
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 + 1 >= 0 /\ Ar_2 >= 1 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2:	T:
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 + 1 >= 0 /\ Ar_2 >= 1 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 2 to obtain the following invariants:
  For symbol f2: X_1 - X_3 + 1 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0
  For symbol f3: X_1 - X_3 + 1 >= 0 /\ X_1 - X_2 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ X_1 - 1 >= 0


This yielded the following problem:
3:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 + 1 >= 0 /\ Ar_2 >= 1 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] with all transitions in problem 3, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
We thus obtain the following problem:
4:	T:
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 + 1 >= 0 /\ Ar_2 >= 1 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 4:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
We thus obtain the following problem:
5:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 + 1 >= 0 /\ Ar_2 >= 1 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 ] with all transitions in problem 5, the following new transition is obtained:
	f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
We thus obtain the following problem:
6:	T:
		(Comp: ?, Cost: 2)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 + 1 >= 0 /\ Ar_2 >= 1 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f3) = 2*V_1 - 2*V_3 + 2
	Pol(f2) = 2*V_1 - 2*V_3 + 3
and size complexities
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\\ Ar_0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\\ Ar_0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\\ Ar_0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-2) = Ar_1 + 1
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_1 + 1 ]", 0-2) = ?
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-0) = Ar_0
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-1) = Ar_1
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-2) = ?
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 + 1 >= 0 /\\ Ar_2 >= 1 /\\ Ar_2 >= Ar_0 + 1 ]", 0-0) = Ar_0
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 + 1 >= 0 /\\ Ar_2 >= 1 /\\ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 + 1 >= 0 /\\ Ar_2 >= 1 /\\ Ar_2 >= Ar_0 + 1 ]", 0-2) = 0
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-2) = Ar_0
orients the transitions
	f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
	f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
weakly and the transitions
	f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
	f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
strictly and produces the following problem:
7:	T:
		(Comp: ?, Cost: 2)                      f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: ?, Cost: 1)                      f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 + 1 >= 0 /\ Ar_2 >= 1 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 2*Ar_0 + 2*Ar_1 + 5, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: 2*Ar_0 + 2*Ar_1 + 5, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                      koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 7 produces the following problem:
8:	T:
		(Comp: ?, Cost: 2)                      f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: 2*Ar_0 + 2*Ar_1 + 5, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 + 1 >= 0 /\ Ar_2 >= 1 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 2*Ar_0 + 2*Ar_1 + 5, Cost: 1)    f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: 2*Ar_0 + 2*Ar_1 + 5, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                      koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = V_1 - V_3 + 1
and size complexities
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\\ Ar_0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\\ Ar_0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\\ Ar_0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-2) = Ar_1 + 1
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_2 >= Ar_1 + 1 ]", 0-2) = 3*Ar_0 + 3*Ar_1 + 54
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-0) = Ar_0
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-1) = Ar_1
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-2) = 3*Ar_0 + 3*Ar_1 + 54
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 + 1 >= 0 /\\ Ar_2 >= 1 /\\ Ar_2 >= Ar_0 + 1 ]", 0-0) = Ar_0
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 + 1 >= 0 /\\ Ar_2 >= 1 /\\ Ar_2 >= Ar_0 + 1 ]", 0-1) = Ar_1
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_0 + 1 >= 0 /\\ Ar_2 >= 1 /\\ Ar_2 >= Ar_0 + 1 ]", 0-2) = 0
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_1 - 1 >= 0 /\\ Ar_0 + Ar_1 - 2 >= 0 /\\ Ar_0 - 1 >= 0 /\\ Ar_1 >= Ar_2 + 1 /\\ Ar_0 >= Ar_2 /\\ Ar_2 + 1 >= 0 ]", 0-2) = Ar_0
orients the transitions
	f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
weakly and the transition
	f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
strictly and produces the following problem:
9:	T:
		(Comp: 10*Ar_0^2 + 16*Ar_0*Ar_1 + 137*Ar_0 + 127*Ar_1 + 6*Ar_1^2 + 280, Cost: 2)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 >= Ar_2 + 1 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: 2*Ar_0 + 2*Ar_1 + 5, Cost: 1)                                                f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, 0)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 + 1 >= 0 /\ Ar_2 >= 1 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 2*Ar_0 + 2*Ar_1 + 5, Cost: 1)                                                f3(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= Ar_2 /\ Ar_2 + 1 >= 0 ]
		(Comp: 2*Ar_0 + 2*Ar_1 + 5, Cost: 1)                                                f2(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ Ar_0 - Ar_2 + 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 2 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_2 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                                                                  koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_1 + 1)) [ 0 <= 0 /\ Ar_0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 20*Ar_0^2 + 32*Ar_0*Ar_1 + 280*Ar_0 + 260*Ar_1 + 12*Ar_1^2 + 576

Time: 0.104 sec (SMT: 0.086 sec)
