
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2:	T:
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(l0) = 1
	Pol(l1) = 1
	Pol(l2) = 0
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3))
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: 1, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2, Ar_3)) with all transitions in problem 3, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
We thus obtain the following problem:
4:	T:
		(Comp: 1, Cost: 2)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ] with all transitions in problem 4, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 2*Ar_3 - Fresh_0, Ar_3 - Fresh_0 - Fresh_0')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 ]
We thus obtain the following problem:
5:	T:
		(Comp: 1, Cost: 3)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 2*Ar_3 - Fresh_0, Ar_3 - Fresh_0 - Fresh_0')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 ]
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 2*Ar_3 - Fresh_0, Ar_3 - Fresh_0 - Fresh_0')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 ] with all transitions in problem 5, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 ]
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 4)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 ]
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 ] with all transitions in problem 6, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 ]
We thus obtain the following problem:
7:	T:
		(Comp: 1, Cost: 5)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 ]
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 ] with all transitions in problem 7, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 ]
We thus obtain the following problem:
8:	T:
		(Comp: 1, Cost: 6)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 ]
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 ] with all transitions in problem 8, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 ]
We thus obtain the following problem:
9:	T:
		(Comp: 1, Cost: 7)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 ]
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 ] with all transitions in problem 9, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 ]
We thus obtain the following problem:
10:	T:
		(Comp: 1, Cost: 8)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 ]
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 ] with all transitions in problem 10, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 ]
We thus obtain the following problem:
11:	T:
		(Comp: 1, Cost: 9)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 ]
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 ] with all transitions in problem 11, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 ]
We thus obtain the following problem:
12:	T:
		(Comp: 1, Cost: 10)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 ]
		(Comp: 1, Cost: 1)     l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 ] with all transitions in problem 12, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 ]
