MAYBE

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 0, Ar_2, Ar_3, Ar_4)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(2, Ar_1, 2, Fresh_2, Ar_4))
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ 0 >= Fresh_1 /\ Fresh_1 >= 1 ]
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Fresh_0, Ar_4)) [ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, 0)) [ 0 >= Ar_1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 1:
	f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 - 1, Ar_1, Ar_2, Fresh_1, Ar_4)) [ 0 >= Fresh_1 /\ Fresh_1 >= 1 ]
We thus obtain the following problem:
2:	T:
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, 0)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 0, Ar_2, Ar_3, Ar_4)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Fresh_0, Ar_4)) [ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(2, Ar_1, 2, Fresh_2, Ar_4))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, 0)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 0, Ar_2, Ar_3, Ar_4)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Fresh_0, Ar_4)) [ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 2 ]
		(Comp: 1, Cost: 1)    f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(2, Ar_1, 2, Fresh_2, Ar_4))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f30(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(f5) = 1
	Pol(f3) = 0
	Pol(f4) = 1
	Pol(f30) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, 0)) [ 0 >= Ar_1 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, 0)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 0, Ar_2, Ar_3, Ar_4)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Fresh_0, Ar_4)) [ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 2 ]
		(Comp: 1, Cost: 1)    f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(2, Ar_1, 2, Fresh_2, Ar_4))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f30(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(f5) = -3*V_1 + 2
	Pol(f3) = -3*V_1 + 2
	Pol(f4) = -3*V_1 + 4
	Pol(f30) = 0
	Pol(koat_start) = 0
orients all transitions weakly and the transition
	f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 0, Ar_2, Ar_3, Ar_4)) [ 1 >= Ar_0 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, 0)) [ 0 >= Ar_1 ]
		(Comp: 0, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 0, Ar_2, Ar_3, Ar_4)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Fresh_0, Ar_4)) [ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 2 ]
		(Comp: 1, Cost: 1)    f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(2, Ar_1, 2, Fresh_2, Ar_4))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f30(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 f4: -X_3 + 2 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 2 >= 0 /\ X_1 + X_3 - 4 >= 0 /\ X_1 - 2 >= 0
  For symbol f5: -X_3 + 2 >= 0 /\ X_2 - X_3 + 1 >= 0 /\ -X_2 - X_3 + 3 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 2 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 4 >= 0 /\ -X_2 + 1 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 2 >= 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(f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(2, Ar_1, 2, Fresh_2, Ar_4))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 1, Ar_2, Ar_3, Ar_4)) [ -Ar_2 + 2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Fresh_0, Ar_4)) [ -Ar_2 + 2 >= 0 /\ Ar_1 - Ar_2 + 1 >= 0 /\ -Ar_1 - Ar_2 + 3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ -Ar_1 + 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Fresh_0 >= 1 ]
		(Comp: 0, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 0, Ar_2, Ar_3, Ar_4)) [ -Ar_2 + 2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - 2 >= 0 /\ 1 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, 0)) [ -Ar_2 + 2 >= 0 /\ Ar_1 - Ar_2 + 1 >= 0 /\ -Ar_1 - Ar_2 + 3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ -Ar_1 + 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_1 ]
	start location:	koat_start
	leaf cost:	0

Testing for unsatisfiable constraints removes the following transitions from problem 6:
	f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 0, Ar_2, Ar_3, Ar_4)) [ -Ar_2 + 2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - 2 >= 0 /\ 1 >= Ar_0 ]
	f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f3(Ar_0, Ar_1, Ar_2, Ar_3, 0)) [ -Ar_2 + 2 >= 0 /\ Ar_1 - Ar_2 + 1 >= 0 /\ -Ar_1 - Ar_2 + 3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ -Ar_1 + 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ 0 >= Ar_1 ]
We thus obtain the following problem:
7:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(2, Ar_1, 2, Fresh_2, Ar_4))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f5(Ar_0, 1, Ar_2, Ar_3, Ar_4)) [ -Ar_2 + 2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f4(Ar_0 + 1, Ar_1, Ar_2, Fresh_0, Ar_4)) [ -Ar_2 + 2 >= 0 /\ Ar_1 - Ar_2 + 1 >= 0 /\ -Ar_1 - Ar_2 + 3 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ Ar_2 - 2 >= 0 /\ Ar_1 + Ar_2 - 3 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 4 >= 0 /\ -Ar_1 + 1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 3 >= 0 /\ Ar_0 - 2 >= 0 /\ Fresh_0 >= 1 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 1.804 sec (SMT: 1.738 sec)