
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Fresh_2, 0, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1, Ar_3)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1, 0)) [ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1, Fresh_1)) [ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1, Fresh_0)) [ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f25(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]
		(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

Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_0, Ar_1, Ar_2].
We thus obtain the following problem:
2:	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: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2))
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	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: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2))
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(koat_start) = 1
	Pol(f0) = 1
	Pol(f6) = 1
	Pol(f25) = 0
	Pol(f10) = 1
	Pol(f14) = 1
orients all transitions weakly and the transition
	f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]
strictly and produces the following problem:
4:	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)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2))
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 4 to obtain the following invariants:
  For symbol f10: X_1 >= 0
  For symbol f14: X_1 - X_3 - 1 >= 0 /\ X_3 + 1 >= 0 /\ X_2 + X_3 + 1 >= 0 /\ X_1 + X_3 + 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
  For symbol f6: -X_2 >= 0


This yielded the following problem:
5:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2))
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(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

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] with all transitions in problem 5, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2))
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 6:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2))
We thus obtain the following problem:
7:	T:
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f14(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 ] with all transitions in problem 7, the following new transitions are obtained:
	f14(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 ]
	f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
We thus obtain the following problem:
8:	T:
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f14(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 ] with all transitions in problem 8, the following new transitions are obtained:
	f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
	f14(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
We thus obtain the following problem:
9:	T:
		(Comp: ?, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f14) = 1
	Pol(f25) = 0
	Pol(f10) = 1
	Pol(f6) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
strictly and produces the following problem:
10:	T:
		(Comp: 1, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f14(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ] with all transitions in problem 10, the following new transition is obtained:
	f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_0 - 1 >= 0 /\ Ar_1 + 1 >= 1 ]
We thus obtain the following problem:
11:	T:
		(Comp: ?, Cost: 4)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_0 - 1 >= 0 /\ Ar_1 + 1 >= 1 ]
		(Comp: 1, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f14) = 0
	Pol(f25) = 0
	Pol(f10) = 1
	Pol(f6) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
strictly and produces the following problem:
12:	T:
		(Comp: ?, Cost: 4)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_0 - 1 >= 0 /\ Ar_1 + 1 >= 1 ]
		(Comp: 1, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f10(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 ] with all transitions in problem 12, the following new transitions are obtained:
	f10(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
	f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
We thus obtain the following problem:
13:	T:
		(Comp: ?, Cost: 2)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 4)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_0 - 1 >= 0 /\ Ar_1 + 1 >= 1 ]
		(Comp: 1, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: 1, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 13 produces the following problem:
14:	T:
		(Comp: ?, Cost: 2)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 4)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_0 - 1 >= 0 /\ Ar_1 + 1 >= 1 ]
		(Comp: 1, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: 1, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f10) = 1
	Pol(f25) = 0
	Pol(f14) = 0
	Pol(f6) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	f10(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
strictly and produces the following problem:
15:	T:
		(Comp: 1, Cost: 2)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 4)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_0 - 1 >= 0 /\ Ar_1 + 1 >= 1 ]
		(Comp: 1, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: 1, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f10) = -V_2 + 1
and size complexities
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]", 0-0) = ?
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]", 0-1) = 0
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2
	S("f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\\ Ar_0 >= 1 ]", 0-0) = ?
	S("f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\\ Ar_0 >= 1 ]", 0-1) = 1
	S("f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\\ Ar_0 >= 1 ]", 0-2) = Ar_2
	S("f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\\ 0 >= Ar_0 ]", 0-0) = ?
	S("f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\\ 0 >= Ar_0 ]", 0-1) = 0
	S("f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\\ 0 >= Ar_0 ]", 0-2) = Ar_2
	S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = ?
	S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = 1
