MAYBE

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(f31(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9))
		(Comp: ?, Cost: 1)    f33(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9))
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(f31(Ar_0, Fresh_10, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(f31(Ar_0, Fresh_8, Ar_2, Fresh_9, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 >= Ar_0 /\ Ar_2 + 999 >= Fresh_9 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(f31(1, Fresh_6, Ar_2, Fresh_7, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 0 >= Ar_0 /\ Fresh_7 >= Ar_2 + 1000 ]
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(f24(0, Ar_1, Fresh_5, Ar_3, Fresh_5, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(f18(1, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_4, Fresh_4, Ar_7, Ar_8, Ar_9)) [ 0 >= Fresh_4 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(f18(1, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_2, 0, 1, Fresh_3, Fresh_3)) [ Fresh_2 >= 1 /\ Fresh_3 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(f31(1, Ar_1, Ar_2, Ar_3, Ar_4, Fresh_0, 0, 1, Fresh_1, Fresh_1)) [ Fresh_0 >= 1 /\ 0 >= Fresh_1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) [ 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_2].
We thus obtain the following problem:
2:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_2) -> Com_1(f0(Ar_0, Ar_2)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f31(1, Ar_2)) [ Fresh_0 >= 1 /\ 0 >= Fresh_1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f18(1, Ar_2)) [ Fresh_2 >= 1 /\ Fresh_3 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f18(1, Ar_2)) [ 0 >= Fresh_4 ]
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_2) -> Com_1(f24(0, Fresh_5)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_2) -> Com_1(f31(1, Ar_2)) [ 0 >= Ar_0 /\ Fresh_7 >= Ar_2 + 1000 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_2) -> Com_1(f31(Ar_0, Ar_2)) [ 0 >= Ar_0 /\ Ar_2 + 999 >= Fresh_9 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_2) -> Com_1(f31(Ar_0, Ar_2)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f33(Ar_0, Ar_2) -> Com_1(f36(Ar_0, Ar_2))
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_2) -> Com_1(f31(Ar_0, Ar_2))
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_2) -> Com_1(f24(Ar_0, Ar_2)) [ 0 >= Ar_0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transitions from problem 2:
	f24(Ar_0, Ar_2) -> Com_1(f31(Ar_0, Ar_2)) [ Ar_0 >= 1 ]
	f33(Ar_0, Ar_2) -> Com_1(f36(Ar_0, Ar_2))
	f18(Ar_0, Ar_2) -> Com_1(f24(Ar_0, Ar_2)) [ 0 >= Ar_0 ]
We thus obtain the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_2) -> Com_1(f31(Ar_0, Ar_2)) [ 0 >= Ar_0 /\ Ar_2 + 999 >= Fresh_9 ]
		(Comp: ?, Cost: 1)    f24(Ar_0, Ar_2) -> Com_1(f31(1, Ar_2)) [ 0 >= Ar_0 /\ Fresh_7 >= Ar_2 + 1000 ]
		(Comp: ?, Cost: 1)    f18(Ar_0, Ar_2) -> Com_1(f24(0, Fresh_5)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_2) -> Com_1(f31(Ar_0, Ar_2))
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f18(1, Ar_2)) [ 0 >= Fresh_4 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f18(1, Ar_2)) [ Fresh_2 >= 1 /\ Fresh_3 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f31(1, Ar_2)) [ Fresh_0 >= 1 /\ 0 >= Fresh_1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_2) -> Com_1(f0(Ar_0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 3 produces the following problem:
4:	T:
		(Comp: 2, Cost: 1)    f24(Ar_0, Ar_2) -> Com_1(f31(Ar_0, Ar_2)) [ 0 >= Ar_0 /\ Ar_2 + 999 >= Fresh_9 ]
		(Comp: 2, Cost: 1)    f24(Ar_0, Ar_2) -> Com_1(f31(1, Ar_2)) [ 0 >= Ar_0 /\ Fresh_7 >= Ar_2 + 1000 ]
		(Comp: 2, Cost: 1)    f18(Ar_0, Ar_2) -> Com_1(f24(0, Fresh_5)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_2) -> Com_1(f31(Ar_0, Ar_2))
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f18(1, Ar_2)) [ 0 >= Fresh_4 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f18(1, Ar_2)) [ Fresh_2 >= 1 /\ Fresh_3 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f31(1, Ar_2)) [ Fresh_0 >= 1 /\ 0 >= Fresh_1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_2) -> Com_1(f0(Ar_0, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 4 to obtain the following invariants:
  For symbol f18: -X_1 + 1 >= 0 /\ X_1 - 1 >= 0
  For symbol f24: -X_1 >= 0 /\ X_1 >= 0
  For symbol f31: -X_1 + 1 >= 0 /\ X_1 >= 0


This yielded the following problem:
5:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_2) -> Com_1(f0(Ar_0, Ar_2)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f31(1, Ar_2)) [ Fresh_0 >= 1 /\ 0 >= Fresh_1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f18(1, Ar_2)) [ Fresh_2 >= 1 /\ Fresh_3 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_2) -> Com_1(f18(1, Ar_2)) [ 0 >= Fresh_4 ]
		(Comp: ?, Cost: 1)    f31(Ar_0, Ar_2) -> Com_1(f31(Ar_0, Ar_2)) [ -Ar_0 + 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: 2, Cost: 1)    f18(Ar_0, Ar_2) -> Com_1(f24(0, Fresh_5)) [ -Ar_0 + 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2, Cost: 1)    f24(Ar_0, Ar_2) -> Com_1(f31(1, Ar_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_0 /\ Fresh_7 >= Ar_2 + 1000 ]
		(Comp: 2, Cost: 1)    f24(Ar_0, Ar_2) -> Com_1(f31(Ar_0, Ar_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_0 /\ Ar_2 + 999 >= Fresh_9 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 1.208 sec (SMT: 1.165 sec)