
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 - 99, 0, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 + 1 = 0 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 2 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(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)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 - 99, 0, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 + 1 = 0 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 2 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f300) = 1
	Pol(f1) = 0
	Pol(f2) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_0 >= 0 ]
strictly and produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 - 99, 0, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 + 1 = 0 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 2 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f300) = -V_2
	Pol(f1) = -V_2
	Pol(f2) = -V_2
	Pol(koat_start) = -V_2
orients all transitions weakly and the transitions
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 2 ]
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 - 99, 0, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 + 1 = 0 ]
strictly and produces the following problem:
4:	T:
		(Comp: Ar_1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 - 99, 0, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 + 1 = 0 ]
		(Comp: ?, Cost: 1)       f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 2 ]
		(Comp: 1, Cost: 1)       f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f300) = -V_1
and size complexities
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))", 0-0) = Ar_0
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))", 0-1) = Ar_1
	S("f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))", 0-2) = Ar_2
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_0 >= 0 ]", 0-0) = Ar_0 + 99
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_0 >= 0 ]", 0-1) = ?
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_0 >= 0 ]", 0-2) = ?
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 2 ]", 0-0) = Ar_0
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 2 ]", 0-1) = Ar_1
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\\ 0 >= Ar_1 + 2 ]", 0-2) = Ar_2
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-0) = Ar_0 + 99
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-1) = ?
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\\ Ar_1 >= 0 ]", 0-2) = Ar_2
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 - 99, 0, Ar_2)) [ 0 >= Ar_0 + 1 /\\ Ar_1 + 1 = 0 ]", 0-0) = Ar_0 + 99
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 - 99, 0, Ar_2)) [ 0 >= Ar_0 + 1 /\\ Ar_1 + 1 = 0 ]", 0-1) = 0
	S("f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 - 99, 0, Ar_2)) [ 0 >= Ar_0 + 1 /\\ Ar_1 + 1 = 0 ]", 0-2) = Ar_2
orients the transitions
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ]
weakly and the transition
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ]
strictly and produces the following problem:
5:	T:
		(Comp: Ar_1, Cost: 1)                          f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 - 99, 0, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 + 1 = 0 ]
		(Comp: Ar_0 + Ar_0*Ar_1 + 99*Ar_1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ Ar_1 >= 0 ]
		(Comp: Ar_1, Cost: 1)                          f300(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0 + 1, Ar_1 + 1, Ar_2)) [ 0 >= Ar_0 + 1 /\ 0 >= Ar_1 + 2 ]
		(Comp: 1, Cost: 1)                             f300(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1, Fresh_0)) [ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)                             f2(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)                             koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 101*Ar_1 + Ar_0 + Ar_0*Ar_1 + 2

Time: 0.050 sec (SMT: 0.045 sec)
