WORST_CASE(?, O(n^1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(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: ?, Cost: 1)    f(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f) = 2*V_1 - V_2 - V_3
	Pol(start) = 2*V_1 - V_2 - V_3
	Pol(koat_start) = 2*V_1 - V_2 - V_3
orients all transitions weakly and the transition
	f(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= Ar_2 + 1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 2*Ar_0 + Ar_1 + Ar_2, Cost: 1)    f(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)                       f(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: 1, Cost: 1)                       start(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)                       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f) = V_1 - V_3
	Pol(start) = V_1 - V_3
	Pol(koat_start) = V_1 - V_3
orients all transitions weakly and the transition
	f(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= Ar_2 + 1 ]
strictly and produces the following problem:
4:	T:
		(Comp: 2*Ar_0 + Ar_1 + Ar_2, Cost: 1)    f(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: Ar_0 + Ar_2, Cost: 1)             f(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= Ar_2 + 1 ]
		(Comp: 1, Cost: 1)                       start(Ar_0, Ar_1, Ar_2) -> Com_1(f(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)                       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 3*Ar_0 + Ar_1 + 2*Ar_2 + 1

Time: 0.442 sec (SMT: 0.425 sec)