WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 >= Ar_2 + 1 /\ Ar_2 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: ?, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: ?, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_0 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= Ar_1 /\ Ar_3 = Ar_1 ] (Comp: ?, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 >= Ar_2 + 1 /\ Ar_2 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: ?, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_0 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= Ar_1 /\ Ar_3 = Ar_1 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(start) = 2 Pol(stop) = 0 Pol(lbl6) = 0 Pol(cut) = 1 Pol(lbl101) = 2 Pol(lbl111) = 2 Pol(start0) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_0 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] cut(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= Ar_1 /\ Ar_3 = Ar_1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 >= Ar_2 + 1 /\ Ar_2 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: ?, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: 2, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_0 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: 2, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= Ar_1 /\ Ar_3 = Ar_1 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(start) = 1 Pol(stop) = 0 Pol(lbl6) = 0 Pol(cut) = 0 Pol(lbl101) = 1 Pol(lbl111) = 1 Pol(start0) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 >= Ar_2 + 1 /\ Ar_2 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 1, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: ?, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: 2, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_0 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: 2, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= Ar_1 /\ Ar_3 = Ar_1 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(start) = -20*V_2 + 31*V_3 + 21*V_4 Pol(stop) = V_2 + 10*V_3 + 21*V_4 - 52 Pol(lbl6) = V_2 + 10*V_3 + 21*V_4 Pol(cut) = V_2 + 10*V_3 + 21*V_4 - 52 Pol(lbl101) = V_2 + 10*V_3 + 21*V_4 - 52 Pol(lbl111) = V_2 + 10*V_3 + 21*V_4 - 52 Pol(start0) = 21*V_1 + 11*V_3 Pol(koat_start) = 21*V_1 + 11*V_3 orients all transitions weakly and the transitions lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 >= Ar_2 + 1 /\ Ar_2 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 1, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: 21*Ar_0 + 11*Ar_2, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: 21*Ar_0 + 11*Ar_2, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: 2, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_0 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: ?, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: 21*Ar_0 + 11*Ar_2, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: 2, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= Ar_1 /\ Ar_3 = Ar_1 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 5 produces the following problem: 6: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_0 /\ Ar_2 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_0 >= Ar_2 + 1 /\ Ar_2 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ] (Comp: 1, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 /\ 0 >= Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 1, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: 21*Ar_0 + 11*Ar_2, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: 21*Ar_0 + 11*Ar_2, Cost: 1) lbl101(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_0 >= Ar_3 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= Ar_3 + Ar_1 ] (Comp: 2, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_0 >= 2*Ar_1 /\ Ar_3 = Ar_1 ] (Comp: 42*Ar_0 + 22*Ar_2 + 1, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl101(Ar_0, Ar_1 - Ar_3, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: 21*Ar_0 + 11*Ar_2, Cost: 1) lbl111(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl111(Ar_0, Ar_1, Ar_2, Ar_3 - Ar_1)) [ Ar_3 >= Ar_1 + 1 /\ Ar_2 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_3 + Ar_1 ] (Comp: 2, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_2 >= Ar_1 /\ Ar_3 = Ar_1 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 105*Ar_0 + 55*Ar_2 + 13 Time: 1.995 sec (SMT: 1.930 sec)