
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f10000(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 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 1 produces the following problem:
2:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f10000(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 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

A polynomial rank function with
	Pol(f0) = 1
	Pol(f1) = 1
	Pol(f2) = 0
	Pol(f10000) = 0
	Pol(koat_start) = 1
orients all transitions weakly and the transitions
	f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
	f1(Ar_0, Ar_1) -> Com_1(f10000(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_0 = Ar_1 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1))
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f10000(Ar_0, Ar_1)) [ Ar_0 >= Ar_1 + 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 3 to obtain the following invariants:
  For symbol f1: X_1 - X_2 >= 0 /\ -X_1 + X_2 >= 0


This yielded the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f10000(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_0 = Ar_1 ]
	start location:	koat_start
	leaf cost:	0

Testing for unsatisfiable constraints removes the following transition from problem 4:
	f1(Ar_0, Ar_1) -> Com_1(f10000(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= Ar_1 + 1 ]
We thus obtain 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)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_0 = Ar_1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ] with all transitions in problem 5, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 ]
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_0 = Ar_1 ]
	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) -> Com_1(f1(Ar_0, Ar_0)) [ Ar_0 = Ar_1 ]
We thus obtain the following problem:
7:	T:
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 ] with all transitions in problem 7, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
8:	T:
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 8, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
9:	T:
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 9, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
10:	T:
		(Comp: 1, Cost: 4)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 10, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
11:	T:
		(Comp: 1, Cost: 5)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 5)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 11, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
12:	T:
		(Comp: 1, Cost: 6)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 6)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 5)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 12, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
13:	T:
		(Comp: 1, Cost: 7)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 7)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 6)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 5)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 13, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 7, Ar_0 + 7)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
14:	T:
		(Comp: 1, Cost: 8)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 7, Ar_0 + 7)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 8)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 7)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 6)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 5)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 7, Ar_0 + 7)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 14, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 8, Ar_0 + 8)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 7, Ar_0 + 7)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
15:	T:
		(Comp: 1, Cost: 9)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 8, Ar_0 + 8)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 9)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 7, Ar_0 + 7)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 8)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 7)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 6)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 5)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 8, Ar_0 + 8)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 15, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 9, Ar_0 + 9)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 8, Ar_0 + 8)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
16:	T:
		(Comp: 1, Cost: 10)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 9, Ar_0 + 9)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 10)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 8, Ar_0 + 8)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 9)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 7, Ar_0 + 7)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 8)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 7)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 6)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 5)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 9, Ar_0 + 9)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 16, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 10, Ar_0 + 10)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 9, Ar_0 + 9)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
17:	T:
		(Comp: 1, Cost: 11)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 10, Ar_0 + 10)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 11)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 9, Ar_0 + 9)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 10)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 8, Ar_0 + 8)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 9)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 7, Ar_0 + 7)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 8)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 7)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 6)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 5)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 10, Ar_0 + 10)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 17, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 11, Ar_0 + 11)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 10, Ar_0 + 10)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
18:	T:
		(Comp: 1, Cost: 12)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 11, Ar_0 + 11)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 12)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 10, Ar_0 + 10)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 11)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 9, Ar_0 + 9)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 10)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 8, Ar_0 + 8)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 9)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 7, Ar_0 + 7)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 8)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 7)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 6)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 5)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 11, Ar_0 + 11)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 18, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 12, Ar_0 + 12)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 11, Ar_0 + 11)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
19:	T:
		(Comp: 1, Cost: 13)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 12, Ar_0 + 12)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 13)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 11, Ar_0 + 11)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 12)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 10, Ar_0 + 10)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 11)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 9, Ar_0 + 9)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 10)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 8, Ar_0 + 8)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 9)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 7, Ar_0 + 7)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 8)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 7)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 6)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 5)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 12, Ar_0 + 12)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 19, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 13, Ar_0 + 13)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 12, Ar_0 + 12)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
20:	T:
		(Comp: 1, Cost: 14)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 13, Ar_0 + 13)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 14)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 12, Ar_0 + 12)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 13)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 11, Ar_0 + 11)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 12)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 10, Ar_0 + 10)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 11)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 9, Ar_0 + 9)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 10)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 8, Ar_0 + 8)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 9)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 7, Ar_0 + 7)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 8)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 7)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 6)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 5)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 13, Ar_0 + 13)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ] with all transitions in problem 20, the following new transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 14, Ar_0 + 14)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 13, Ar_0 + 13)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
We thus obtain the following problem:
21:	T:
		(Comp: 1, Cost: 15)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 14, Ar_0 + 14)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 15)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 13, Ar_0 + 13)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 14)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 12, Ar_0 + 12)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 13)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 11, Ar_0 + 11)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 12)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 10, Ar_0 + 10)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 11)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 9, Ar_0 + 9)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 10)    koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 8, Ar_0 + 8)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 9)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 7, Ar_0 + 7)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 8)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 6, Ar_0 + 6)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 7)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 5, Ar_0 + 5)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 6)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 4, Ar_0 + 4)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 5)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 3, Ar_0 + 3)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 4)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 2, Ar_0 + 2)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 3)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0 + 1, Ar_0 + 1)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: 1, Cost: 2)     koat_start(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_0)) [ 0 <= 0 /\ Ar_0 = Ar_1 /\ 0 >= 0 ]
		(Comp: ?, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f1(Ar_0 + 1, Ar_1 + 1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)     f1(Ar_0, Ar_1) -> Com_1(f2(Ar_0, Ar_1)) [ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.256 sec (SMT: 0.213 sec)
