
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 1:
	f4(Ar_0, Ar_1, Ar_2) -> Com_1(f5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= Ar_1 + 1 ]
We thus obtain the following problem:
2:	T:
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1))
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1))
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 3 to obtain the following invariants:
  For symbol f4: X_1 - X_2 + 1 >= 0 /\ -X_1 + X_2 - 1 >= 0


This yielded the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1)) [ 0 <= 0 ]
We thus obtain the following problem:
5:	T:
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 5:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1))
We thus obtain the following problem:
6:	T:
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_1, Fresh_1 + 1, Ar_1)) [ 0 <= 0 ] with all transitions in problem 6, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_1 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
7:	T:
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_1 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_1 + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 7, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
8:	T:
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 8, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
9:	T:
		(Comp: 1, Cost: 4)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 9, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
10:	T:
		(Comp: 1, Cost: 5)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 10, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
11:	T:
		(Comp: 1, Cost: 6)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 11, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
12:	T:
		(Comp: 1, Cost: 7)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 12, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
13:	T:
		(Comp: 1, Cost: 8)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 13, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
14:	T:
		(Comp: 1, Cost: 9)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 14, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
15:	T:
		(Comp: 1, Cost: 10)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 15, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
16:	T:
		(Comp: 1, Cost: 11)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 16, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
17:	T:
		(Comp: 1, Cost: 12)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 17, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
18:	T:
		(Comp: 1, Cost: 13)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0'', Fresh_0'' + 1, Fresh_0' + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 18, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
19:	T:
		(Comp: 1, Cost: 14)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Fresh_0'' + 1)) [ 0 <= 0 /\ 0 >= 0 ] with all transitions in problem 19, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
We thus obtain the following problem:
20:	T:
		(Comp: 1, Cost: 15)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0', Fresh_0' + 1, Fresh_0 + 1)) [ 0 <= 0 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Fresh_0, Fresh_0 + 1, Ar_1)) [ Ar_0 - Ar_1 + 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.079 sec (SMT: 0.062 sec)
