WORST_CASE(?, O(1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f8(0, 10, 0))
		(Comp: ?, Cost: 1)    f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0 + 2, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f8(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ 2*Ar_1 >= Ar_0 + 1 /\ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f8(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 2*Ar_1 /\ Ar_2 >= Ar_1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(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: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f8(0, 10, 0))
		(Comp: ?, Cost: 1)    f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0 + 2, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f8(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ 2*Ar_1 >= Ar_0 + 1 /\ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f8(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 2*Ar_1 /\ Ar_2 >= Ar_1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = 1
	Pol(f8) = 1
	Pol(f6) = 0
	Pol(koat_start) = 1
orients all transitions weakly and the transitions
	f8(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ 2*Ar_1 >= Ar_0 + 1 /\ Ar_2 >= Ar_1 ]
	f8(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 2*Ar_1 /\ Ar_2 >= Ar_1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f8(0, 10, 0))
		(Comp: ?, Cost: 1)    f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0 + 2, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 1 ]
		(Comp: 1, Cost: 1)    f8(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ 2*Ar_1 >= Ar_0 + 1 /\ Ar_2 >= Ar_1 ]
		(Comp: 1, Cost: 1)    f8(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 2*Ar_1 /\ Ar_2 >= Ar_1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = 10
	Pol(f8) = V_2 - V_3
	Pol(f6) = V_2 - V_3
	Pol(koat_start) = 10
orients all transitions weakly and the transition
	f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0 + 2, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 1 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)     f0(Ar_0, Ar_1, Ar_2) -> Com_1(f8(0, 10, 0))
		(Comp: 10, Cost: 1)    f8(Ar_0, Ar_1, Ar_2) -> Com_1(f8(Ar_0 + 2, Ar_1, Ar_2 + 1)) [ Ar_1 >= Ar_2 + 1 ]
		(Comp: 1, Cost: 1)     f8(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ 2*Ar_1 >= Ar_0 + 1 /\ Ar_2 >= Ar_1 ]
		(Comp: 1, Cost: 1)     f8(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 2*Ar_1 /\ Ar_2 >= Ar_1 ]
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 13

Time: 0.401 sec (SMT: 0.389 sec)