We thus obtain the following problem:
13:	T:
		(Comp: 1, Cost: 11)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 ]
		(Comp: 1, Cost: 1)     l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 ] with all transitions in problem 13, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 ]
We thus obtain the following problem:
14:	T:
		(Comp: 1, Cost: 12)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 ]
		(Comp: 1, Cost: 1)     l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 ] with all transitions in problem 14, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 12*Ar_3 - 11*Fresh_0 - 10*Fresh_0' - 9*Fresh_0'' - 8*Fresh_0''' - 7*Fresh_0'''' - 6*Fresh_0''''' - 5*Fresh_0'''''' - 4*Fresh_0''''''' - 3*Fresh_0'''''''' - 2*Fresh_0''''''''' - Fresh_0'''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''' - Fresh_0''''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 /\ Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''' > 0 /\ Fresh_0''''''''''' > 0 ]
We thus obtain the following problem:
15:	T:
		(Comp: 1, Cost: 13)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 12*Ar_3 - 11*Fresh_0 - 10*Fresh_0' - 9*Fresh_0'' - 8*Fresh_0''' - 7*Fresh_0'''' - 6*Fresh_0''''' - 5*Fresh_0'''''' - 4*Fresh_0''''''' - 3*Fresh_0'''''''' - 2*Fresh_0''''''''' - Fresh_0'''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''' - Fresh_0''''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 /\ Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''' > 0 /\ Fresh_0''''''''''' > 0 ]
		(Comp: 1, Cost: 1)     l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 12*Ar_3 - 11*Fresh_0 - 10*Fresh_0' - 9*Fresh_0'' - 8*Fresh_0''' - 7*Fresh_0'''' - 6*Fresh_0''''' - 5*Fresh_0'''''' - 4*Fresh_0''''''' - 3*Fresh_0'''''''' - 2*Fresh_0''''''''' - Fresh_0'''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''' - Fresh_0''''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 /\ Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''' > 0 /\ Fresh_0''''''''''' > 0 ] with all transitions in problem 15, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 13*Ar_3 - 12*Fresh_0 - 11*Fresh_0' - 10*Fresh_0'' - 9*Fresh_0''' - 8*Fresh_0'''' - 7*Fresh_0''''' - 6*Fresh_0'''''' - 5*Fresh_0''''''' - 4*Fresh_0'''''''' - 3*Fresh_0''''''''' - 2*Fresh_0'''''''''' - Fresh_0''''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''' - Fresh_0''''''''''' - Fresh_0'''''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 /\ Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''' > 0 /\ Fresh_0''''''''''' > 0 /\ Ar_2 + 12*Ar_3 - 11*Fresh_0 - 10*Fresh_0' - 9*Fresh_0'' - 8*Fresh_0''' - 7*Fresh_0'''' - 6*Fresh_0''''' - 5*Fresh_0'''''' - 4*Fresh_0''''''' - 3*Fresh_0'''''''' - 2*Fresh_0''''''''' - Fresh_0'''''''''' > 0 /\ Fresh_0'''''''''''' > 0 ]
We thus obtain the following problem:
16:	T:
