MAYBE

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2) -> Com_1(f5(Ar_0, Ar_1, 1))
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f2(0, Ar_1, Ar_2)) [ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f3(0, Ar_1, Ar_2)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f5(0, Ar_1, Ar_2)) [ 0 >= Ar_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)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2) -> Com_1(f5(Ar_0, Ar_1, 1))
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f2(0, Ar_1, Ar_2)) [ Ar_2 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f3(0, Ar_1, Ar_2)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f5(0, Ar_1, Ar_2)) [ 0 >= Ar_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(f2) = 1
	Pol(f3) = 1
	Pol(f5) = 0
	Pol(f0) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	f3(Ar_0, Ar_1, Ar_2) -> Com_1(f5(0, Ar_1, Ar_2)) [ 0 >= Ar_1 ]
strictly and produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f5(Ar_0, Ar_1, Ar_2) -> Com_1(f5(Ar_0, Ar_1, 1))
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f2(0, Ar_1, Ar_2)) [ Ar_2 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f3(0, Ar_1, Ar_2)) [ 0 >= Ar_2 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f5(0, Ar_1, Ar_2)) [ 0 >= Ar_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(f2) = V_2
	Pol(f3) = V_2
	Pol(f5) = V_2
	Pol(f0) = V_2
	Pol(koat_start) = V_2
orients all transitions weakly and the transition
	f3(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_1 >= 1 ]
strictly and produces the following problem:
4:	T:
		(Comp: ?, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1, Ar_2))
		(Comp: Ar_1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1 - 1, Ar_2)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)       f5(Ar_0, Ar_1, Ar_2) -> Com_1(f5(Ar_0, Ar_1, 1))
		(Comp: 1, Cost: 1)       f0(Ar_0, Ar_1, Ar_2) -> Com_1(f2(0, Ar_1, Ar_2)) [ Ar_2 >= 1 ]
		(Comp: 1, Cost: 1)       f0(Ar_0, Ar_1, Ar_2) -> Com_1(f3(0, Ar_1, Ar_2)) [ 0 >= Ar_2 ]
		(Comp: 1, Cost: 1)       f3(Ar_0, Ar_1, Ar_2) -> Com_1(f5(0, Ar_1, Ar_2)) [ 0 >= Ar_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

Applied AI with 'oct' on problem 4 to obtain the following invariants:
  For symbol f2: X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_1 >= 0
  For symbol f3: -X_3 >= 0 /\ X_1 - X_3 >= 0 /\ -X_1 - X_3 >= 0 /\ -X_1 >= 0 /\ X_1 >= 0
  For symbol f5: -X_2 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 - X_2 >= 0 /\ -X_1 >= 0 /\ X_1 >= 0


This yielded the following problem:
5:	T:
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)       f3(Ar_0, Ar_1, Ar_2) -> Com_1(f5(0, Ar_1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ -Ar_0 - Ar_2 >= 0 /\ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: 1, Cost: 1)       f0(Ar_0, Ar_1, Ar_2) -> Com_1(f3(0, Ar_1, Ar_2)) [ 0 >= Ar_2 ]
		(Comp: 1, Cost: 1)       f0(Ar_0, Ar_1, Ar_2) -> Com_1(f2(0, Ar_1, Ar_2)) [ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)       f5(Ar_0, Ar_1, Ar_2) -> Com_1(f5(Ar_0, Ar_1, 1)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 - Ar_1 >= 0 /\ -Ar_0 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1 - 1, Ar_2)) [ -Ar_2 >= 0 /\ Ar_0 - Ar_2 >= 0 /\ -Ar_0 - Ar_2 >= 0 /\ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_0 >= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 1.816 sec (SMT: 1.751 sec)