
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_1 >= 0 /\ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_1 = Ar_3 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(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: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_1 >= 0 /\ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_1 = Ar_3 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f6) = 1
	Pol(f7) = 1
	Pol(f0) = 1
	Pol(f4) = 1
	Pol(f14) = 0
	Pol(koat_start) = 1
orients all transitions weakly and the transitions
	f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]
	f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_1 = Ar_3 ]
strictly and produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_1 >= 0 /\ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_3 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, 0)) [ Ar_3 >= Ar_2 + 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(0, Ar_1, Ar_2, Ar_3)) [ Ar_0 = 0 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_1 = Ar_3 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 3 to obtain the following invariants:
  For symbol f4: X_3 - X_4 + 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ -X_2 + X_3 >= 0 /\ X_2 >= 0
  For symbol f6: X_3 - X_4 + 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ -X_2 + X_3 >= 0 /\ X_2 >= 0
  For symbol f7: X_3 - X_4 + 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 >= 0 /\ -X_2 + X_3 >= 0 /\ X_2 >= 0


This yielded the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 = Ar_3 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, 0)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_3 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_3 + 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_1 >= 0 /\ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_1 ]
We thus obtain the following problem:
5:	T:
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 = Ar_3 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, 0)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_3 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_3 + 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_1 >= 0 /\ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 5:
	f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_1 >= 0 /\ Ar_2 >= Ar_1 ]
We thus obtain the following problem:
6:	T:
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_3 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 = Ar_3 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_3 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, 0)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_1 ] with all transitions in problem 6, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_1 + 1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_1 /\ Ar_2 - Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 + 1 >= Ar_1 + 1 ]
We thus obtain the following problem:
7:	T:
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_1 + 1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_1 /\ Ar_2 - Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 + 1 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_3 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 = Ar_3 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_3 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, 0)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_1 + 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, 0)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 ] with all transitions in problem 7, the following new transitions are obtained:
	f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, 0)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 /\ Ar_2 + 1 >= 0 /\ Ar_1 >= 1 ]
	f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 /\ Ar_2 + 1 >= 0 /\ Ar_1 = 0 ]
We thus obtain the following problem:
8:	T:
		(Comp: ?, Cost: 2)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, 0)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 /\ Ar_2 + 1 >= 0 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 2)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 /\ Ar_2 + 1 >= 0 /\ Ar_1 = 0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_1 + 1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_1 /\ Ar_2 - Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 + 1 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_3 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 = Ar_3 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_3 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_1 + 1 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f7) = 1
	Pol(f6) = 1
	Pol(f14) = 0
	Pol(koat_start) = 1
	Pol(f4) = 1
orients all transitions weakly and the transition
	f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 /\ Ar_2 + 1 >= 0 /\ Ar_1 = 0 ]
strictly and produces the following problem:
9:	T:
		(Comp: ?, Cost: 2)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, 0)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 /\ Ar_2 + 1 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_2 + 1 /\ Ar_2 + 1 >= 0 /\ Ar_1 = 0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_1 + 1)) [ 0 <= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_1 /\ Ar_2 - Ar_1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 + 1 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_1, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 >= Ar_3 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2, Ar_1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_1 = Ar_3 ]
		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f4(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_2 >= Ar_3 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f7(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 - Ar_3 + 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_1 >= 0 /\ Ar_3 >= Ar_1 + 1 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.182 sec (SMT: 0.144 sec)
