
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2:	T:
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(l0) = 2
	Pol(l1) = 2
	Pol(l2) = 1
	Pol(l3) = 0
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ]
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]
		(Comp: ?, Cost: 1)    l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: 2, Cost: 1)    l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ]
		(Comp: ?, Cost: 1)    l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(l1) = V_3
and size complexities
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2
	S("l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]", 0-0) = ?
	S("l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]", 0-1) = ?
	S("l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]", 0-2) = ?
	S("l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ]", 0-0) = ?
	S("l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ]", 0-1) = ?
	S("l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ]", 0-2) = ?
	S("l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]", 0-0) = ?
	S("l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]", 0-1) = ?
	S("l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]", 0-2) = ?
	S("l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]", 0-0) = ?
	S("l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]", 0-1) = Ar_1
	S("l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]", 0-2) = Ar_2
	S("l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]", 0-0) = ?
	S("l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]", 0-1) = Ar_1
	S("l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]", 0-2) = Ar_2
	S("l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]", 0-0) = Ar_0
	S("l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]", 0-1) = Ar_1
	S("l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]", 0-2) = Ar_2
orients the transitions
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]
weakly and the transition
	l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)       l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: 2, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 4 to obtain the following invariants:
  For symbol l1: X_1 - 1 >= 0


This yielded the following problem:
5:	T:
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: 2, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] with all transitions in problem 5, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: 2, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 1, Cost: 1)       l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 6:
	l0(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ Ar_0 > 0 ]
We thus obtain the following problem:
7:	T:
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: 2, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 ] with all transitions in problem 7, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 ]
We thus obtain the following problem:
8:	T:
		(Comp: 2, Cost: 2)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 ] with all transitions in problem 8, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 2, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 ]
We thus obtain the following problem:
9:	T:
		(Comp: 2, Cost: 3)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 2, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 2, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 ] with all transitions in problem 9, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 3, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 ]
We thus obtain the following problem:
10:	T:
		(Comp: 2, Cost: 4)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 3, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 3, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 ] with all transitions in problem 10, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 4, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 ]
We thus obtain the following problem:
11:	T:
		(Comp: 2, Cost: 5)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 4, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 4, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 ] with all transitions in problem 11, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 5, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 ]
We thus obtain the following problem:
12:	T:
		(Comp: 2, Cost: 6)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 5, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 5, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 ] with all transitions in problem 12, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 6, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 ]
We thus obtain the following problem:
13:	T:
		(Comp: 2, Cost: 7)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 6, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 6, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 ] with all transitions in problem 13, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 7, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 ]
We thus obtain the following problem:
14:	T:
		(Comp: 2, Cost: 8)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 7, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 7, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 ] with all transitions in problem 14, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 8, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 ]
We thus obtain the following problem:
15:	T:
		(Comp: 2, Cost: 9)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 8, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 8, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 ] with all transitions in problem 15, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 9, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 ]
We thus obtain the following problem:
16:	T:
		(Comp: 2, Cost: 10)      l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 9, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 9, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 ] with all transitions in problem 16, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 10, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 ]
We thus obtain the following problem:
17:	T:
		(Comp: 2, Cost: 11)      l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 10, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 10, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 ] with all transitions in problem 17, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 11, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 /\ Ar_0 - 10 > 0 ]
We thus obtain the following problem:
18:	T:
		(Comp: 2, Cost: 12)      l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 11, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 /\ Ar_0 - 10 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 11, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 /\ Ar_0 - 10 > 0 ] with all transitions in problem 18, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 12, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 /\ Ar_0 - 10 > 0 /\ Ar_0 - 11 > 0 ]
We thus obtain the following problem:
19:	T:
		(Comp: 2, Cost: 13)      l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 12, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 /\ Ar_0 - 10 > 0 /\ Ar_0 - 11 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 12, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 /\ Ar_0 - 10 > 0 /\ Ar_0 - 11 > 0 ] with all transitions in problem 19, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 13, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 /\ Ar_0 - 10 > 0 /\ Ar_0 - 11 > 0 /\ Ar_0 - 12 > 0 ]
We thus obtain the following problem:
20:	T:
		(Comp: 2, Cost: 14)      l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 13, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 /\ Ar_0 - 10 > 0 /\ Ar_0 - 11 > 0 /\ Ar_0 - 12 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 13, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 /\ Ar_0 - 10 > 0 /\ Ar_0 - 11 > 0 /\ Ar_0 - 12 > 0 ] with all transitions in problem 20, the following new transition is obtained:
	l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 14, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 /\ Ar_0 - 10 > 0 /\ Ar_0 - 11 > 0 /\ Ar_0 - 12 > 0 /\ Ar_0 - 13 > 0 ]
We thus obtain the following problem:
21:	T:
		(Comp: 2, Cost: 15)      l2(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 14, Ar_1, Ar_2)) [ Ar_0 >= Ar_1^2 /\ Ar_0 > 0 /\ Ar_0 - 1 > 0 /\ Ar_0 - 2 > 0 /\ Ar_0 - 3 > 0 /\ Ar_0 - 4 > 0 /\ Ar_0 - 5 > 0 /\ Ar_0 - 6 > 0 /\ Ar_0 - 7 > 0 /\ Ar_0 - 8 > 0 /\ Ar_0 - 9 > 0 /\ Ar_0 - 10 > 0 /\ Ar_0 - 11 > 0 /\ Ar_0 - 12 > 0 /\ Ar_0 - 13 > 0 ]
		(Comp: ?, Cost: 1)       l3(Ar_0, Ar_1, Ar_2) -> Com_1(l3(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       l2(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0 + Ar_2^2, Ar_1 + 1, Ar_2 + 1)) [ Ar_0 < Ar_1^2 ]
		(Comp: Ar_2, Cost: 1)    l1(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0 + Ar_2, Ar_1, Ar_2 - 1)) [ Ar_0 - 1 >= 0 /\ Ar_2 > 0 ]
		(Comp: 2, Cost: 1)       l1(Ar_0, Ar_1, Ar_2) -> Com_1(l2(Ar_0, Ar_1, Ar_2)) [ Ar_0 - 1 >= 0 /\ Ar_2 <= 0 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(l1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 /\ Ar_0 > 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.309 sec (SMT: 0.247 sec)
