WORST_CASE(?, O(1)) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Fresh_0, 0, Ar_2)) (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0, Ar_1 + 1, Ar_2)) [ 9 >= Ar_1 ] (Comp: ?, Cost: 1) f19(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2 + 1)) [ 9 >= Ar_2 ] (Comp: ?, Cost: 1) f19(Ar_0, Ar_1, Ar_2) -> Com_1(f29(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 10 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, 0)) [ Ar_1 >= 10 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 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) -> Com_1(f8(Fresh_0, 0, Ar_2)) (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0, Ar_1 + 1, Ar_2)) [ 9 >= Ar_1 ] (Comp: ?, Cost: 1) f19(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2 + 1)) [ 9 >= Ar_2 ] (Comp: ?, Cost: 1) f19(Ar_0, Ar_1, Ar_2) -> Com_1(f29(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 10 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, 0)) [ Ar_1 >= 10 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 2 Pol(f8) = 2 Pol(f19) = 1 Pol(f29) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions f8(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, 0)) [ Ar_1 >= 10 ] f19(Ar_0, Ar_1, Ar_2) -> Com_1(f29(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 10 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Fresh_0, 0, Ar_2)) (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0, Ar_1 + 1, Ar_2)) [ 9 >= Ar_1 ] (Comp: ?, Cost: 1) f19(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2 + 1)) [ 9 >= Ar_2 ] (Comp: 2, Cost: 1) f19(Ar_0, Ar_1, Ar_2) -> Com_1(f29(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 10 ] (Comp: 2, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, 0)) [ Ar_1 >= 10 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 10 Pol(f8) = -V_2 + 10 Pol(f19) = -V_2 - V_3 - 9 Pol(f29) = -V_2 - V_3 - 9 Pol(koat_start) = 10 orients all transitions weakly and the transition f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0, Ar_1 + 1, Ar_2)) [ 9 >= Ar_1 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Fresh_0, 0, Ar_2)) (Comp: 10, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0, Ar_1 + 1, Ar_2)) [ 9 >= Ar_1 ] (Comp: ?, Cost: 1) f19(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2 + 1)) [ 9 >= Ar_2 ] (Comp: 2, Cost: 1) f19(Ar_0, Ar_1, Ar_2) -> Com_1(f29(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 10 ] (Comp: 2, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, 0)) [ Ar_1 >= 10 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 10 Pol(f8) = 10 Pol(f19) = -V_3 + 10 Pol(f29) = -V_3 + 10 Pol(koat_start) = 10 orients all transitions weakly and the transition f19(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2 + 1)) [ 9 >= Ar_2 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Fresh_0, 0, Ar_2)) (Comp: 10, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0, Ar_1 + 1, Ar_2)) [ 9 >= Ar_1 ] (Comp: 10, Cost: 1) f19(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2 + 1)) [ 9 >= Ar_2 ] (Comp: 2, Cost: 1) f19(Ar_0, Ar_1, Ar_2) -> Com_1(f29(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 10 ] (Comp: 2, Cost: 1) f8(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, 0)) [ Ar_1 >= 10 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 25 Time: 0.749 sec (SMT: 0.726 sec)