 1: lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_0 = 0 /\ Ar_2 = 100 /\ Ar_1 = 0 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) lbl111(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_4 >= 40 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl91(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_4 = 40 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ Ar_1 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_0 = 0 /\ Ar_2 = 100 /\ Ar_1 = 0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 = Ar_1 /\ 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(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ Ar_0 = Ar_1 /\ 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(lbl91(Ar_0, Ar_1, 100, Ar_3, 1, Ar_5)) [ Ar_0 = 0 /\ Ar_1 = 0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: ?, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_1, Ar_1, 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 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) lbl111(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_4 >= 40 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl91(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_4 = 40 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ Ar_1 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_0 = 0 /\ Ar_2 = 100 /\ Ar_1 = 0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 = Ar_1 /\ 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(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ Ar_0 = Ar_1 /\ 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(lbl91(Ar_0, Ar_1, 100, Ar_3, 1, Ar_5)) [ Ar_0 = 0 /\ Ar_1 = 0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_1, Ar_1, 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(lbl111) = 1 Pol(stop) = -179 Pol(lbl91) = -178 Pol(start) = 1 Pol(start0) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition lbl111(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_4 >= 40 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) lbl111(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_4 >= 40 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl91(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_4 = 40 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ Ar_1 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_0 = 0 /\ Ar_2 = 100 /\ Ar_1 = 0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 = Ar_1 /\ 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(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ Ar_0 = Ar_1 /\ 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(lbl91(Ar_0, Ar_1, 100, Ar_3, 1, Ar_5)) [ Ar_0 = 0 /\ Ar_1 = 0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_1, Ar_1, 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(lbl111) = 0 Pol(stop) = 0 Pol(lbl91) = 1 Pol(start) = 1 Pol(start0) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition lbl91(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_4 = 40 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) lbl111(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_4 >= 40 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) lbl91(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_4 = 40 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ Ar_1 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_0 = 0 /\ Ar_2 = 100 /\ Ar_1 = 0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 = Ar_1 /\ 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(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ Ar_0 = Ar_1 /\ 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(lbl91(Ar_0, Ar_1, 100, Ar_3, 1, Ar_5)) [ Ar_0 = 0 /\ Ar_1 = 0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_1, Ar_1, 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(lbl111) = 157*V_1 - 4*V_5 Pol(stop) = 157*V_1 - 164 Pol(lbl91) = 157*V_1 + V_3 - V_5 + 39 Pol(start) = 157*V_1 + 138 Pol(start0) = 157*V_2 + 138 Pol(koat_start) = 157*V_2 + 138 orients all transitions weakly and the transitions lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_0 = 0 /\ Ar_2 = 100 /\ Ar_1 = 0 ] lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ Ar_1 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) lbl111(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_4 >= 40 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) lbl91(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_4 = 40 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] (Comp: 157*Ar_1 + 138, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ Ar_1 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: 157*Ar_1 + 138, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_0 = 0 /\ Ar_2 = 100 /\ Ar_1 = 0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 = Ar_1 /\ 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(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ Ar_0 = Ar_1 /\ 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(lbl91(Ar_0, Ar_1, 100, Ar_3, 1, Ar_5)) [ Ar_0 = 0 /\ Ar_1 = 0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_1, Ar_1, 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(lbl111) = -40*V_2 - V_5 Pol(stop) = -40*V_2 - 41 Pol(lbl91) = -40*V_2 Pol(start) = -40*V_2 Pol(start0) = -40*V_2 Pol(koat_start) = -40*V_2 orients all transitions weakly and the transition lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) lbl111(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_4 >= 40 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: 1, Cost: 1) lbl91(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_4 = 40 /\ Ar_2 = 100 /\ Ar_0 = 0 /\ Ar_1 = 0 ] (Comp: 157*Ar_1 + 138, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ Ar_1 >= 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: 40*Ar_1, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ 39 >= Ar_4 /\ Ar_4 >= 2 /\ 41 >= Ar_4 /\ Ar_2 = 100 /\ Ar_0 = Ar_1 ] (Comp: 157*Ar_1 + 138, Cost: 1) lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl91(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ 39 >= Ar_4 /\ Ar_4 >= 1 /\ 40 >= Ar_4 /\ Ar_0 = 0 /\ Ar_2 = 100 /\ Ar_1 = 0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 = Ar_1 /\ 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(lbl111(Ar_0, Ar_1, 100, Ar_3, 2, Ar_5)) [ 0 >= Ar_1 + 1 /\ Ar_0 = Ar_1 /\ 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(lbl91(Ar_0, Ar_1, 100, Ar_3, 1, Ar_5)) [ Ar_0 = 0 /\ Ar_1 = 0 /\ Ar_2 = Ar_3 /\ Ar_4 = Ar_5 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_1, Ar_1, 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 354*Ar_1 + 282 Time: 3.293 sec (SMT: 3.185 sec)