
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(1, Ar_1 + 1, Ar_2, Fresh_0)) [ Ar_1 + 1 = Ar_2 /\ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1 + 1, Ar_2 - 1, Ar_3)) [ Ar_2 >= Ar_1 + 2 /\ Ar_2 >= Ar_1 + 1 /\ Ar_0 = 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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)    f3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(1, Ar_1 + 1, Ar_2, Fresh_0)) [ Ar_1 + 1 = Ar_2 /\ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1 + 1, Ar_2 - 1, Ar_3)) [ Ar_2 >= Ar_1 + 2 /\ Ar_2 >= Ar_1 + 1 /\ Ar_0 = 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f3) = 1
	Pol(f1) = 1
	Pol(f2) = 0
	Pol(koat_start) = 1
orients all transitions weakly and the transitions
	f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(1, Ar_1 + 1, Ar_2, Fresh_0)) [ Ar_1 + 1 = Ar_2 /\ Ar_0 = 0 ]
	f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(1, Ar_1 + 1, Ar_2, Fresh_0)) [ Ar_1 + 1 = Ar_2 /\ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1 + 1, Ar_2 - 1, Ar_3)) [ Ar_2 >= Ar_1 + 2 /\ Ar_2 >= Ar_1 + 1 /\ Ar_0 = 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f3) = -V_2 + V_3
	Pol(f1) = -V_2 + V_3
	Pol(f2) = -V_2 + V_3
	Pol(koat_start) = -V_2 + V_3
orients all transitions weakly and the transition
	f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1 + 1, Ar_2 - 1, Ar_3)) [ Ar_2 >= Ar_1 + 2 /\ Ar_2 >= Ar_1 + 1 /\ Ar_0 = 0 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)              f3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)              f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(Ar_0, Ar_1, Ar_2, Fresh_1)) [ Ar_1 >= Ar_2 ]
		(Comp: 1, Cost: 1)              f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(1, Ar_1 + 1, Ar_2, Fresh_0)) [ Ar_1 + 1 = Ar_2 /\ Ar_0 = 0 ]
		(Comp: Ar_1 + Ar_2, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(0, Ar_1 + 1, Ar_2 - 1, Ar_3)) [ Ar_2 >= Ar_1 + 2 /\ Ar_2 >= Ar_1 + 1 /\ Ar_0 = 0 ]
		(Comp: 1, Cost: 0)              koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound Ar_1 + Ar_2 + 3

Time: 0.039 sec (SMT: 0.032 sec)
