WORST_CASE(?, O(n^1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cont1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 /\ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop2(Ar_0, Ar_1, 1, Ar_3 - 1)) [ Ar_3 >= 1 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(a(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) a(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(b(Ar_0, Ar_1, Fresh_0, Ar_3 - 1)) [ Ar_0 >= Ar_3 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_1, Ar_1, Ar_0)) [ Ar_0 >= 0 /\ Ar_1 >= 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: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cont1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 /\ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop2(Ar_0, Ar_1, 1, Ar_3 - 1)) [ Ar_3 >= 1 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(a(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) a(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(b(Ar_0, Ar_1, Fresh_0, Ar_3 - 1)) [ Ar_0 >= Ar_3 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_1, Ar_1, Ar_0)) [ Ar_0 >= 0 /\ Ar_1 >= 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(stop1) = 0 Pol(cont1) = 1 Pol(stop2) = 0 Pol(a) = 1 Pol(b) = 1 Pol(stop3) = 0 Pol(start0) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transitions start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 = 0 ] cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop2(Ar_0, Ar_1, 1, Ar_3 - 1)) [ Ar_3 >= 1 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 /\ Ar_2 = 0 ] b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 = 0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cont1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 /\ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: 1, Cost: 1) cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop2(Ar_0, Ar_1, 1, Ar_3 - 1)) [ Ar_3 >= 1 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(a(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) a(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(b(Ar_0, Ar_1, Fresh_0, Ar_3 - 1)) [ Ar_0 >= Ar_3 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_1, Ar_1, Ar_0)) [ Ar_0 >= 0 /\ Ar_1 >= 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) = 4*V_4 + 3 Pol(stop1) = 4*V_4 + 3 Pol(cont1) = 4*V_4 + 2 Pol(stop2) = 4*V_4 + 6 Pol(a) = 4*V_4 + 1 Pol(b) = 4*V_4 + 4 Pol(stop3) = 4*V_4 + 4 Pol(start0) = 4*V_1 + 3 Pol(koat_start) = 4*V_1 + 3 orients all transitions weakly and the transitions start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cont1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 /\ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 ] cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(a(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 ] b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 = 0 ] (Comp: 4*Ar_0 + 3, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cont1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 /\ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: 1, Cost: 1) cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop2(Ar_0, Ar_1, 1, Ar_3 - 1)) [ Ar_3 >= 1 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 /\ Ar_2 = 0 ] (Comp: 4*Ar_0 + 3, Cost: 1) cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(a(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) a(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(b(Ar_0, Ar_1, Fresh_0, Ar_3 - 1)) [ Ar_0 >= Ar_3 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 1 ] (Comp: 4*Ar_0 + 3, Cost: 1) b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_1, Ar_1, Ar_0)) [ Ar_0 >= 0 /\ Ar_1 >= 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 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 = 0 ] (Comp: 4*Ar_0 + 3, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(cont1(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= 1 /\ Ar_0 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: 1, Cost: 1) cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop2(Ar_0, Ar_1, 1, Ar_3 - 1)) [ Ar_3 >= 1 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 /\ Ar_2 = 0 ] (Comp: 4*Ar_0 + 3, Cost: 1) cont1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(a(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 1 /\ Ar_3 >= 1 /\ Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 ] (Comp: 4*Ar_0 + 3, Cost: 1) a(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(b(Ar_0, Ar_1, Fresh_0, Ar_3 - 1)) [ Ar_0 >= Ar_3 /\ Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_3 >= 1 ] (Comp: 4*Ar_0 + 3, Cost: 1) b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) b(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_1, Ar_1, Ar_0)) [ Ar_0 >= 0 /\ Ar_1 >= 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 16*Ar_0 + 16 Time: 1.182 sec (SMT: 1.152 sec)