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(lbl71(Ar_0, Ar_1, 1, Ar_3, 0, Ar_5)) [ Ar_0 >= 2 /\ 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(stop(Ar_0, Ar_1, 0, Ar_3, 1, Ar_5)) [ 1 >= Ar_0 /\ 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(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\ Ar_0 >= Ar_2 + 1 /\ Ar_0 >= Ar_4 + 2 /\ Ar_2 >= 1 /\ Ar_4 >= 0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\ Ar_0 >= Ar_4 + 2 /\ Ar_0 >= 2 /\ Ar_4 >= 0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (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 + 1, Ar_5)) [ Ar_0 >= 2 /\ Ar_4 + 2 = Ar_0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 1 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, 0, Ar_3, Ar_4 + 1, Ar_5)) [ 1 >= Ar_0 /\ Ar_0 >= Ar_4 + 3 /\ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 1 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, 0, Ar_3, Ar_4 + 1, Ar_5)) [ 1 >= Ar_0 /\ Ar_0 >= 3 /\ Ar_2 + 1 = Ar_0 /\ Ar_4 + 2 = Ar_0 /\ Ar_1 = Ar_0 ] (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 Testing for reachability in the complexity graph removes the following transitions from problem 1: cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, 0, Ar_3, Ar_4 + 1, Ar_5)) [ 1 >= Ar_0 /\ Ar_0 >= Ar_4 + 3 /\ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 1 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, 0, Ar_3, Ar_4 + 1, Ar_5)) [ 1 >= Ar_0 /\ Ar_0 >= 3 /\ Ar_2 + 1 = Ar_0 /\ Ar_4 + 2 = Ar_0 /\ Ar_1 = Ar_0 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 1 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\ Ar_0 >= Ar_4 + 2 /\ Ar_0 >= 2 /\ Ar_4 >= 0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (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 + 1, Ar_5)) [ Ar_0 >= 2 /\ Ar_4 + 2 = Ar_0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\ Ar_0 >= Ar_2 + 1 /\ Ar_0 >= Ar_4 + 2 /\ Ar_2 >= 1 /\ Ar_4 >= 0 /\ Ar_1 = 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, 0, Ar_3, 1, Ar_5)) [ 1 >= 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_3, 0, Ar_5)) [ Ar_0 >= 2 /\ Ar_1 = Ar_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_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 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 1 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\ Ar_0 >= Ar_4 + 2 /\ Ar_0 >= 2 /\ Ar_4 >= 0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (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 + 1, Ar_5)) [ Ar_0 >= 2 /\ Ar_4 + 2 = Ar_0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\ Ar_0 >= Ar_2 + 1 /\ Ar_0 >= Ar_4 + 2 /\ Ar_2 >= 1 /\ Ar_4 >= 0 /\ Ar_1 = 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, 0, Ar_3, 1, Ar_5)) [ 1 >= 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_3, 0, Ar_5)) [ Ar_0 >= 2 /\ Ar_1 = Ar_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_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(cut) = 1 Pol(lbl71) = 1 Pol(stop) = 0 Pol(start) = 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 + 1, Ar_5)) [ Ar_0 >= 2 /\ Ar_4 + 2 = Ar_0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] strictly and produces the following problem: 4: T: (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 1 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\ Ar_0 >= Ar_4 + 2 /\ Ar_0 >= 2 /\ Ar_4 >= 0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (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 + 1, Ar_5)) [ Ar_0 >= 2 /\ Ar_4 + 2 = Ar_0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\ Ar_0 >= Ar_2 + 1 /\ Ar_0 >= Ar_4 + 2 /\ Ar_2 >= 1 /\ Ar_4 >= 0 /\ Ar_1 = 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, 0, Ar_3, 1, Ar_5)) [ 1 >= 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_3, 0, Ar_5)) [ Ar_0 >= 2 /\ Ar_1 = Ar_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_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(cut) = 3*V_1 - 3*V_5 + 2 Pol(lbl71) = 3*V_1 - 3*V_5 Pol(stop) = 3*V_1 - 3*V_3 Pol(start) = 3*V_1 Pol(start0) = 3*V_1 Pol(koat_start) = 3*V_1 orients all transitions weakly and the transition lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\ Ar_0 >= Ar_4 + 2 /\ Ar_0 >= 2 /\ Ar_4 >= 0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] strictly and produces the following problem: 5: T: (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 1 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: 