
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Fresh_0)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(1, 2, Ar_2)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, 2, Ar_2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, 2, Ar_2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(1, Ar_1 + 1, Ar_2)) [ Ar_1 >= 2 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(1, Ar_1 + 1, Ar_2)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(1, Ar_1 + 1, Ar_2)) [ Ar_1 >= 2 /\ 0 >= Ar_1 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ Ar_1 >= 2 /\ 0 >= Ar_1 /\ Ar_0 = 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2)) [ 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].
We thus obtain the following problem:
2:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 0 >= Ar_1 /\ Ar_0 = 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 0 >= Ar_1 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 2)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transitions from problem 2:
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 0 >= Ar_1 /\ Ar_0 = 2 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 0 >= Ar_1 /\ 2 >= D /\ Ar_0 = 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ Ar_1 >= 2 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ Ar_1 >= 2 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
We thus obtain the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 2)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 3 produces the following problem:
4:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 2)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = 1
	Pol(f300) = 0
	Pol(f1) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 2)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = -V_2 + 2
	Pol(f300) = -V_2
	Pol(f1) = -V_2 + 2
	Pol(koat_start) = -V_2 + 2
orients all transitions weakly and the transitions
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 2)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
strictly and produces the following problem:
6:	T:
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 2)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: ?, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)           f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = -V_1 + 1
	Pol(f300) = -V_1
	Pol(f1) = -V_1 + 1
	Pol(koat_start) = -V_1 + 1
orients all transitions weakly and the transition
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
strictly and produces the following problem:
7:	T:
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 2)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)           f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 2)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 ] with all transitions in problem 7, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 3)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 ]
We thus obtain the following problem:
8:	T:
		(Comp: Ar_1 + 2, Cost: 2)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 3)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)           f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 3)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 ] with all transitions in problem 8, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 4)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' ]
We thus obtain the following problem:
9:	T:
		(Comp: Ar_1 + 2, Cost: 3)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 4)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)           f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 4)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' ] with all transitions in problem 9, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 5)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' ]
We thus obtain the following problem:
10:	T:
		(Comp: Ar_1 + 2, Cost: 4)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 5)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)           f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 5)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' ] with all transitions in problem 10, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 6)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' ]
We thus obtain the following problem:
11:	T:
		(Comp: Ar_1 + 2, Cost: 5)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 6)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)           f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 6)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' ] with all transitions in problem 11, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 7)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' ]
We thus obtain the following problem:
12:	T:
		(Comp: Ar_1 + 2, Cost: 6)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 7)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)           f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 7)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' ] with all transitions in problem 12, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 8)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' ]
We thus obtain the following problem:
13:	T:
		(Comp: Ar_1 + 2, Cost: 7)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 8)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)           f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 8)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' ] with all transitions in problem 13, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 9)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' ]
We thus obtain the following problem:
14:	T:
		(Comp: Ar_1 + 2, Cost: 8)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 9)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)           f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 9)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' ] with all transitions in problem 14, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 10)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' ]
We thus obtain the following problem:
15:	T:
