
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2)) with all transitions in problem 2, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
We thus obtain the following problem:
3:	T:
		(Comp: 1, Cost: 2)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ] with all transitions in problem 3, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 2*Ar_1 - Ar_2, Ar_1 - 2*Ar_2 - 1, Ar_2 + 2)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 ]
We thus obtain the following problem:
4:	T:
		(Comp: 1, Cost: 3)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 2*Ar_1 - Ar_2, Ar_1 - 2*Ar_2 - 1, Ar_2 + 2)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 2*Ar_1 - Ar_2, Ar_1 - 2*Ar_2 - 1, Ar_2 + 2)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 ] with all transitions in problem 4, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 3*Ar_1 - 3*Ar_2 - 1, Ar_1 - 3*Ar_2 - 3, Ar_2 + 3)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 ]
We thus obtain the following problem:
5:	T:
		(Comp: 1, Cost: 4)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 3*Ar_1 - 3*Ar_2 - 1, Ar_1 - 3*Ar_2 - 3, Ar_2 + 3)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 3*Ar_1 - 3*Ar_2 - 1, Ar_1 - 3*Ar_2 - 3, Ar_2 + 3)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 ] with all transitions in problem 5, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 4*Ar_1 - 6*Ar_2 - 4, Ar_1 - 4*Ar_2 - 6, Ar_2 + 4)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 ]
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 5)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 4*Ar_1 - 6*Ar_2 - 4, Ar_1 - 4*Ar_2 - 6, Ar_2 + 4)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 4*Ar_1 - 6*Ar_2 - 4, Ar_1 - 4*Ar_2 - 6, Ar_2 + 4)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 ] with all transitions in problem 6, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 5*Ar_1 - 10*Ar_2 - 10, Ar_1 - 5*Ar_2 - 10, Ar_2 + 5)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 ]
We thus obtain the following problem:
7:	T:
		(Comp: 1, Cost: 6)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 5*Ar_1 - 10*Ar_2 - 10, Ar_1 - 5*Ar_2 - 10, Ar_2 + 5)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 5*Ar_1 - 10*Ar_2 - 10, Ar_1 - 5*Ar_2 - 10, Ar_2 + 5)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 ] with all transitions in problem 7, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 6*Ar_1 - 15*Ar_2 - 20, Ar_1 - 6*Ar_2 - 15, Ar_2 + 6)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 ]
We thus obtain the following problem:
8:	T:
		(Comp: 1, Cost: 7)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 6*Ar_1 - 15*Ar_2 - 20, Ar_1 - 6*Ar_2 - 15, Ar_2 + 6)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 6*Ar_1 - 15*Ar_2 - 20, Ar_1 - 6*Ar_2 - 15, Ar_2 + 6)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 ] with all transitions in problem 8, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 7*Ar_1 - 21*Ar_2 - 35, Ar_1 - 7*Ar_2 - 21, Ar_2 + 7)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 ]
We thus obtain the following problem:
9:	T:
		(Comp: 1, Cost: 8)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 7*Ar_1 - 21*Ar_2 - 35, Ar_1 - 7*Ar_2 - 21, Ar_2 + 7)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 7*Ar_1 - 21*Ar_2 - 35, Ar_1 - 7*Ar_2 - 21, Ar_2 + 7)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 ] with all transitions in problem 9, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 8*Ar_1 - 28*Ar_2 - 56, Ar_1 - 8*Ar_2 - 28, Ar_2 + 8)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 ]
We thus obtain the following problem:
10:	T:
		(Comp: 1, Cost: 9)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 8*Ar_1 - 28*Ar_2 - 56, Ar_1 - 8*Ar_2 - 28, Ar_2 + 8)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 8*Ar_1 - 28*Ar_2 - 56, Ar_1 - 8*Ar_2 - 28, Ar_2 + 8)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 ] with all transitions in problem 10, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 9*Ar_1 - 36*Ar_2 - 84, Ar_1 - 9*Ar_2 - 36, Ar_2 + 9)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 ]
We thus obtain the following problem:
11:	T:
		(Comp: 1, Cost: 10)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 9*Ar_1 - 36*Ar_2 - 84, Ar_1 - 9*Ar_2 - 36, Ar_2 + 9)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 9*Ar_1 - 36*Ar_2 - 84, Ar_1 - 9*Ar_2 - 36, Ar_2 + 9)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 ] with all transitions in problem 11, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 10*Ar_1 - 45*Ar_2 - 120, Ar_1 - 10*Ar_2 - 45, Ar_2 + 10)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 ]
