
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_6, Ar_2)) [ Fresh_6 >= 1 /\ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_5, Ar_2)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_3, Fresh_4)) [ Fresh_3 >= 1 /\ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_1, Fresh_2)) [ 0 >= Fresh_1 + 1 /\ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, 0, Ar_2)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, 0, Fresh_0)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(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)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_6, Ar_2)) [ Fresh_6 >= 1 /\ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_5, Ar_2)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_3, Fresh_4)) [ Fresh_3 >= 1 /\ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_1, Fresh_2)) [ 0 >= Fresh_1 + 1 /\ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, 0, Ar_2)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, 0, Fresh_0)) [ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = 1
	Pol(f1) = 0
	Pol(f300) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transitions
	f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_3, Fresh_4)) [ Fresh_3 >= 1 /\ 1 >= Ar_0 ]
	f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_1, Fresh_2)) [ 0 >= Fresh_1 + 1 /\ 1 >= Ar_0 ]
strictly and produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_6, Ar_2)) [ Fresh_6 >= 1 /\ Ar_0 >= 2 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_5, Ar_2)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 2 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_3, Fresh_4)) [ Fresh_3 >= 1 /\ 1 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_1, Fresh_2)) [ 0 >= Fresh_1 + 1 /\ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, 0, Ar_2)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, 0, Fresh_0)) [ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)    f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f2) = V_1
	Pol(f1) = V_1
	Pol(f300) = V_1
	Pol(koat_start) = V_1
orients all transitions weakly and the transitions
	f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_6, Ar_2)) [ Fresh_6 >= 1 /\ Ar_0 >= 2 ]
	f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_5, Ar_2)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 2 ]
strictly and produces the following problem:
4:	T:
		(Comp: Ar_0, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_6, Ar_2)) [ Fresh_6 >= 1 /\ Ar_0 >= 2 ]
		(Comp: Ar_0, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_5, Ar_2)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 2 ]
		(Comp: 1, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_3, Fresh_4)) [ Fresh_3 >= 1 /\ 1 >= Ar_0 ]
		(Comp: 1, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_1, Fresh_2)) [ 0 >= Fresh_1 + 1 /\ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, 0, Ar_2)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, 0, Fresh_0)) [ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)       f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f300(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
We thus obtain the following problem:
5:	T:
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: Ar_0, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_6, Ar_2)) [ Fresh_6 >= 1 /\ Ar_0 >= 2 ]
		(Comp: Ar_0, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_5, Ar_2)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 2 ]
		(Comp: 1, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_3, Fresh_4)) [ Fresh_3 >= 1 /\ 1 >= Ar_0 ]
		(Comp: 1, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_1, Fresh_2)) [ 0 >= Fresh_1 + 1 /\ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, 0, Ar_2)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, 0, Fresh_0)) [ 0 >= Ar_0 ]
		(Comp: 1, Cost: 1)       f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2))
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 5:
	f300(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, Ar_1, Ar_2))
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, 0, Fresh_0)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0, 0, Ar_2)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_1, Fresh_2)) [ 0 >= Fresh_1 + 1 /\ 1 >= Ar_0 ]
		(Comp: 1, Cost: 1)       f2(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0 - 1, Fresh_3, Fresh_4)) [ Fresh_3 >= 1 /\ 1 >= Ar_0 ]
		(Comp: Ar_0, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_5, Ar_2)) [ 0 >= Fresh_5 + 1 /\ Ar_0 >= 2 ]
		(Comp: Ar_0, Cost: 1)    f2(Ar_0, Ar_1, Ar_2) -> Com_1(f2(Ar_0 - 1, Fresh_6, Ar_2)) [ Fresh_6 >= 1 /\ Ar_0 >= 2 ]
		(Comp: 1, Cost: 1)       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 ?

Time: 0.093 sec (SMT: 0.079 sec)