3*Ar_0, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\ Ar_0 >= Ar_4 + 2 /\ Ar_0 >= 2 /\ Ar_4 >= 0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (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 + 1, Ar_5)) [ Ar_0 >= 2 /\ Ar_4 + 2 = Ar_0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\ Ar_0 >= Ar_2 + 1 /\ Ar_0 >= Ar_4 + 2 /\ Ar_2 >= 1 /\ Ar_4 >= 0 /\ Ar_1 = 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, 0, Ar_3, 1, Ar_5)) [ 1 >= 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_3, 0, Ar_5)) [ Ar_0 >= 2 /\ Ar_1 = Ar_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_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 5 produces the following problem: 6: T: (Comp: 3*Ar_0, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 1 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: 3*Ar_0, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\ Ar_0 >= Ar_4 + 2 /\ Ar_0 >= 2 /\ Ar_4 >= 0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (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 + 1, Ar_5)) [ Ar_0 >= 2 /\ Ar_4 + 2 = Ar_0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: ?, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\ Ar_0 >= Ar_2 + 1 /\ Ar_0 >= Ar_4 + 2 /\ Ar_2 >= 1 /\ Ar_4 >= 0 /\ Ar_1 = 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, 0, Ar_3, 1, Ar_5)) [ 1 >= 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_3, 0, Ar_5)) [ Ar_0 >= 2 /\ Ar_1 = Ar_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_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(lbl71) = V_1 - V_3 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_0, Ar_3, Ar_3, Ar_5, Ar_5))", 0-0) = Ar_0 S("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))", 0-1) = Ar_0 S("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))", 0-2) = Ar_3 S("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))", 0-3) = Ar_3 S("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))", 0-4) = Ar_5 S("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))", 0-5) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, 0, Ar_5)) [ Ar_0 >= 2 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 0-0) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, 0, Ar_5)) [ Ar_0 >= 2 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 0-1) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, 0, Ar_5)) [ Ar_0 >= 2 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 0-2) = 1 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, 0, Ar_5)) [ Ar_0 >= 2 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 0-3) = Ar_3 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, 0, Ar_5)) [ Ar_0 >= 2 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 0-4) = 0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, 0, Ar_5)) [ Ar_0 >= 2 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 0-5) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, 0, Ar_3, 1, Ar_5)) [ 1 >= Ar_0 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 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, 0, Ar_3, 1, Ar_5)) [ 1 >= Ar_0 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 0-1) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, 0, Ar_3, 1, Ar_5)) [ 1 >= Ar_0 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 0-2) = 0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, 0, Ar_3, 1, Ar_5)) [ 1 >= Ar_0 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 0-3) = Ar_3 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, 0, Ar_3, 1, Ar_5)) [ 1 >= Ar_0 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 0-4) = 1 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(stop(Ar_0, Ar_1, 0, Ar_3, 1, Ar_5)) [ 1 >= Ar_0 /\\ Ar_1 = Ar_0 /\\ Ar_2 = Ar_3 /\\ Ar_4 = Ar_5 ]", 0-5) = Ar_5 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\\ Ar_0 >= Ar_2 + 1 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_2 >= 1 /\\ Ar_4 >= 0 /\\ Ar_1 = Ar_0 ]", 0-0) = Ar_0 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\\ Ar_0 >= Ar_2 + 1 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_2 >= 1 /\\ Ar_4 >= 0 /\\ Ar_1 = Ar_0 ]", 0-1) = Ar_0 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\\ Ar_0 >= Ar_2 + 1 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_2 >= 1 /\\ Ar_4 >= 0 /\\ Ar_1 = Ar_0 ]", 0-2) = Ar_0 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\\ Ar_0 >= Ar_2 + 1 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_2 >= 1 /\\ Ar_4 >= 0 /\\ Ar_1 = Ar_0 ]", 0-3) = Ar_3 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\\ Ar_0 >= Ar_2 + 1 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_2 >= 1 /\\ Ar_4 >= 0 /\\ Ar_1 = Ar_0 ]", 0-4) = Ar_0 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\\ Ar_0 >= Ar_2 + 1 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_2 >= 1 /\\ Ar_4 >= 0 /\\ Ar_1 = Ar_0 ]", 0-5) = Ar_5 S("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 + 1, Ar_5)) [ Ar_0 >= 2 /\\ Ar_4 + 2 = Ar_0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-0) = Ar_0 S("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 + 1, Ar_5)) [ Ar_0 >= 2 /\\ Ar_4 + 2 = Ar_0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-1) = Ar_0 S("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 + 1, Ar_5)) [ Ar_0 >= 2 /\\ Ar_4 + 2 = Ar_0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-2) = Ar_0 + 1 S("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 + 1, Ar_5)) [ Ar_0 >= 2 /\\ Ar_4 + 2 = Ar_0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-3) = Ar_3 S("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 + 1, Ar_5)) [ Ar_0 >= 2 /\\ Ar_4 + 2 = Ar_0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-4) = Ar_0 S("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 + 1, Ar_5)) [ Ar_0 >= 2 /\\ Ar_4 + 2 = Ar_0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-5) = Ar_5 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_0 >= 2 /\\ Ar_4 >= 0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-0) = Ar_0 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_0 >= 2 /\\ Ar_4 >= 0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-1) = Ar_0 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_0 >= 2 /\\ Ar_4 >= 0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-2) = Ar_0 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_0 >= 2 /\\ Ar_4 >= 0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-3) = Ar_3 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_0 >= 2 /\\ Ar_4 >= 0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-4) = Ar_0 S("lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_0 >= 2 /\\ Ar_4 >= 0 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-5) = Ar_5 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_4 >= 1 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-0) = Ar_0 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_4 >= 1 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-1) = Ar_0 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_4 >= 1 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-2) = 1 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_4 >= 1 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-3) = Ar_3 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_4 >= 1 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-4) = Ar_0 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\\ Ar_0 >= Ar_4 + 2 /\\ Ar_4 >= 1 /\\ Ar_2 + 1 = Ar_0 /\\ Ar_1 = Ar_0 ]", 0-5) = Ar_5 orients the transitions lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\ Ar_0 >= Ar_2 + 1 /\ Ar_0 >= Ar_4 + 2 /\ Ar_2 >= 1 /\ Ar_4 >= 0 /\ Ar_1 = Ar_0 ] weakly and the transition lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\ Ar_0 >= Ar_2 + 1 /\ Ar_0 >= Ar_4 + 2 /\ Ar_2 >= 1 /\ Ar_4 >= 0 /\ Ar_1 = Ar_0 ] strictly and produces the following problem: 7: T: (Comp: 3*Ar_0, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 1 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: 3*Ar_0, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 3 /\ Ar_0 >= Ar_4 + 2 /\ Ar_0 >= 2 /\ Ar_4 >= 0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (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 + 1, Ar_5)) [ Ar_0 >= 2 /\ Ar_4 + 2 = Ar_0 /\ Ar_2 + 1 = Ar_0 /\ Ar_1 = Ar_0 ] (Comp: 3*Ar_0^2 + 4*Ar_0 + 1, Cost: 1) lbl71(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(lbl71(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ Ar_0 >= Ar_2 + 2 /\ Ar_0 >= Ar_2 + 1 /\ Ar_0 >= Ar_4 + 2 /\ Ar_2 >= 1 /\ Ar_4 >= 0 /\ Ar_1 = 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, 0, Ar_3, 1, Ar_5)) [ 1 >= 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_3, 0, Ar_5)) [ Ar_0 >= 2 /\ Ar_1 = Ar_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_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 10*Ar_0 + 3*Ar_0^2 + 5 Time: 1.440 sec (SMT: 1.376 sec)