
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1, Fresh_1)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0))
		(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 1 produces the following problem:
2:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1, Fresh_1)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0))
		(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

A polynomial rank function with
	Pol(f0) = 1
	Pol(f1) = 1
	Pol(f4) = 0
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1, Fresh_1)) [ 0 >= Ar_1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1, Fresh_1)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0))
		(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

A polynomial rank function with
	Pol(f0) = V_2
	Pol(f1) = V_2
	Pol(f4) = V_2
	Pol(koat_start) = V_2
orients all transitions weakly and the transition
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ Ar_1 >= 1 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)       f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2))
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1, Fresh_1)) [ 0 >= Ar_1 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0))
		(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 4 to obtain the following invariants:
  For symbol f1: -X_1 >= 0 /\ X_1 >= 0
  For symbol f4: -X_2 >= 0 /\ X_1 - X_2 >= 0 /\ X_1 >= 0


This yielded the following problem:
5:	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: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1, Fresh_1)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2))
	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 5, the following new transition is obtained:
	koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: 1, Cost: 1)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1, Fresh_1)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2))
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 6:
	f0(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2))
We thus obtain the following problem:
7:	T:
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1, Fresh_1)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(Ar_0, Ar_1, Fresh_1)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 ] with all transitions in problem 7, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 ]
We thus obtain the following problem:
8:	T:
		(Comp: 1, Cost: 2)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 ] with all transitions in problem 8, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
9:	T:
		(Comp: 1, Cost: 3)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 9, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
10:	T:
		(Comp: 1, Cost: 4)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 10, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
11:	T:
		(Comp: 1, Cost: 5)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 11, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
12:	T:
		(Comp: 1, Cost: 6)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 12, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
13:	T:
		(Comp: 1, Cost: 7)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 13, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
14:	T:
		(Comp: 1, Cost: 8)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 14, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
15:	T:
		(Comp: 1, Cost: 9)       f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 15, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
16:	T:
		(Comp: 1, Cost: 10)      f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 16, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
17:	T:
		(Comp: 1, Cost: 11)      f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 17, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
18:	T:
		(Comp: 1, Cost: 12)      f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 18, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
19:	T:
		(Comp: 1, Cost: 13)      f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 19, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
20:	T:
		(Comp: 1, Cost: 14)      f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ] with all transitions in problem 20, the following new transition is obtained:
	f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
We thus obtain the following problem:
21:	T:
		(Comp: 1, Cost: 15)      f1(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0')) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_1 /\ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_1 + 1 >= 0 /\ 1 >= 0 ]
		(Comp: ?, Cost: 1)       f4(Ar_0, Ar_1, Ar_2) -> Com_1(f4(1, Ar_1, Fresh_0)) [ -Ar_1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 0 ]
		(Comp: Ar_1, Cost: 1)    f1(Ar_0, Ar_1, Ar_2) -> Com_1(f1(Ar_0, Ar_1 - 1, Fresh_2)) [ -Ar_0 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f1(0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.116 sec (SMT: 0.094 sec)
