MAYBE

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f41(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14) -> Com_1(f41(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14))
		(Comp: ?, Cost: 1)    f43(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14) -> Com_1(f46(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14))
		(Comp: ?, Cost: 1)    f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14) -> Com_1(f41(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14) -> Com_1(f41(Ar_0, Ar_1, Fresh_7, 0, Fresh_7, Fresh_7, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14)) [ 0 >= Ar_0 /\ Ar_1 + 999 >= Fresh_7 ]
		(Comp: ?, Cost: 1)    f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14) -> Com_1(f41(1, Ar_1, Fresh_6, 0, Fresh_6, Fresh_6, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14)) [ 0 >= Ar_0 /\ Fresh_6 >= Ar_1 + 1000 ]
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14) -> Com_1(f29(0, Fresh_5, Fresh_5, Ar_3, Ar_4, Ar_5, 0, Fresh_5, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14)) [ 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, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14) -> Com_1(f21(1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_4, Fresh_4, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14)) [ 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, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14) -> Com_1(f21(1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_2, 0, 1, Fresh_3, Fresh_3, 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, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14) -> Com_1(f41(1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Fresh_0, 0, 1, Fresh_1, Fresh_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, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14)) [ 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(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f41(1, Ar_1)) [ Fresh_0 >= 1 /\ 0 >= Fresh_1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f21(1, Ar_1)) [ Fresh_2 >= 1 /\ Fresh_3 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f21(1, Ar_1)) [ 0 >= Fresh_4 ]
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1) -> Com_1(f29(0, Fresh_5)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f29(Ar_0, Ar_1) -> Com_1(f41(1, Ar_1)) [ 0 >= Ar_0 /\ Fresh_6 >= Ar_1 + 1000 ]
		(Comp: ?, Cost: 1)    f29(Ar_0, Ar_1) -> Com_1(f41(Ar_0, Ar_1)) [ 0 >= Ar_0 /\ Ar_1 + 999 >= Fresh_7 ]
		(Comp: ?, Cost: 1)    f29(Ar_0, Ar_1) -> Com_1(f41(Ar_0, Ar_1)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f43(Ar_0, Ar_1) -> Com_1(f46(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    f41(Ar_0, Ar_1) -> Com_1(f41(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1) -> Com_1(f29(Ar_0, Ar_1)) [ 0 >= Ar_0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transitions from problem 2:
	f29(Ar_0, Ar_1) -> Com_1(f41(Ar_0, Ar_1)) [ Ar_0 >= 1 ]
	f43(Ar_0, Ar_1) -> Com_1(f46(Ar_0, Ar_1))
	f21(Ar_0, Ar_1) -> Com_1(f29(Ar_0, Ar_1)) [ 0 >= Ar_0 ]
We thus obtain the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f29(Ar_0, Ar_1) -> Com_1(f41(Ar_0, Ar_1)) [ 0 >= Ar_0 /\ Ar_1 + 999 >= Fresh_7 ]
		(Comp: ?, Cost: 1)    f29(Ar_0, Ar_1) -> Com_1(f41(1, Ar_1)) [ 0 >= Ar_0 /\ Fresh_6 >= Ar_1 + 1000 ]
		(Comp: ?, Cost: 1)    f21(Ar_0, Ar_1) -> Com_1(f29(0, Fresh_5)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f41(Ar_0, Ar_1) -> Com_1(f41(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f21(1, Ar_1)) [ 0 >= Fresh_4 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f21(1, Ar_1)) [ Fresh_2 >= 1 /\ Fresh_3 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f41(1, Ar_1)) [ Fresh_0 >= 1 /\ 0 >= Fresh_1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f0(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: 2, Cost: 1)    f29(Ar_0, Ar_1) -> Com_1(f41(Ar_0, Ar_1)) [ 0 >= Ar_0 /\ Ar_1 + 999 >= Fresh_7 ]
		(Comp: 2, Cost: 1)    f29(Ar_0, Ar_1) -> Com_1(f41(1, Ar_1)) [ 0 >= Ar_0 /\ Fresh_6 >= Ar_1 + 1000 ]
		(Comp: 2, Cost: 1)    f21(Ar_0, Ar_1) -> Com_1(f29(0, Fresh_5)) [ Ar_0 >= 1 ]
		(Comp: ?, Cost: 1)    f41(Ar_0, Ar_1) -> Com_1(f41(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f21(1, Ar_1)) [ 0 >= Fresh_4 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f21(1, Ar_1)) [ Fresh_2 >= 1 /\ Fresh_3 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f41(1, Ar_1)) [ Fresh_0 >= 1 /\ 0 >= Fresh_1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 4 to obtain the following invariants:
  For symbol f21: -X_1 + 1 >= 0 /\ X_1 - 1 >= 0
  For symbol f29: -X_1 >= 0 /\ X_1 >= 0
  For symbol f41: -X_1 + 1 >= 0 /\ X_1 >= 0


This yielded the following problem:
5:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f41(1, Ar_1)) [ Fresh_0 >= 1 /\ 0 >= Fresh_1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f21(1, Ar_1)) [ Fresh_2 >= 1 /\ Fresh_3 >= 1 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f21(1, Ar_1)) [ 0 >= Fresh_4 ]
		(Comp: ?, Cost: 1)    f41(Ar_0, Ar_1) -> Com_1(f41(Ar_0, Ar_1)) [ -Ar_0 + 1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: 2, Cost: 1)    f21(Ar_0, Ar_1) -> Com_1(f29(0, Fresh_5)) [ -Ar_0 + 1 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_0 >= 1 ]
		(Comp: 2, Cost: 1)    f29(Ar_0, Ar_1) -> Com_1(f41(1, Ar_1)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_0 /\ Fresh_6 >= Ar_1 + 1000 ]
		(Comp: 2, Cost: 1)    f29(Ar_0, Ar_1) -> Com_1(f41(Ar_0, Ar_1)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_0 /\ Ar_1 + 999 >= Fresh_7 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 1.336 sec (SMT: 1.286 sec)