		(Comp: 1, Cost: 14)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 13*Ar_3 - 12*Fresh_0 - 11*Fresh_0' - 10*Fresh_0'' - 9*Fresh_0''' - 8*Fresh_0'''' - 7*Fresh_0''''' - 6*Fresh_0'''''' - 5*Fresh_0''''''' - 4*Fresh_0'''''''' - 3*Fresh_0''''''''' - 2*Fresh_0'''''''''' - Fresh_0''''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''' - Fresh_0''''''''''' - Fresh_0'''''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 /\ Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''' > 0 /\ Fresh_0''''''''''' > 0 /\ Ar_2 + 12*Ar_3 - 11*Fresh_0 - 10*Fresh_0' - 9*Fresh_0'' - 8*Fresh_0''' - 7*Fresh_0'''' - 6*Fresh_0''''' - 5*Fresh_0'''''' - 4*Fresh_0''''''' - 3*Fresh_0'''''''' - 2*Fresh_0''''''''' - Fresh_0'''''''''' > 0 /\ Fresh_0'''''''''''' > 0 ]
		(Comp: 1, Cost: 1)     l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 13*Ar_3 - 12*Fresh_0 - 11*Fresh_0' - 10*Fresh_0'' - 9*Fresh_0''' - 8*Fresh_0'''' - 7*Fresh_0''''' - 6*Fresh_0'''''' - 5*Fresh_0''''''' - 4*Fresh_0'''''''' - 3*Fresh_0''''''''' - 2*Fresh_0'''''''''' - Fresh_0''''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''' - Fresh_0''''''''''' - Fresh_0'''''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 /\ Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''' > 0 /\ Fresh_0''''''''''' > 0 /\ Ar_2 + 12*Ar_3 - 11*Fresh_0 - 10*Fresh_0' - 9*Fresh_0'' - 8*Fresh_0''' - 7*Fresh_0'''' - 6*Fresh_0''''' - 5*Fresh_0'''''' - 4*Fresh_0''''''' - 3*Fresh_0'''''''' - 2*Fresh_0''''''''' - Fresh_0'''''''''' > 0 /\ Fresh_0'''''''''''' > 0 ] with all transitions in problem 16, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 14*Ar_3 - 13*Fresh_0 - 12*Fresh_0' - 11*Fresh_0'' - 10*Fresh_0''' - 9*Fresh_0'''' - 8*Fresh_0''''' - 7*Fresh_0'''''' - 6*Fresh_0''''''' - 5*Fresh_0'''''''' - 4*Fresh_0''''''''' - 3*Fresh_0'''''''''' - 2*Fresh_0''''''''''' - Fresh_0'''''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''' - Fresh_0''''''''''' - Fresh_0'''''''''''' - Fresh_0''''''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 /\ Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''' > 0 /\ Fresh_0''''''''''' > 0 /\ Ar_2 + 12*Ar_3 - 11*Fresh_0 - 10*Fresh_0' - 9*Fresh_0'' - 8*Fresh_0''' - 7*Fresh_0'''' - 6*Fresh_0''''' - 5*Fresh_0'''''' - 4*Fresh_0''''''' - 3*Fresh_0'''''''' - 2*Fresh_0''''''''' - Fresh_0'''''''''' > 0 /\ Fresh_0'''''''''''' > 0 /\ Ar_2 + 13*Ar_3 - 12*Fresh_0 - 11*Fresh_0' - 10*Fresh_0'' - 9*Fresh_0''' - 8*Fresh_0'''' - 7*Fresh_0''''' - 6*Fresh_0'''''' - 5*Fresh_0''''''' - 4*Fresh_0'''''''' - 3*Fresh_0''''''''' - 2*Fresh_0'''''''''' - Fresh_0''''''''''' > 0 /\ Fresh_0''''''''''''' > 0 ]
We thus obtain the following problem:
17:	T:
		(Comp: 1, Cost: 15)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 14*Ar_3 - 13*Fresh_0 - 12*Fresh_0' - 11*Fresh_0'' - 10*Fresh_0''' - 9*Fresh_0'''' - 8*Fresh_0''''' - 7*Fresh_0'''''' - 6*Fresh_0''''''' - 5*Fresh_0'''''''' - 4*Fresh_0''''''''' - 3*Fresh_0'''''''''' - 2*Fresh_0''''''''''' - Fresh_0'''''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''' - Fresh_0''''''''''' - Fresh_0'''''''''''' - Fresh_0''''''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 /\ Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''' > 0 /\ Fresh_0''''''''''' > 0 /\ Ar_2 + 12*Ar_3 - 11*Fresh_0 - 10*Fresh_0' - 9*Fresh_0'' - 8*Fresh_0''' - 7*Fresh_0'''' - 6*Fresh_0''''' - 5*Fresh_0'''''' - 4*Fresh_0''''''' - 3*Fresh_0'''''''' - 2*Fresh_0''''''''' - Fresh_0'''''''''' > 0 /\ Fresh_0'''''''''''' > 0 /\ Ar_2 + 13*Ar_3 - 12*Fresh_0 - 11*Fresh_0' - 10*Fresh_0'' - 9*Fresh_0''' - 8*Fresh_0'''' - 7*Fresh_0''''' - 6*Fresh_0'''''' - 5*Fresh_0''''''' - 4*Fresh_0'''''''' - 3*Fresh_0''''''''' - 2*Fresh_0'''''''''' - Fresh_0''''''''''' > 0 /\ Fresh_0''''''''''''' > 0 ]
