WORST_CASE(?, O(n^1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(0, 0, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f6(Ar_0 + 2, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_2 + 1, Ar_1, Ar_2, 1)) [ Ar_0 = Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, 0)) [ Ar_2 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_2, 0)) [ Ar_0 >= Ar_2 + 2 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f15(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= Ar_2 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f15(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 1 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1, Ar_0, 1)) [ Ar_1 >= Ar_2 /\ Ar_0 = Ar_2 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_0, Ar_1, Ar_2].
We thus obtain the following problem:
2:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_2 /\ Ar_0 = Ar_2 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 2 ]
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_2 + 1, Ar_1, Ar_2)) [ Ar_0 = Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0 + 2, Ar_1 + 1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f6(0, 0, Ar_2))
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_2 /\ Ar_0 = Ar_2 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 /\ Ar_1 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 2 ]
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_2 + 1, Ar_1, Ar_2)) [ Ar_0 = Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0 + 2, Ar_1 + 1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f6(0, 0, Ar_2))
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(koat_start) = 2
	Pol(f0) = 2
	Pol(f6) = 2
	Pol(f19) = 0
	Pol(f15) = 1
orients all transitions weakly and the transitions
	f6(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_2 /\ Ar_0 = Ar_2 ]
	f6(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 /\ Ar_2 >= Ar_0 + 1 ]
	f6(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 /\ Ar_1 >= Ar_2 ]
	f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_2 + 1, Ar_1, Ar_2)) [ Ar_0 = Ar_2 + 1 ]
	f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ]
	f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 2 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_2 /\ Ar_0 = Ar_2 ]
		(Comp: 2, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 /\ Ar_1 >= Ar_2 ]
		(Comp: 2, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 2, Cost: 1)    f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 2 ]
		(Comp: 2, Cost: 1)    f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ]
		(Comp: 2, Cost: 1)    f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_2 + 1, Ar_1, Ar_2)) [ Ar_0 = Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0 + 2, Ar_1 + 1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f6(0, 0, Ar_2))
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(koat_start) = V_3
	Pol(f0) = V_3
	Pol(f6) = -V_2 + V_3
	Pol(f19) = -V_2 + V_3
	Pol(f15) = -V_2 + V_3
orients all transitions weakly and the transitions
	f6(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0 + 2, Ar_1 + 1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
	f6(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)       f6(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_0)) [ Ar_1 >= Ar_2 /\ Ar_0 = Ar_2 ]
		(Comp: 2, Cost: 1)       f6(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 1 /\ Ar_1 >= Ar_2 ]
		(Comp: 2, Cost: 1)       f6(Ar_0, Ar_1, Ar_2) -> Com_1(f15(Ar_0, Ar_1, Ar_2)) [ Ar_1 >= Ar_2 /\ Ar_2 >= Ar_0 + 1 ]
		(Comp: 2, Cost: 1)       f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_2 + 2 ]
		(Comp: 2, Cost: 1)       f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= Ar_0 ]
		(Comp: 2, Cost: 1)       f15(Ar_0, Ar_1, Ar_2) -> Com_1(f19(Ar_2 + 1, Ar_1, Ar_2)) [ Ar_0 = Ar_2 + 1 ]
		(Comp: Ar_2, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0 + 2, Ar_1 + 1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: Ar_2, Cost: 1)    f6(Ar_0, Ar_1, Ar_2) -> Com_1(f6(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)       f0(Ar_0, Ar_1, Ar_2) -> Com_1(f6(0, 0, Ar_2))
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 2*Ar_2 + 13

Time: 0.957 sec (SMT: 0.931 sec)