WORST_CASE(?, O(1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, 2)) [ Ar_0 >= 0 /\ 3 >= Ar_0 /\ 3 >= Ar_1 /\ Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]
		(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(f1(Ar_0, Ar_1, 2)) [ Ar_0 >= 0 /\ 3 >= Ar_0 /\ 3 >= Ar_1 /\ Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]
		(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(f1) = -V_1 + 2*V_2 - V_3
and size complexities
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]", 0-0) = 3
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]", 0-1) = ?
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]", 0-2) = 2
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]", 0-0) = 3
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]", 0-1) = ?
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]", 0-2) = 2
	S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, 2)) [ Ar_0 >= 0 /\\ 3 >= Ar_0 /\\ 3 >= Ar_1 /\\ Ar_1 >= 0 ]", 0-0) = 3
	S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, 2)) [ Ar_0 >= 0 /\\ 3 >= Ar_0 /\\ 3 >= Ar_1 /\\ Ar_1 >= 0 ]", 0-1) = 3
	S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, 2)) [ Ar_0 >= 0 /\\ 3 >= Ar_0 /\\ 3 >= Ar_1 /\\ Ar_1 >= 0 ]", 0-2) = 2
orients the transitions
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]
weakly and the transition
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)     f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, 2)) [ Ar_0 >= 0 /\ 3 >= Ar_0 /\ 3 >= Ar_1 /\ Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]
		(Comp: 11, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]
		(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(f1) = V_1 - 2*V_2 + V_3
and size complexities
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]", 0-0) = 3
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]", 0-1) = 14
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]", 0-2) = 2
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]", 0-0) = 3
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]", 0-1) = ?
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]", 0-2) = 2
	S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, 2)) [ Ar_0 >= 0 /\\ 3 >= Ar_0 /\\ 3 >= Ar_1 /\\ Ar_1 >= 0 ]", 0-0) = 3
	S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, 2)) [ Ar_0 >= 0 /\\ 3 >= Ar_0 /\\ 3 >= Ar_1 /\\ Ar_1 >= 0 ]", 0-1) = 3
	S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, 2)) [ Ar_0 >= 0 /\\ 3 >= Ar_0 /\\ 3 >= Ar_1 /\\ Ar_1 >= 0 ]", 0-2) = 2
orients the transitions
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]
weakly and the transition
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)     f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, 2)) [ Ar_0 >= 0 /\ 3 >= Ar_0 /\ 3 >= Ar_1 /\ Ar_1 >= 0 ]
		(Comp: 11, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 + Ar_0 >= 2*Ar_1 + 1 ]
		(Comp: 11, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Ar_2)) [ 2*Ar_1 >= Ar_2 + Ar_0 + 2 ]
		(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 23

Time: 0.822 sec (SMT: 0.797 sec)