WORST_CASE(?, O(n^2))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0 + 1, 0, Ar_2)) [ Ar_2 >= Ar_0 + 2 /\ Ar_1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(0, 0, Ar_2)) [ Ar_2 >= 1 ]
		(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: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0 + 1, 0, Ar_2)) [ Ar_2 >= Ar_0 + 2 /\ Ar_1 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(0, 0, Ar_2)) [ Ar_2 >= 1 ]
		(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(f4) = -V_1 + V_3
	Pol(f0) = V_3
	Pol(koat_start) = V_3
orients all transitions weakly and the transition
	f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0 + 1, 0, Ar_2)) [ Ar_2 >= Ar_0 + 2 /\ Ar_1 >= Ar_0 ]
strictly and produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: Ar_2, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0 + 1, 0, Ar_2)) [ Ar_2 >= Ar_0 + 2 /\ Ar_1 >= Ar_0 ]
		(Comp: 1, Cost: 1)       f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(0, 0, Ar_2)) [ Ar_2 >= 1 ]
		(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(f4) = V_1 - V_2
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("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(0, 0, Ar_2)) [ Ar_2 >= 1 ]", 0-0) = 0
	S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(0, 0, Ar_2)) [ Ar_2 >= 1 ]", 0-1) = 0
	S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(0, 0, Ar_2)) [ Ar_2 >= 1 ]", 0-2) = Ar_2
	S("f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0 + 1, 0, Ar_2)) [ Ar_2 >= Ar_0 + 2 /\\ Ar_1 >= Ar_0 ]", 0-0) = Ar_2
	S("f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0 + 1, 0, Ar_2)) [ Ar_2 >= Ar_0 + 2 /\\ Ar_1 >= Ar_0 ]", 0-1) = 0
	S("f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0 + 1, 0, Ar_2)) [ Ar_2 >= Ar_0 + 2 /\\ Ar_1 >= Ar_0 ]", 0-2) = Ar_2
	S("f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_2
	S("f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = ?
	S("f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_2
orients the transitions
	f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
weakly and the transition
	f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
strictly and produces the following problem:
4:	T:
		(Comp: Ar_2^2, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: Ar_2, Cost: 1)      f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0 + 1, 0, Ar_2)) [ Ar_2 >= Ar_0 + 2 /\ Ar_1 >= Ar_0 ]
		(Comp: 1, Cost: 1)         f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(0, 0, Ar_2)) [ Ar_2 >= 1 ]
		(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 Ar_2^2 + Ar_2 + 1

Time: 0.469 sec (SMT: 0.451 sec)