MAYBE

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f1(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) -> Com_1(f1(Ar_0, Ar_1 + 1, Ar_3, Fresh_33, Ar_3, Fresh_34, Ar_1, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f1(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) -> Com_1(f4(Fresh_24, Fresh_25, Fresh_26, Fresh_27, Fresh_28, Ar_5, Ar_6, Fresh_29, Fresh_30, Fresh_31, Fresh_32, Ar_2, Ar_12, Ar_13)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_25 >= Fresh_29 /\ Fresh_29 >= 2 ]
		(Comp: ?, Cost: 1)    f3(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) -> Com_1(f4(Fresh_14, Fresh_15, Fresh_16, Fresh_17, Fresh_18, Ar_5, Ar_6, Fresh_19, Fresh_20, Fresh_21, Fresh_22, 0, Fresh_23, Ar_13)) [ 0 >= Fresh_19 /\ 0 >= X' ]
		(Comp: ?, Cost: 1)    f3(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) -> Com_1(f1(Fresh_9, 2, Fresh_10, Fresh_11, Fresh_10, Ar_5, Ar_6, Fresh_9, Fresh_10, Ar_9, Ar_10, Ar_11, Fresh_12, Fresh_13)) [ Fresh_9 >= 2 ]
		(Comp: ?, Cost: 1)    f3(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) -> Com_1(f4(Fresh_0, Fresh_1, Fresh_2, Fresh_3, Fresh_4, Ar_5, Ar_6, 1, Fresh_5, Fresh_6, Fresh_7, Ar_3, Fresh_8, Ar_13))
		(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) -> Com_1(f3(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)) [ 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(f3(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, Fresh_1))
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f1(Fresh_9, 2)) [ Fresh_9 >= 2 ]
		(Comp: ?, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f4(Fresh_14, Fresh_15)) [ 0 >= Fresh_19 /\ 0 >= X' ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f4(Fresh_24, Fresh_25)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_25 >= Fresh_29 /\ Fresh_29 >= 2 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ]
	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) -> Com_1(f3(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, Fresh_1))
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f1(Fresh_9, 2)) [ Fresh_9 >= 2 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f4(Fresh_14, Fresh_15)) [ 0 >= Fresh_19 /\ 0 >= X' ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f4(Fresh_24, Fresh_25)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_25 >= Fresh_29 /\ Fresh_29 >= 2 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(koat_start) = 1
	Pol(f3) = 1
	Pol(f4) = 0
	Pol(f1) = 1
orients all transitions weakly and the transition
	f1(Ar_0, Ar_1) -> Com_1(f4(Fresh_24, Fresh_25)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_25 >= Fresh_29 /\ Fresh_29 >= 2 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f3(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, Fresh_1))
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f1(Fresh_9, 2)) [ Fresh_9 >= 2 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f4(Fresh_14, Fresh_15)) [ 0 >= Fresh_19 /\ 0 >= X' ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f4(Fresh_24, Fresh_25)) [ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_25 >= Fresh_29 /\ Fresh_29 >= 2 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 4 to obtain the following invariants:
  For symbol f1: X_1 - X_2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 4 >= 0 /\ X_1 - 2 >= 0


This yielded the following problem:
5:	T:
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_0 >= Ar_1 + 1 /\ Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f4(Fresh_24, Fresh_25)) [ Ar_0 - Ar_1 >= 0 /\ Ar_1 - 2 >= 0 /\ Ar_0 + Ar_1 - 4 >= 0 /\ Ar_0 - 2 >= 0 /\ Ar_1 >= Ar_0 /\ Ar_1 >= 0 /\ Fresh_25 >= Fresh_29 /\ Fresh_29 >= 2 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f4(Fresh_14, Fresh_15)) [ 0 >= Fresh_19 /\ 0 >= X' ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f1(Fresh_9, 2)) [ Fresh_9 >= 2 ]
		(Comp: 1, Cost: 1)    f3(Ar_0, Ar_1) -> Com_1(f4(Fresh_0, Fresh_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f3(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 1.280 sec (SMT: 1.240 sec)