WORST_CASE(?, O(n^2)) 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_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl72(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_0 >= 1 /\ Ar_3 = 0 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_5, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_3 >= 1 /\ 0 >= Ar_0 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 + 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 + 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 >= Ar_3 /\ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 /\ Ar_3 >= 1 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0)) (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 transition from problem 1: lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_5, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_3 >= 1 /\ 0 >= Ar_0 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 + 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 + 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl72(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_0 >= 1 /\ Ar_3 = 0 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 >= Ar_3 /\ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 /\ Ar_3 >= 1 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (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_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0)) (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) lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 + 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl72(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_0 >= 1 /\ Ar_3 = 0 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 >= Ar_3 /\ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 /\ Ar_3 >= 1 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (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_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0)) (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(lbl72) = 1 Pol(lbl62) = 1 Pol(stop) = 0 Pol(start) = 1 Pol(start0) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition lbl72(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_0 >= 1 /\ Ar_3 = 0 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] strictly and produces the following problem: 4: T: (Comp: ?, Cost: 1) lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 + 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) lbl72(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_0 >= 1 /\ Ar_3 = 0 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 >= Ar_3 /\ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 /\ Ar_3 >= 1 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (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_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0)) (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(lbl72) = 2*V_4 Pol(lbl62) = 2*V_4 - 1 Pol(stop) = 2*V_4 Pol(start) = 2*V_6 Pol(start0) = 2*V_1 Pol(koat_start) = 2*V_1 orients all transitions weakly and the transition lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] strictly and produces the following problem: 5: T: (Comp: ?, Cost: 1) lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 + 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) lbl72(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_0 >= 1 /\ Ar_3 = 0 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 >= Ar_3 /\ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 /\ Ar_3 >= 1 /\ Ar_5 = Ar_0 ] (Comp: 2*Ar_0, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (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_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0)) (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 5 produces the following problem: 6: T: (Comp: 2*Ar_0, Cost: 1) lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 + 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) lbl72(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_0 >= 1 /\ Ar_3 = 0 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: ?, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 >= Ar_3 /\ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 /\ Ar_3 >= 1 /\ Ar_5 = Ar_0 ] (Comp: 2*Ar_0, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (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_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0)) (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(lbl62) = V_2 and size complexities S("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 ]", 0-0) = Ar_0 S("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 ]", 0-1) = Ar_1 S("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 ]", 0-2) = Ar_2 S("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 ]", 0-3) = Ar_3 S("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 ]", 0-4) = Ar_4 S("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 ]", 0-5) = Ar_5 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0))", 0-0) = Ar_0 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0))", 0-1) = Ar_2 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0))", 0-2) = Ar_2 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0))", 0-3) = Ar_4 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0))", 0-4) = Ar_4 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0))", 0-5) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-0) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-1) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-2) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-3) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-4) = Ar_4 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-5) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-0) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-1) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-2) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-3) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-4) = Ar_4 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_0 ]", 0-5) = Ar_0 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\\ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-0) = Ar_0 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\\ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-1) = 0 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\\ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-2) = Ar_2 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\\ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-3) = Ar_0 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\\ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-4) = Ar_4 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\\ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-5) = Ar_0 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\\ Ar_0 >= Ar_3 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 /\\ Ar_3 >= 1 /\\ Ar_5 = Ar_0 ]", 0-0) = Ar_0 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\\ Ar_0 >= Ar_3 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 /\\ Ar_3 >= 1 /\\ Ar_5 = Ar_0 ]", 0-1) = Ar_0 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\\ Ar_0 >= Ar_3 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 /\\ Ar_3 >= 1 /\\ Ar_5 = Ar_0 ]", 0-2) = Ar_2 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\\ Ar_0 >= Ar_3 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 /\\ Ar_3 >= 1 /\\ Ar_5 = Ar_0 ]", 0-3) = Ar_0 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\\ Ar_0 >= Ar_3 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 /\\ Ar_3 >= 1 /\\ Ar_5 = Ar_0 ]", 0-4) = Ar_4 S("lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\\ Ar_0 >= Ar_3 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_1 >= 0 /\\ Ar_3 >= 1 /\\ Ar_5 = Ar_0 ]", 0-5) = Ar_0 S("lbl72(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_0 >= 1 /\\ Ar_3 = 0 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-0) = Ar_0 S("lbl72(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_0 >= 1 /\\ Ar_3 = 0 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-1) = 0 S("lbl72(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_0 >= 1 /\\ Ar_3 = 0 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-2) = Ar_2 S("lbl72(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_0 >= 1 /\\ Ar_3 = 0 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-3) = 0 S("lbl72(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_0 >= 1 /\\ Ar_3 = 0 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-4) = Ar_4 S("lbl72(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_0 >= 1 /\\ Ar_3 = 0 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-5) = Ar_0 S("lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_3 >= 0 /\\ Ar_0 >= Ar_3 + 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-0) = Ar_0 S("lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_3 >= 0 /\\ Ar_0 >= Ar_3 + 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-1) = Ar_0 S("lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_3 >= 0 /\\ Ar_0 >= Ar_3 + 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-2) = Ar_2 S("lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_3 >= 0 /\\ Ar_0 >= Ar_3 + 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-3) = Ar_0 S("lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_3 >= 0 /\\ Ar_0 >= Ar_3 + 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-4) = Ar_4 S("lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_3 >= 0 /\\ Ar_0 >= Ar_3 + 1 /\\ Ar_1 = 0 /\\ Ar_5 = Ar_0 ]", 0-5) = Ar_0 orients the transitions lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 >= Ar_3 /\ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 /\ Ar_3 >= 1 /\ Ar_5 = Ar_0 ] weakly and the transition lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 >= Ar_3 /\ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 /\ Ar_3 >= 1 /\ Ar_5 = Ar_0 ] strictly and produces the following problem: 7: T: (Comp: 2*Ar_0, Cost: 1) lbl72(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 + 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) lbl72(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_0 >= 1 /\ Ar_3 = 0 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: 2*Ar_0^2 + Ar_0, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_1 - 1, Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_1 >= 1 /\ Ar_0 >= Ar_3 /\ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 /\ Ar_3 >= 1 /\ Ar_5 = Ar_0 ] (Comp: 2*Ar_0, Cost: 1) lbl62(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl72(Ar_0, Ar_1, Ar_2, Ar_3 - 1, Ar_4, Ar_5)) [ Ar_0 >= Ar_3 /\ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_1 = 0 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl62(Ar_0, Ar_5 - 1, Ar_2, Ar_5, Ar_4, Ar_5)) [ Ar_0 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (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_5, Ar_4, Ar_5)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_0 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_4, Ar_4, Ar_0)) (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 5*Ar_0 + 2*Ar_0^2 + 4 Time: 1.860 sec (SMT: 1.803 sec)