		(Comp: 1, Cost: 1)     l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 14*Ar_3 - 13*Fresh_0 - 12*Fresh_0' - 11*Fresh_0'' - 10*Fresh_0''' - 9*Fresh_0'''' - 8*Fresh_0''''' - 7*Fresh_0'''''' - 6*Fresh_0''''''' - 5*Fresh_0'''''''' - 4*Fresh_0''''''''' - 3*Fresh_0'''''''''' - 2*Fresh_0''''''''''' - Fresh_0'''''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''' - Fresh_0''''''''''' - Fresh_0'''''''''''' - Fresh_0''''''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 /\ Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''' > 0 /\ Fresh_0''''''''''' > 0 /\ Ar_2 + 12*Ar_3 - 11*Fresh_0 - 10*Fresh_0' - 9*Fresh_0'' - 8*Fresh_0''' - 7*Fresh_0'''' - 6*Fresh_0''''' - 5*Fresh_0'''''' - 4*Fresh_0''''''' - 3*Fresh_0'''''''' - 2*Fresh_0''''''''' - Fresh_0'''''''''' > 0 /\ Fresh_0'''''''''''' > 0 /\ Ar_2 + 13*Ar_3 - 12*Fresh_0 - 11*Fresh_0' - 10*Fresh_0'' - 9*Fresh_0''' - 8*Fresh_0'''' - 7*Fresh_0''''' - 6*Fresh_0'''''' - 5*Fresh_0''''''' - 4*Fresh_0'''''''' - 3*Fresh_0''''''''' - 2*Fresh_0'''''''''' - Fresh_0''''''''''' > 0 /\ Fresh_0''''''''''''' > 0 ] with all transitions in problem 17, the following new transition is obtained:
	l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 15*Ar_3 - 14*Fresh_0 - 13*Fresh_0' - 12*Fresh_0'' - 11*Fresh_0''' - 10*Fresh_0'''' - 9*Fresh_0''''' - 8*Fresh_0'''''' - 7*Fresh_0''''''' - 6*Fresh_0'''''''' - 5*Fresh_0''''''''' - 4*Fresh_0'''''''''' - 3*Fresh_0''''''''''' - 2*Fresh_0'''''''''''' - Fresh_0''''''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''' - Fresh_0''''''''''' - Fresh_0'''''''''''' - Fresh_0''''''''''''' - Fresh_0'''''''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 /\ Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''' > 0 /\ Fresh_0''''''''''' > 0 /\ Ar_2 + 12*Ar_3 - 11*Fresh_0 - 10*Fresh_0' - 9*Fresh_0'' - 8*Fresh_0''' - 7*Fresh_0'''' - 6*Fresh_0''''' - 5*Fresh_0'''''' - 4*Fresh_0''''''' - 3*Fresh_0'''''''' - 2*Fresh_0''''''''' - Fresh_0'''''''''' > 0 /\ Fresh_0'''''''''''' > 0 /\ Ar_2 + 13*Ar_3 - 12*Fresh_0 - 11*Fresh_0' - 10*Fresh_0'' - 9*Fresh_0''' - 8*Fresh_0'''' - 7*Fresh_0''''' - 6*Fresh_0'''''' - 5*Fresh_0''''''' - 4*Fresh_0'''''''' - 3*Fresh_0''''''''' - 2*Fresh_0'''''''''' - Fresh_0''''''''''' > 0 /\ Fresh_0''''''''''''' > 0 /\ Ar_2 + 14*Ar_3 - 13*Fresh_0 - 12*Fresh_0' - 11*Fresh_0'' - 10*Fresh_0''' - 9*Fresh_0'''' - 8*Fresh_0''''' - 7*Fresh_0'''''' - 6*Fresh_0''''''' - 5*Fresh_0'''''''' - 4*Fresh_0''''''''' - 3*Fresh_0'''''''''' - 2*Fresh_0''''''''''' - Fresh_0'''''''''''' > 0 /\ Fresh_0'''''''''''''' > 0 ]
We thus obtain the following problem:
18:	T:
