WORST_CASE(?, O(1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f9(0, Fresh_0, 0))
		(Comp: ?, Cost: 1)    f9(Ar_0, Ar_1, Ar_2) -> Com_1(f9(Ar_0, Ar_1, Ar_2 + 1)) [ 49 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f17(Ar_0, Ar_1, Ar_2) -> Com_1(f17(Ar_0 + 1, Ar_1, Ar_2)) [ 49 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f17(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 50 ]
		(Comp: ?, Cost: 1)    f9(Ar_0, Ar_1, Ar_2) -> Com_1(f17(0, Ar_1, Ar_2)) [ Ar_2 >= 50 ]
		(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(f9(0, Fresh_0, 0))
		(Comp: ?, Cost: 1)    f9(Ar_0, Ar_1, Ar_2) -> Com_1(f9(Ar_0, Ar_1, Ar_2 + 1)) [ 49 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f17(Ar_0, Ar_1, Ar_2) -> Com_1(f17(Ar_0 + 1, Ar_1, Ar_2)) [ 49 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f17(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 50 ]
		(Comp: ?, Cost: 1)    f9(Ar_0, Ar_1, Ar_2) -> Com_1(f17(0, Ar_1, Ar_2)) [ Ar_2 >= 50 ]
		(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(f9) = 2
	Pol(f17) = 1
	Pol(f24) = 0
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	f9(Ar_0, Ar_1, Ar_2) -> Com_1(f17(0, Ar_1, Ar_2)) [ Ar_2 >= 50 ]
	f17(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 50 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f9(0, Fresh_0, 0))
		(Comp: ?, Cost: 1)    f9(Ar_0, Ar_1, Ar_2) -> Com_1(f9(Ar_0, Ar_1, Ar_2 + 1)) [ 49 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f17(Ar_0, Ar_1, Ar_2) -> Com_1(f17(Ar_0 + 1, Ar_1, Ar_2)) [ 49 >= Ar_0 ]
		(Comp: 2, Cost: 1)    f17(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 50 ]
		(Comp: 2, Cost: 1)    f9(Ar_0, Ar_1, Ar_2) -> Com_1(f17(0, Ar_1, Ar_2)) [ Ar_2 >= 50 ]
		(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) = 50
	Pol(f9) = -V_3 + 50
	Pol(f17) = -V_1 - V_3 - 49
	Pol(f24) = -V_1 - V_3 - 49
	Pol(koat_start) = 50
orients all transitions weakly and the transition
	f9(Ar_0, Ar_1, Ar_2) -> Com_1(f9(Ar_0, Ar_1, Ar_2 + 1)) [ 49 >= Ar_2 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)     f0(Ar_0, Ar_1, Ar_2) -> Com_1(f9(0, Fresh_0, 0))
		(Comp: 50, Cost: 1)    f9(Ar_0, Ar_1, Ar_2) -> Com_1(f9(Ar_0, Ar_1, Ar_2 + 1)) [ 49 >= Ar_2 ]
		(Comp: ?, Cost: 1)     f17(Ar_0, Ar_1, Ar_2) -> Com_1(f17(Ar_0 + 1, Ar_1, Ar_2)) [ 49 >= Ar_0 ]
		(Comp: 2, Cost: 1)     f17(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 50 ]
		(Comp: 2, Cost: 1)     f9(Ar_0, Ar_1, Ar_2) -> Com_1(f17(0, Ar_1, Ar_2)) [ Ar_2 >= 50 ]
		(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) = 50
	Pol(f9) = 50
	Pol(f17) = -V_1 + 50
	Pol(f24) = -V_1 + 50
	Pol(koat_start) = 50
orients all transitions weakly and the transition
	f17(Ar_0, Ar_1, Ar_2) -> Com_1(f17(Ar_0 + 1, Ar_1, Ar_2)) [ 49 >= Ar_0 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)     f0(Ar_0, Ar_1, Ar_2) -> Com_1(f9(0, Fresh_0, 0))
		(Comp: 50, Cost: 1)    f9(Ar_0, Ar_1, Ar_2) -> Com_1(f9(Ar_0, Ar_1, Ar_2 + 1)) [ 49 >= Ar_2 ]
		(Comp: 50, Cost: 1)    f17(Ar_0, Ar_1, Ar_2) -> Com_1(f17(Ar_0 + 1, Ar_1, Ar_2)) [ 49 >= Ar_0 ]
		(Comp: 2, Cost: 1)     f17(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 50 ]
		(Comp: 2, Cost: 1)     f9(Ar_0, Ar_1, Ar_2) -> Com_1(f17(0, Ar_1, Ar_2)) [ Ar_2 >= 50 ]
		(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 105

Time: 0.693 sec (SMT: 0.668 sec)