MAYBE

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(0, 0, Ar_2, Ar_3, Ar_4))
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 1, Fresh_4, Ar_4)) [ Ar_2 >= 1 /\ Fresh_4 >= 1 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 2, Fresh_3, Ar_4)) [ Ar_2 >= 1 /\ 0 >= Fresh_3 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_2)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(1, Ar_1, Ar_2, Ar_3, Fresh_1)) [ Ar_4 >= 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ 0 >= Ar_4 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 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, Ar_3, Ar_4) -> Com_1(f3(0, 0, Ar_2, Ar_3, Ar_4))
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 1, Fresh_4, Ar_4)) [ Ar_2 >= 1 /\ Fresh_4 >= 1 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 2, Fresh_3, Ar_4)) [ Ar_2 >= 1 /\ 0 >= Fresh_3 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_2)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(1, Ar_1, Ar_2, Ar_3, Fresh_1)) [ Ar_4 >= 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ 0 >= Ar_4 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = 1
	Pol(f3) = 1
	Pol(f6) = 0
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_2)) [ 0 >= Ar_2 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(0, 0, Ar_2, Ar_3, Ar_4))
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 1, Fresh_4, Ar_4)) [ Ar_2 >= 1 /\ Fresh_4 >= 1 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 2, Fresh_3, Ar_4)) [ Ar_2 >= 1 /\ 0 >= Fresh_3 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_2)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(1, Ar_1, Ar_2, Ar_3, Fresh_1)) [ Ar_4 >= 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ 0 >= Ar_4 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = V_3 + 1
	Pol(f3) = V_3 + 1
	Pol(f6) = V_3 + 1
	Pol(koat_start) = V_3 + 1
orients all transitions weakly and the transition
	f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 2, Fresh_3, Ar_4)) [ Ar_2 >= 1 /\ 0 >= Fresh_3 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)           f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(0, 0, Ar_2, Ar_3, Ar_4))
		(Comp: ?, Cost: 1)           f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 1, Fresh_4, Ar_4)) [ Ar_2 >= 1 /\ Fresh_4 >= 1 ]
		(Comp: Ar_2 + 1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 2, Fresh_3, Ar_4)) [ Ar_2 >= 1 /\ 0 >= Fresh_3 ]
		(Comp: 1, Cost: 1)           f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_2)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)           f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(1, Ar_1, Ar_2, Ar_3, Fresh_1)) [ Ar_4 >= 1 ]
		(Comp: ?, Cost: 1)           f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ 0 >= Ar_4 ]
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = V_3
	Pol(f3) = V_3
	Pol(f6) = V_3
	Pol(koat_start) = V_3
orients all transitions weakly and the transition
	f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 1, Fresh_4, Ar_4)) [ Ar_2 >= 1 /\ Fresh_4 >= 1 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)           f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(0, 0, Ar_2, Ar_3, Ar_4))
		(Comp: Ar_2, Cost: 1)        f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 1, Fresh_4, Ar_4)) [ Ar_2 >= 1 /\ Fresh_4 >= 1 ]
		(Comp: Ar_2 + 1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 2, Fresh_3, Ar_4)) [ Ar_2 >= 1 /\ 0 >= Fresh_3 ]
		(Comp: 1, Cost: 1)           f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_2)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)           f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(1, Ar_1, Ar_2, Ar_3, Fresh_1)) [ Ar_4 >= 1 ]
		(Comp: ?, Cost: 1)           f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ 0 >= Ar_4 ]
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 5 to obtain the following invariants:
  For symbol f3: -X_2 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 >= 0 /\ X_1 >= 0
  For symbol f6: -X_3 >= 0 /\ X_2 - X_3 >= 0 /\ -X_2 - X_3 >= 0 /\ X_1 - X_3 >= 0 /\ -X_2 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0


This yielded the following problem:
6:	T:
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)           f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ -Ar_2 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ -Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_4 ]
		(Comp: ?, Cost: 1)           f6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(1, Ar_1, Ar_2, Ar_3, Fresh_1)) [ -Ar_2 >= 0 /\ Ar_1 - Ar_2 >= 0 /\ -Ar_1 - Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_4 >= 1 ]
		(Comp: 1, Cost: 1)           f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_2)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 ]
		(Comp: Ar_2 + 1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 2, Fresh_3, Ar_4)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_3 ]
		(Comp: Ar_2, Cost: 1)        f3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2 - 1, Fresh_4, Ar_4)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_4 >= 1 ]
		(Comp: 1, Cost: 1)           f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(0, 0, Ar_2, Ar_3, Ar_4))
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 3.830 sec (SMT: 3.706 sec)