	S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-2) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 ]", 0-0) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 ]", 0-1) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 ]", 0-2) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 /\\ 0 >= Fresh_1 + 1 ]", 0-0) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 /\\ 0 >= Fresh_1 + 1 ]", 0-1) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 /\\ 0 >= Fresh_1 + 1 ]", 0-2) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 /\\ Fresh_0 >= 1 ]", 0-0) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 /\\ Fresh_0 >= 1 ]", 0-1) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ Ar_2 >= 1 /\\ Fresh_0 >= 1 ]", 0-2) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 /\\ Ar_1 >= 1 ]", 0-0) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 /\\ Ar_1 >= 1 ]", 0-1) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 /\\ Ar_1 >= 1 ]", 0-2) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ 0 >= Ar_0 ]", 0-0) = 0
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ 0 >= Ar_0 ]", 0-1) = 0
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ 0 >= Ar_0 ]", 0-2) = 1
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ Ar_0 >= 1 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 + 1 >= 1 ]", 0-0) = ?
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ Ar_0 >= 1 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 + 1 >= 1 ]", 0-1) = 0
	S("f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\\ Ar_2 + 1 >= 0 /\\ Ar_1 + Ar_2 + 1 >= 0 /\\ Ar_0 + Ar_2 + 1 >= 0 /\\ Ar_1 >= 0 /\\ Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 0 /\\ 0 >= Ar_2 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ Ar_0 >= 1 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 + 1 >= 1 ]", 0-2) = ?
	S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ Ar_0 >= 1 ]", 0-0) = ?
	S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ Ar_0 >= 1 ]", 0-1) = 1
	S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ Ar_0 >= 1 ]", 0-2) = Ar_2
	S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ 0 >= Ar_0 ]", 0-0) = 0
	S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ 0 >= Ar_0 ]", 0-1) = 1
	S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\\ 0 >= Ar_1 /\\ -Ar_1 >= 0 /\\ 0 >= Ar_0 ]", 0-2) = Ar_2
orients the transitions
	f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
weakly and the transition
	f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
strictly and produces the following problem:
16:	T:
		(Comp: 1, Cost: 2)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: 2, Cost: 2)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 4)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_0 - 1 >= 0 /\ Ar_1 + 1 >= 1 ]
		(Comp: 1, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: 1, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Fresh_2, 0, Ar_2)) [ 0 <= 0 ] with all transitions in problem 16, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Fresh_2, 0, Ar_2)) [ 0 <= 0 /\ 0 >= 0 /\ 0 >= Fresh_2 ]
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Fresh_2 - 1, 1, Ar_2)) [ 0 <= 0 /\ 0 >= 0 /\ Fresh_2 >= 1 ]
We thus obtain the following problem:
17:	T:
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Fresh_2, 0, Ar_2)) [ 0 <= 0 /\ 0 >= 0 /\ 0 >= Fresh_2 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Fresh_2 - 1, 1, Ar_2)) [ 0 <= 0 /\ 0 >= 0 /\ Fresh_2 >= 1 ]
		(Comp: 1, Cost: 2)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: 2, Cost: 2)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 4)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_0 - 1 >= 0 /\ Ar_1 + 1 >= 1 ]
		(Comp: 1, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: 1, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transitions from problem 17:
	f10(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
	f10(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
	f6(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
	f6(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 - 1, Ar_1 + 1, Ar_2)) [ -Ar_1 >= 0 /\ Ar_0 >= 1 ]
We thus obtain the following problem:
18:	T:
		(Comp: ?, Cost: 4)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_0 - 1 >= 0 /\ Ar_1 + 1 >= 1 ]
		(Comp: 1, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: 1, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Fresh_2 - 1, 1, Ar_2)) [ 0 <= 0 /\ 0 >= 0 /\ Fresh_2 >= 1 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Fresh_2, 0, Ar_2)) [ 0 <= 0 /\ 0 >= 0 /\ 0 >= Fresh_2 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Fresh_2 - 1, 1, Ar_2)) [ 0 <= 0 /\ 0 >= 0 /\ Fresh_2 >= 1 ] with all transitions in problem 18, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Fresh_2 - 1, 0, Fresh_2 - 2)) [ 0 <= 0 /\ 0 >= 0 /\ Fresh_2 >= 1 /\ Fresh_2 - 1 >= 0 /\ 1 >= 1 ]
We thus obtain the following problem:
19:	T:
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Fresh_2 - 1, 0, Fresh_2 - 2)) [ 0 <= 0 /\ 0 >= 0 /\ Fresh_2 >= 1 /\ Fresh_2 - 1 >= 0 /\ 1 >= 1 ]
		(Comp: ?, Cost: 4)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_0 - 1 >= 0 /\ Ar_1 + 1 >= 1 ]
		(Comp: 1, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: 1, Cost: 1)    f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Fresh_2, 0, Ar_2)) [ 0 <= 0 /\ 0 >= 0 /\ 0 >= Fresh_2 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 19:
	f10(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 >= 0 /\ Ar_1 >= 1 ]
We thus obtain the following problem:
20:	T:
		(Comp: ?, Cost: 2)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1 - 1, Ar_0 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 4)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1, Ar_0 - 2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 >= 1 /\ Ar_0 - 1 >= 0 /\ Ar_1 + 1 >= 1 ]
		(Comp: 1, Cost: 3)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_2 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ Fresh_0 >= 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0 - 1, Ar_1 + 1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 /\ 0 >= Fresh_1 + 1 ]
		(Comp: ?, Cost: 1)    f14(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_0 - Ar_2 - 1 >= 0 /\ Ar_2 + 1 >= 0 /\ Ar_1 + Ar_2 + 1 >= 0 /\ Ar_0 + Ar_2 + 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f14(Fresh_2 - 1, 0, Fresh_2 - 2)) [ 0 <= 0 /\ 0 >= 0 /\ Fresh_2 >= 1 /\ Fresh_2 - 1 >= 0 /\ 1 >= 1 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f25(Fresh_2, 0, Ar_2)) [ 0 <= 0 /\ 0 >= 0 /\ 0 >= Fresh_2 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.542 sec (SMT: 0.445 sec)
