WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(30, 30, 1, 0, 2, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_2, Ar_4 + 1, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_1 >= Ar_4 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2, Ar_2, Ar_2)) [ Ar_4 >= Ar_1 + 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 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, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(30, 30, 1, 0, 2, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_2, Ar_4 + 1, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_1 >= Ar_4 ] (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2, Ar_2, Ar_2)) [ Ar_4 >= Ar_1 + 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 1 Pol(f7) = 1 Pol(f19) = 0 Pol(koat_start) = 1 orients all transitions weakly and the transition f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2, Ar_2, Ar_2)) [ Ar_4 >= Ar_1 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(30, 30, 1, 0, 2, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: ?, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_2, Ar_4 + 1, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_1 >= Ar_4 ] (Comp: 1, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2, Ar_2, Ar_2)) [ Ar_4 >= Ar_1 + 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 29 Pol(f7) = V_2 - V_5 + 1 Pol(f19) = V_2 - V_5 + 1 Pol(koat_start) = 29 orients all transitions weakly and the transition f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_2, Ar_4 + 1, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_1 >= Ar_4 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(30, 30, 1, 0, 2, Ar_5, Ar_6, Ar_7, Ar_8)) (Comp: 29, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_2, Ar_4 + 1, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_1 >= Ar_4 ] (Comp: 1, Cost: 1) f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2, Ar_2, Ar_2)) [ Ar_4 >= Ar_1 + 1 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 31 Time: 0.849 sec (SMT: 0.828 sec)