
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0) -> Com_1(f1(Ar_0))
		(Comp: ?, Cost: 1)    f1(Ar_0) -> Com_1(f1(Ar_0 - 1000)) [ Ar_0 >= 1001 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 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)    f0(Ar_0) -> Com_1(f1(Ar_0))
		(Comp: ?, Cost: 1)    f1(Ar_0) -> Com_1(f1(Ar_0 - 1000)) [ Ar_0 >= 1001 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = V_1
	Pol(f1) = V_1
	Pol(koat_start) = V_1
orients all transitions weakly and the transition
	f1(Ar_0) -> Com_1(f1(Ar_0 - 1000)) [ Ar_0 >= 1001 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)       f0(Ar_0) -> Com_1(f1(Ar_0))
		(Comp: Ar_0, Cost: 1)    f1(Ar_0) -> Com_1(f1(Ar_0 - 1000)) [ Ar_0 >= 1001 ]
		(Comp: 1, Cost: 0)       koat_start(Ar_0) -> Com_1(f0(Ar_0)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound Ar_0 + 1

Time: 0.011 sec (SMT: 0.010 sec)
