MAYBE

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f15(Ar_0, 0, Fresh_2, Ar_3)) [ 0 >= Ar_0 /\ Fresh_2 >= 1 ]
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f15(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    f25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f9(Fresh_1, Ar_1, Ar_2, 0)) [ 0 >= Ar_2 ]
		(Comp: ?, Cost: 1)    f9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f9(Fresh_0, 0, Ar_2, 0))
		(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

Testing for reachability in the complexity graph removes the following transitions from problem 1:
	f25(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, Ar_2, Ar_3))
	f15(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f9(Fresh_1, Ar_1, Ar_2, 0)) [ 0 >= Ar_2 ]
We thus obtain the following problem:
2:	T:
		(Comp: ?, Cost: 1)    f23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f15(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f15(Ar_0, 0, Fresh_2, Ar_3)) [ 0 >= Ar_0 /\ Fresh_2 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f9(Fresh_0, 0, Ar_2, 0))
		(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

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f15(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 1 ]
		(Comp: 1, Cost: 1)    f9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 1 ]
		(Comp: 1, Cost: 1)    f9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f15(Ar_0, 0, Fresh_2, Ar_3)) [ 0 >= Ar_0 /\ Fresh_2 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f9(Fresh_0, 0, Ar_2, 0))
		(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

Applied AI with 'oct' on problem 3 to obtain the following invariants:
  For symbol f15: -X_4 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_2 - X_4 >= 0 /\ -X_2 - X_4 >= 0 /\ -X_1 - X_4 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 >= 0 /\ -X_2 + X_4 >= 0 /\ -X_1 + X_4 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ -X_2 >= 0 /\ -X_1 - X_2 >= 0 /\ X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 >= 0
  For symbol f23: -X_4 >= 0 /\ X_2 - X_4 >= 0 /\ -X_2 - X_4 >= 0 /\ X_1 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_2 + X_4 >= 0 /\ -X_2 + X_4 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_2 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
  For symbol f9: -X_4 >= 0 /\ X_2 - X_4 >= 0 /\ -X_2 - X_4 >= 0 /\ X_4 >= 0 /\ X_2 + X_4 >= 0 /\ -X_2 + X_4 >= 0 /\ -X_2 >= 0 /\ X_2 >= 0


This yielded the following problem:
4:	T:
		(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 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f9(Fresh_0, 0, Ar_2, 0))
		(Comp: 1, Cost: 1)    f9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f15(Ar_0, 0, Fresh_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_1 - Ar_3 >= 0 /\ -Ar_1 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ -Ar_1 >= 0 /\ Ar_1 >= 0 /\ 0 >= Ar_0 /\ Fresh_2 >= 1 ]
		(Comp: 1, Cost: 1)    f9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_1 - Ar_3 >= 0 /\ -Ar_1 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ -Ar_1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f15(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f15(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_2 - Ar_3 - 1 >= 0 /\ Ar_1 - Ar_3 >= 0 /\ -Ar_1 - Ar_3 >= 0 /\ -Ar_0 - Ar_3 >= 0 /\ Ar_3 >= 0 /\ Ar_2 + Ar_3 - 1 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ -Ar_0 + Ar_3 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 - 1 >= 0 /\ -Ar_0 + Ar_2 - 1 >= 0 /\ -Ar_1 >= 0 /\ -Ar_0 - Ar_1 >= 0 /\ Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ -Ar_0 >= 0 /\ Ar_2 >= 1 ]
		(Comp: ?, Cost: 1)    f23(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3)) [ -Ar_3 >= 0 /\ Ar_1 - Ar_3 >= 0 /\ -Ar_1 - Ar_3 >= 0 /\ Ar_0 - Ar_3 - 1 >= 0 /\ Ar_3 >= 0 /\ Ar_1 + Ar_3 >= 0 /\ -Ar_1 + Ar_3 >= 0 /\ Ar_0 + Ar_3 - 1 >= 0 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 2.349 sec (SMT: 2.276 sec)