		(Comp: 1, Cost: 16)    l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + 15*Ar_3 - 14*Fresh_0 - 13*Fresh_0' - 12*Fresh_0'' - 11*Fresh_0''' - 10*Fresh_0'''' - 9*Fresh_0''''' - 8*Fresh_0'''''' - 7*Fresh_0''''''' - 6*Fresh_0'''''''' - 5*Fresh_0''''''''' - 4*Fresh_0'''''''''' - 3*Fresh_0''''''''''' - 2*Fresh_0'''''''''''' - Fresh_0''''''''''''', Ar_3 - Fresh_0 - Fresh_0' - Fresh_0'' - Fresh_0''' - Fresh_0'''' - Fresh_0''''' - Fresh_0'''''' - Fresh_0''''''' - Fresh_0'''''''' - Fresh_0''''''''' - Fresh_0'''''''''' - Fresh_0''''''''''' - Fresh_0'''''''''''' - Fresh_0''''''''''''' - Fresh_0'''''''''''''')) [ Ar_2 > 0 /\ Fresh_0 > 0 /\ Ar_2 + Ar_3 > 0 /\ Fresh_0' > 0 /\ Ar_2 + 2*Ar_3 - Fresh_0 > 0 /\ Fresh_0'' > 0 /\ Ar_2 + 3*Ar_3 - 2*Fresh_0 - Fresh_0' > 0 /\ Fresh_0''' > 0 /\ Ar_2 + 4*Ar_3 - 3*Fresh_0 - 2*Fresh_0' - Fresh_0'' > 0 /\ Fresh_0'''' > 0 /\ Ar_2 + 5*Ar_3 - 4*Fresh_0 - 3*Fresh_0' - 2*Fresh_0'' - Fresh_0''' > 0 /\ Fresh_0''''' > 0 /\ Ar_2 + 6*Ar_3 - 5*Fresh_0 - 4*Fresh_0' - 3*Fresh_0'' - 2*Fresh_0''' - Fresh_0'''' > 0 /\ Fresh_0'''''' > 0 /\ Ar_2 + 7*Ar_3 - 6*Fresh_0 - 5*Fresh_0' - 4*Fresh_0'' - 3*Fresh_0''' - 2*Fresh_0'''' - Fresh_0''''' > 0 /\ Fresh_0''''''' > 0 /\ Ar_2 + 8*Ar_3 - 7*Fresh_0 - 6*Fresh_0' - 5*Fresh_0'' - 4*Fresh_0''' - 3*Fresh_0'''' - 2*Fresh_0''''' - Fresh_0'''''' > 0 /\ Fresh_0'''''''' > 0 /\ Ar_2 + 9*Ar_3 - 8*Fresh_0 - 7*Fresh_0' - 6*Fresh_0'' - 5*Fresh_0''' - 4*Fresh_0'''' - 3*Fresh_0''''' - 2*Fresh_0'''''' - Fresh_0''''''' > 0 /\ Fresh_0''''''''' > 0 /\ Ar_2 + 10*Ar_3 - 9*Fresh_0 - 8*Fresh_0' - 7*Fresh_0'' - 6*Fresh_0''' - 5*Fresh_0'''' - 4*Fresh_0''''' - 3*Fresh_0'''''' - 2*Fresh_0''''''' - Fresh_0'''''''' > 0 /\ Fresh_0'''''''''' > 0 /\ Ar_2 + 11*Ar_3 - 10*Fresh_0 - 9*Fresh_0' - 8*Fresh_0'' - 7*Fresh_0''' - 6*Fresh_0'''' - 5*Fresh_0''''' - 4*Fresh_0'''''' - 3*Fresh_0''''''' - 2*Fresh_0'''''''' - Fresh_0''''''''' > 0 /\ Fresh_0''''''''''' > 0 /\ Ar_2 + 12*Ar_3 - 11*Fresh_0 - 10*Fresh_0' - 9*Fresh_0'' - 8*Fresh_0''' - 7*Fresh_0'''' - 6*Fresh_0''''' - 5*Fresh_0'''''' - 4*Fresh_0''''''' - 3*Fresh_0'''''''' - 2*Fresh_0''''''''' - Fresh_0'''''''''' > 0 /\ Fresh_0'''''''''''' > 0 /\ Ar_2 + 13*Ar_3 - 12*Fresh_0 - 11*Fresh_0' - 10*Fresh_0'' - 9*Fresh_0''' - 8*Fresh_0'''' - 7*Fresh_0''''' - 6*Fresh_0'''''' - 5*Fresh_0''''''' - 4*Fresh_0'''''''' - 3*Fresh_0''''''''' - 2*Fresh_0'''''''''' - Fresh_0''''''''''' > 0 /\ Fresh_0''''''''''''' > 0 /\ Ar_2 + 14*Ar_3 - 13*Fresh_0 - 12*Fresh_0' - 11*Fresh_0'' - 10*Fresh_0''' - 9*Fresh_0'''' - 8*Fresh_0''''' - 7*Fresh_0'''''' - 6*Fresh_0''''''' - 5*Fresh_0'''''''' - 4*Fresh_0''''''''' - 3*Fresh_0'''''''''' - 2*Fresh_0''''''''''' - Fresh_0'''''''''''' > 0 /\ Fresh_0'''''''''''''' > 0 ]
		(Comp: 1, Cost: 1)     l0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)     l1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l1(2*Ar_0, 3*Ar_1, Ar_2, Ar_3)) [ Ar_1 < Ar_0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)     l2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l2(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_3 - Fresh_0)) [ Ar_2 > 0 /\ Fresh_0 > 0 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(l0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.770 sec (SMT: 0.610 sec)