We thus obtain the following problem:
12:	T:
		(Comp: 1, Cost: 11)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 10*Ar_1 - 45*Ar_2 - 120, Ar_1 - 10*Ar_2 - 45, Ar_2 + 10)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 10*Ar_1 - 45*Ar_2 - 120, Ar_1 - 10*Ar_2 - 45, Ar_2 + 10)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 ] with all transitions in problem 12, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 11*Ar_1 - 55*Ar_2 - 165, Ar_1 - 11*Ar_2 - 55, Ar_2 + 11)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 ]
We thus obtain the following problem:
13:	T:
		(Comp: 1, Cost: 12)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 11*Ar_1 - 55*Ar_2 - 165, Ar_1 - 11*Ar_2 - 55, Ar_2 + 11)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 11*Ar_1 - 55*Ar_2 - 165, Ar_1 - 11*Ar_2 - 55, Ar_2 + 11)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 ] with all transitions in problem 13, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 12*Ar_1 - 66*Ar_2 - 220, Ar_1 - 12*Ar_2 - 66, Ar_2 + 12)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 /\ Ar_0 + 11*Ar_1 - 55*Ar_2 - 165 >= 1 ]
We thus obtain the following problem:
14:	T:
		(Comp: 1, Cost: 13)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 12*Ar_1 - 66*Ar_2 - 220, Ar_1 - 12*Ar_2 - 66, Ar_2 + 12)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 /\ Ar_0 + 11*Ar_1 - 55*Ar_2 - 165 >= 1 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 12*Ar_1 - 66*Ar_2 - 220, Ar_1 - 12*Ar_2 - 66, Ar_2 + 12)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 /\ Ar_0 + 11*Ar_1 - 55*Ar_2 - 165 >= 1 ] with all transitions in problem 14, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 13*Ar_1 - 78*Ar_2 - 286, Ar_1 - 13*Ar_2 - 78, Ar_2 + 13)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 /\ Ar_0 + 11*Ar_1 - 55*Ar_2 - 165 >= 1 /\ Ar_0 + 12*Ar_1 - 66*Ar_2 - 220 >= 1 ]
We thus obtain the following problem:
15:	T:
		(Comp: 1, Cost: 14)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 13*Ar_1 - 78*Ar_2 - 286, Ar_1 - 13*Ar_2 - 78, Ar_2 + 13)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 /\ Ar_0 + 11*Ar_1 - 55*Ar_2 - 165 >= 1 /\ Ar_0 + 12*Ar_1 - 66*Ar_2 - 220 >= 1 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 13*Ar_1 - 78*Ar_2 - 286, Ar_1 - 13*Ar_2 - 78, Ar_2 + 13)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 /\ Ar_0 + 11*Ar_1 - 55*Ar_2 - 165 >= 1 /\ Ar_0 + 12*Ar_1 - 66*Ar_2 - 220 >= 1 ] with all transitions in problem 15, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 14*Ar_1 - 91*Ar_2 - 364, Ar_1 - 14*Ar_2 - 91, Ar_2 + 14)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 /\ Ar_0 + 11*Ar_1 - 55*Ar_2 - 165 >= 1 /\ Ar_0 + 12*Ar_1 - 66*Ar_2 - 220 >= 1 /\ Ar_0 + 13*Ar_1 - 78*Ar_2 - 286 >= 1 ]
We thus obtain the following problem:
16:	T:
		(Comp: 1, Cost: 15)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 14*Ar_1 - 91*Ar_2 - 364, Ar_1 - 14*Ar_2 - 91, Ar_2 + 14)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 /\ Ar_0 + 11*Ar_1 - 55*Ar_2 - 165 >= 1 /\ Ar_0 + 12*Ar_1 - 66*Ar_2 - 220 >= 1 /\ Ar_0 + 13*Ar_1 - 78*Ar_2 - 286 >= 1 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 14*Ar_1 - 91*Ar_2 - 364, Ar_1 - 14*Ar_2 - 91, Ar_2 + 14)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 /\ Ar_0 + 11*Ar_1 - 55*Ar_2 - 165 >= 1 /\ Ar_0 + 12*Ar_1 - 66*Ar_2 - 220 >= 1 /\ Ar_0 + 13*Ar_1 - 78*Ar_2 - 286 >= 1 ] with all transitions in problem 16, the following new transition is obtained:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 15*Ar_1 - 105*Ar_2 - 455, Ar_1 - 15*Ar_2 - 105, Ar_2 + 15)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 /\ Ar_0 + 11*Ar_1 - 55*Ar_2 - 165 >= 1 /\ Ar_0 + 12*Ar_1 - 66*Ar_2 - 220 >= 1 /\ Ar_0 + 13*Ar_1 - 78*Ar_2 - 286 >= 1 /\ Ar_0 + 14*Ar_1 - 91*Ar_2 - 364 >= 1 ]
We thus obtain the following problem:
17:	T:
		(Comp: 1, Cost: 16)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + 15*Ar_1 - 105*Ar_2 - 455, Ar_1 - 15*Ar_2 - 105, Ar_2 + 15)) [ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 - Ar_2 >= 1 /\ Ar_0 + 3*Ar_1 - 3*Ar_2 - 1 >= 1 /\ Ar_0 + 4*Ar_1 - 6*Ar_2 - 4 >= 1 /\ Ar_0 + 5*Ar_1 - 10*Ar_2 - 10 >= 1 /\ Ar_0 + 6*Ar_1 - 15*Ar_2 - 20 >= 1 /\ Ar_0 + 7*Ar_1 - 21*Ar_2 - 35 >= 1 /\ Ar_0 + 8*Ar_1 - 28*Ar_2 - 56 >= 1 /\ Ar_0 + 9*Ar_1 - 36*Ar_2 - 84 >= 1 /\ Ar_0 + 10*Ar_1 - 45*Ar_2 - 120 >= 1 /\ Ar_0 + 11*Ar_1 - 55*Ar_2 - 165 >= 1 /\ Ar_0 + 12*Ar_1 - 66*Ar_2 - 220 >= 1 /\ Ar_0 + 13*Ar_1 - 78*Ar_2 - 286 >= 1 /\ Ar_0 + 14*Ar_1 - 91*Ar_2 - 364 >= 1 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 + Ar_1, Ar_1 - Ar_2, Ar_2 + 1)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 1.155 sec (SMT: 1.097 sec)
