
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ 0 >= Ar_0 + 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ 0 >= Ar_0 + 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transitions from problem 1:
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ 0 >= Ar_0 + 1 /\ Ar_0 + Ar_1 >= 2 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ 0 >= Ar_0 + 1 /\ Ar_0 + Ar_1 >= 2 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ Ar_1 >= 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ Ar_1 >= 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ 0 >= Ar_1 + 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ 0 >= Ar_1 + 1 ]
We thus obtain the following problem:
2:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = -V_1 + V_2
and size complexities
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_1
orients the transitions
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
weakly and the transition
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
strictly and produces the following problem:
4:	T:
		(Comp: ?, Cost: 1)              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: 1, Cost: 1)              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)              koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = V_2
and size complexities
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_1
orients the transitions
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
weakly and the transition
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
strictly and produces the following problem:
5:	T:
		(Comp: ?, Cost: 1)                            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)                            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)                            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)                            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)                            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)                            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                  f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: Ar_0*Ar_1 + Ar_1^2 + Ar_1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: 1, Cost: 1)                            f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                            f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)                            f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                            f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)                            koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = V_1 + V_2
and size complexities
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_1
orients the transitions
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
weakly and the transition
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
strictly and produces the following problem:
6:	T:
		(Comp: ?, Cost: 1)                            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)                            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)                            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)                            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)                            f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                  f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                  f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: Ar_0*Ar_1 + Ar_1^2 + Ar_1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: 1, Cost: 1)                            f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                            f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)                            f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                            f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)                            koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = -V_2
and size complexities
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_1
orients the transitions
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
weakly and the transition
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
strictly and produces the following problem:
7:	T:
		(Comp: 3*Ar_1 + Ar_0^2 + Ar_0*Ar_1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)                              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)                              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)                              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)                              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: Ar_0*Ar_1 + Ar_1^2 + Ar_1, Cost: 1)      f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)                              koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = V_1
and size complexities
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_1
orients the transitions
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
weakly and the transition
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
strictly and produces the following problem:
8:	T:
		(Comp: 3*Ar_1 + Ar_0^2 + Ar_0*Ar_1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)                              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)                              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)                              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: Ar_0^2 + Ar_0*Ar_1 + Ar_0, Cost: 1)      f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: Ar_0*Ar_1 + Ar_1^2 + Ar_1, Cost: 1)      f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)                              koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = -V_1 - V_2
and size complexities
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_1
orients the transitions
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
weakly and the transition
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
strictly and produces the following problem:
9:	T:
		(Comp: 3*Ar_1 + Ar_0^2 + Ar_0*Ar_1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)                              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)                              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: Ar_0^2 + Ar_0*Ar_1 + Ar_0, Cost: 1)      f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: Ar_0*Ar_1 + Ar_1^2 + Ar_1, Cost: 1)      f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)                              koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = -V_1
and size complexities
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_1
orients the transitions
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
weakly and the transition
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
strictly and produces the following problem:
10:	T:
		(Comp: 3*Ar_1 + Ar_0^2 + Ar_0*Ar_1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: ?, Cost: 1)                              f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
		(Comp: Ar_0^2 + Ar_0*Ar_1 + Ar_0, Cost: 1)      f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: Ar_0^2 + Ar_0*Ar_1 + Ar_0, Cost: 1)      f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: Ar_0*Ar_1 + Ar_1^2 + Ar_1, Cost: 1)      f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)                              koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = V_1 - V_2
and size complexities
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ Ar_1 >= 2 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ Ar_0 >= 0 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\\ 0 >= Ar_1 /\\ Ar_0 >= 1 /\\ Ar_0 + Ar_1 >= 2 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ Ar_0 >= 2 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ Ar_1 >= 0 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\\ Ar_1 >= Ar_0 + 1 /\\ 0 >= Ar_0 + 2 /\\ Ar_1 >= 1 ]", 0-1) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\\ Ar_0 >= Ar_1 + 1 /\\ 0 >= Ar_0 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-0) = Ar_0 + Ar_1
	S("f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\\ 0 >= Ar_1 + 2 /\\ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + Ar_0 + 1 ]", 0-1) = Ar_1
orients the transitions
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
weakly and the transition
	f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
strictly and produces the following problem:
11:	T:
		(Comp: 3*Ar_1 + Ar_0^2 + Ar_0*Ar_1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ 0 >= Ar_1 + 2 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ 0 >= Ar_0 /\ 0 >= Ar_1 + 1 ]
		(Comp: Ar_0^2 + Ar_0*Ar_1 + Ar_0, Cost: 1)      f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ 0 >= Ar_0 + 2 /\ Ar_1 >= 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 + 1)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + Ar_0 + 1 ]
		(Comp: Ar_0^2 + Ar_0*Ar_1 + Ar_0, Cost: 1)      f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 - 1, Ar_1)) [ 1 >= Ar_0 + Ar_1 /\ Ar_0 >= Ar_1 + 1 /\ Ar_0 >= 2 /\ 0 >= Ar_1 + 1 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ 0 >= Ar_1 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: Ar_0 + Ar_1, Cost: 1)                    f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_1)) [ Ar_1 + Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: Ar_0*Ar_1 + Ar_1^2 + Ar_1, Cost: 1)      f2(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1 - 1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= 2 /\ Ar_0 >= 1 /\ Ar_0 + Ar_1 >= 2 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                              f0(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 0)                              koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 8*Ar_1 + 3*Ar_0^2 + 4*Ar_0*Ar_1 + 6*Ar_0 + Ar_1^2 + 4

Time: 0.229 sec (SMT: 0.188 sec)
