WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f300(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 101 /\ 9 >= Ar_1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f2(Ar_0, Ar_1, 0, 0, 0)) [ 100 >= Ar_0 /\ 9 >= Ar_1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f2(Ar_0, Ar_1, 0, 0, 0)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f300(1000, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f300(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 101 /\ 9 >= Ar_1 ] (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f2(Ar_0, Ar_1, 0, 0, 0)) [ 100 >= Ar_0 /\ 9 >= Ar_1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f2(Ar_0, Ar_1, 0, 0, 0)) [ Ar_1 >= 10 ] (Comp: 1, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f300(1000, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f300) = 1 Pol(f2) = 0 Pol(f1) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f2(Ar_0, Ar_1, 0, 0, 0)) [ 100 >= Ar_0 /\ 9 >= Ar_1 ] strictly and produces the following problem: 3: T: (Comp: ?, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f300(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 101 /\ 9 >= Ar_1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f2(Ar_0, Ar_1, 0, 0, 0)) [ 100 >= Ar_0 /\ 9 >= Ar_1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f2(Ar_0, Ar_1, 0, 0, 0)) [ Ar_1 >= 10 ] (Comp: 1, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f300(1000, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f300) = V_1 - 100 Pol(f2) = V_1 - 100 Pol(f1) = 900 Pol(koat_start) = 900 orients all transitions weakly and the transition f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f300(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 101 /\ 9 >= Ar_1 ] strictly and produces the following problem: 4: T: (Comp: 900, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f300(Ar_0 - 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 101 /\ 9 >= Ar_1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f2(Ar_0, Ar_1, 0, 0, 0)) [ 100 >= Ar_0 /\ 9 >= Ar_1 ] (Comp: 1, Cost: 1) f300(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f2(Ar_0, Ar_1, 0, 0, 0)) [ Ar_1 >= 10 ] (Comp: 1, Cost: 1) f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f300(1000, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 903 Time: 0.667 sec (SMT: 0.650 sec)