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

A polynomial rank function with
	Pol(f1) = V_1 - V_2
	Pol(f3) = V_1 - V_2
	Pol(koat_start) = V_1 - V_2
orients all transitions weakly and the transition
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
strictly and produces the following problem:
3:	T:
		(Comp: Ar_0 + Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)              f3(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)              f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 2 /\ Ar_1 >= Ar_0 ]
		(Comp: 1, Cost: 0)              koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f1) = V_2 - V_3
and size complexities
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 2 /\\ Ar_1 >= Ar_0 ]", 0-0) = Ar_0
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 2 /\\ Ar_1 >= Ar_0 ]", 0-1) = 2*Ar_0 + 2*Ar_1
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 2 /\\ Ar_1 >= Ar_0 ]", 0-2) = ?
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ]", 0-0) = Ar_0
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ]", 0-1) = Ar_1
	S("f3(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ]", 0-2) = Ar_2
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_0
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = 2*Ar_0 + 2*Ar_1
	S("f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = Ar_2
orients the transitions
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 2 /\ Ar_1 >= Ar_0 ]
weakly and the transition
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 2 /\ Ar_1 >= Ar_0 ]
strictly and produces the following problem:
4:	T:
		(Comp: Ar_0 + Ar_1, Cost: 1)                                                                f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                                                                          f3(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 + 1 ]
		(Comp: Ar_1 + Ar_2 + 2*Ar_0^2 + 4*Ar_0*Ar_1 + 2*Ar_1^2 + Ar_0*Ar_2 + Ar_1*Ar_2, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 2 /\ Ar_1 >= Ar_0 ]
		(Comp: 1, Cost: 0)                                                                          koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f3(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound Ar_0 + 2*Ar_1 + Ar_2 + 2*Ar_0^2 + 4*Ar_0*Ar_1 + 2*Ar_1^2 + Ar_0*Ar_2 + Ar_1*Ar_2 + 1

Time: 0.023 sec (SMT: 0.019 sec)
