WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_1, Ar_3, Ar_4)) [ 199 >= Ar_1 ] (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 200 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_0, Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, 100, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 100 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_1, Ar_3, Ar_4)) [ 199 >= Ar_1 ] (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 200 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_0, Ar_0)) [ 99 >= Ar_0 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, 100, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 100 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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(f0) = 2 Pol(f4) = 2 Pol(f24) = 1 Pol(f37) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, 100, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 100 ] f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 200 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_1, Ar_3, Ar_4)) [ 199 >= Ar_1 ] (Comp: 2, Cost: 1) f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 200 ] (Comp: ?, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_0, Ar_0)) [ 99 >= Ar_0 ] (Comp: 2, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, 100, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 100 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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(f0) = 100 Pol(f4) = -V_1 + 100 Pol(f24) = -V_1 - V_2 - 199 Pol(f37) = -V_1 - V_2 - 199 Pol(koat_start) = 100 orients all transitions weakly and the transition f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_0, Ar_0)) [ 99 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_1, Ar_3, Ar_4)) [ 199 >= Ar_1 ] (Comp: 2, Cost: 1) f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 200 ] (Comp: 100, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_0, Ar_0)) [ 99 >= Ar_0 ] (Comp: 2, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, 100, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 100 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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(f0) = 100 Pol(f4) = 100 Pol(f24) = -V_2 + 200 Pol(f37) = -V_2 + 200 Pol(koat_start) = 100 orients all transitions weakly and the transition f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_1, Ar_3, Ar_4)) [ 199 >= Ar_1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 100, Cost: 1) f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_1, Ar_3, Ar_4)) [ 199 >= Ar_1 ] (Comp: 2, Cost: 1) f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 200 ] (Comp: 100, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Ar_0, Ar_0)) [ 99 >= Ar_0 ] (Comp: 2, Cost: 1) f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f24(Ar_0, 100, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 100 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 205 Time: 0.943 sec (SMT: 0.915 sec)