
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, 0))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1)) [ 0 >= C + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ 0 >= C + 1 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 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 1 produces the following problem:
2:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, 0))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1)) [ 0 >= C + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ 0 >= C + 1 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 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(f0) = 1
	Pol(f4) = 1
	Pol(f14) = 0
	Pol(koat_start) = 1
orients all transitions weakly and the transitions
	f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ 0 >= C + 1 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
	f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
	f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ]
	f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, 0))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1)) [ 0 >= C + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1))
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ 0 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ 0 >= C + 1 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 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

Applied AI with 'oct' on problem 3 to obtain the following invariants:
  For symbol f4: X_2 >= 0


This yielded the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ 0 >= C + 1 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1)) [ Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1)) [ Ar_1 >= 0 /\ 0 >= C + 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, 0))
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, 0)) [ 0 <= 0 ]
We thus obtain the following problem:
5:	T:
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, 0)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ 0 >= C + 1 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1)) [ Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1)) [ Ar_1 >= 0 /\ 0 >= C + 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, 0))
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 5:
	f0(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, 0))
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ 0 >= C + 1 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1)) [ Ar_1 >= 0 /\ 0 >= C + 1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0, Ar_1 + 1)) [ Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f14(Ar_0, Ar_1)) [ Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, 0)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.049 sec (SMT: 0.040 sec)