		(Comp: Ar_1 + 2, Cost: 9)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 10)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)           f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)           f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)           koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 10)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' ] with all transitions in problem 15, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 11)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' ]
We thus obtain the following problem:
16:	T:
		(Comp: Ar_1 + 2, Cost: 10)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 11)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)            f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)            koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 11)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' ] with all transitions in problem 16, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 12)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' ]
We thus obtain the following problem:
17:	T:
		(Comp: Ar_1 + 2, Cost: 11)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 12)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)            f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)            koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 12)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' ] with all transitions in problem 17, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 13)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' ]
We thus obtain the following problem:
18:	T:
		(Comp: Ar_1 + 2, Cost: 12)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 13)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)            f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)            koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 13)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' ] with all transitions in problem 18, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 14)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' /\ 13 >= 2 /\ 2 >= D'''''''''''' ]
We thus obtain the following problem:
19:	T:
		(Comp: Ar_1 + 2, Cost: 13)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 14)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' /\ 13 >= 2 /\ 2 >= D'''''''''''' ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)            f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)            koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 14)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' /\ 13 >= 2 /\ 2 >= D'''''''''''' ] with all transitions in problem 19, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 15)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' /\ 13 >= 2 /\ 2 >= D'''''''''''' /\ 14 >= 2 /\ 2 >= D''''''''''''' ]
We thus obtain the following problem:
20:	T:
		(Comp: Ar_1 + 2, Cost: 14)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 15)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' /\ 13 >= 2 /\ 2 >= D'''''''''''' /\ 14 >= 2 /\ 2 >= D''''''''''''' ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)            f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)            koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 15)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' /\ 13 >= 2 /\ 2 >= D'''''''''''' /\ 14 >= 2 /\ 2 >= D''''''''''''' ] with all transitions in problem 20, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 16)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' /\ 13 >= 2 /\ 2 >= D'''''''''''' /\ 14 >= 2 /\ 2 >= D''''''''''''' /\ 15 >= 2 /\ 2 >= D'''''''''''''' ]
We thus obtain the following problem:
21:	T:
		(Comp: Ar_1 + 2, Cost: 15)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 16)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' /\ 13 >= 2 /\ 2 >= D'''''''''''' /\ 14 >= 2 /\ 2 >= D''''''''''''' /\ 15 >= 2 /\ 2 >= D'''''''''''''' ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)            f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)            koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1) -> Com_1(f2(1, 16)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' /\ 13 >= 2 /\ 2 >= D'''''''''''' /\ 14 >= 2 /\ 2 >= D''''''''''''' /\ 15 >= 2 /\ 2 >= D'''''''''''''' ] with all transitions in problem 21, the following new transition is obtained:
	f2(Ar_0, Ar_1) -> Com_1(f2(1, 17)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' /\ 13 >= 2 /\ 2 >= D'''''''''''' /\ 14 >= 2 /\ 2 >= D''''''''''''' /\ 15 >= 2 /\ 2 >= D'''''''''''''' /\ 16 >= 2 /\ 2 >= D''''''''''''''' ]
We thus obtain the following problem:
22:	T:
		(Comp: Ar_1 + 2, Cost: 16)    f2(Ar_0, Ar_1) -> Com_1(f2(1, 17)) [ 1 >= D /\ Ar_1 = 1 /\ Ar_0 = 1 /\ 2 >= 2 /\ 2 >= D' /\ 1 = 1 /\ 3 >= 2 /\ 2 >= D'' /\ 4 >= 2 /\ 2 >= D''' /\ 5 >= 2 /\ 2 >= D'''' /\ 6 >= 2 /\ 2 >= D''''' /\ 7 >= 2 /\ 2 >= D'''''' /\ 8 >= 2 /\ 2 >= D''''''' /\ 9 >= 2 /\ 2 >= D'''''''' /\ 10 >= 2 /\ 2 >= D''''''''' /\ 11 >= 2 /\ 2 >= D'''''''''' /\ 12 >= 2 /\ 2 >= D''''''''''' /\ 13 >= 2 /\ 2 >= D'''''''''''' /\ 14 >= 2 /\ 2 >= D''''''''''''' /\ 15 >= 2 /\ 2 >= D'''''''''''''' /\ 16 >= 2 /\ 2 >= D''''''''''''''' ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= 3 /\ Ar_1 >= 2 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ Ar_0 >= 2 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, 2)) [ 0 >= Ar_0 /\ 1 >= D /\ Ar_1 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ 0 >= Ar_1 /\ 1 >= Ar_1 /\ Ar_0 = 1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 ]
		(Comp: Ar_1 + 2, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ 1 >= Ar_1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= D /\ Ar_0 = 1 ]
		(Comp: 1, Cost: 1)            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ Ar_0 = 2 ]
		(Comp: Ar_0 + 1, Cost: 1)     f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1 + 1)) [ Ar_1 >= 2 /\ 2 >= Ar_0 /\ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)            f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)            koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.329 sec (SMT: 0.257 sec)
