MAYBE

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0 + 1, Ar_1, Fresh_5, Ar_3)) [ Fresh_5 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0 + 1, Ar_1, Fresh_4, Ar_3)) [ 0 >= Fresh_4 + 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0, Ar_1, 0, Ar_3)) [ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0 + 1, Ar_0, Fresh_3, Ar_3)) [ Fresh_3 >= 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0 + 1, Ar_0, Fresh_2, Ar_3)) [ 0 >= Fresh_2 + 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f1(Ar_0, Ar_0, 0, Ar_3)) [ Ar_1 >= E /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1, Ar_2, Fresh_1)) [ Ar_0 >= Ar_1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f300(Ar_0, Ar_1, Ar_2, Fresh_0)) [ Ar_0 >= Ar_1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f2(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].
We thus obtain the following problem:
2:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_1 >= E /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ 0 >= Fresh_2 + 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ Fresh_3 >= 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ 0 >= Fresh_4 + 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ Fresh_5 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1))
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 2:
	f1(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 /\ Ar_1 >= Ar_0 + 1 ]
We thus obtain the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ Fresh_5 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ 0 >= Fresh_4 + 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ Fresh_3 >= 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ 0 >= Fresh_2 + 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_1 >= E /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 3 produces the following problem:
4:	T:
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ Fresh_5 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ 0 >= Fresh_4 + 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ Fresh_3 >= 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ 0 >= Fresh_2 + 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_1 >= E /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    f2(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

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

A polynomial rank function with
	Pol(f1) = -V_1 + V_2 + 1
	Pol(f300) = -V_1 + V_2 + 1
	Pol(f2) = -V_1 + V_2 + 1
	Pol(koat_start) = -V_1 + V_2 + 1
orients all transitions weakly and the transitions
	f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ 0 >= Fresh_4 + 1 /\ Ar_1 >= Ar_0 + 1 ]
	f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ Fresh_3 >= 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
	f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ 0 >= Fresh_2 + 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
strictly and produces the following problem:
6:	T:
		(Comp: ?, Cost: 1)                  f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ Fresh_5 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: Ar_0 + Ar_1 + 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ 0 >= Fresh_4 + 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)                  f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ]
		(Comp: Ar_0 + Ar_1 + 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ Fresh_3 >= 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: Ar_0 + Ar_1 + 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ 0 >= Fresh_2 + 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)                  f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_1 >= E /\ Ar_0 = Ar_1 ]
		(Comp: 1, Cost: 1)                  f1(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                  f2(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)                  koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f1) = -V_1 + V_2
	Pol(f300) = -V_1 + V_2
	Pol(f2) = -V_1 + V_2
	Pol(koat_start) = -V_1 + V_2
orients all transitions weakly and the transition
	f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ Fresh_5 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
strictly and produces the following problem:
7:	T:
		(Comp: Ar_0 + Ar_1, Cost: 1)        f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ Fresh_5 >= 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: Ar_0 + Ar_1 + 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1)) [ 0 >= Fresh_4 + 1 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: ?, Cost: 1)                  f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ Ar_1 >= Ar_0 + 1 ]
		(Comp: Ar_0 + Ar_1 + 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ Fresh_3 >= 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: Ar_0 + Ar_1 + 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0)) [ 0 >= Fresh_2 + 1 /\ Ar_1 >= F /\ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)                  f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_1 >= E /\ Ar_0 = Ar_1 ]
		(Comp: 1, Cost: 1)                  f1(Ar_0, Ar_1) -> Com_1(f300(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)                  f2(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)                  koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 1.695 sec (SMT: 1.612 sec)