
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f1(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f1(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)    f1(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f0) = V_1
and size complexities
	S("koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-0) = Ar_0 + Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\\ 0 >= Ar_1 + 1 ]", 0-1) = Ar_1
	S("f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-0) = ?
	S("f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\\ Ar_1 >= 1 ]", 0-1) = Ar_1
	S("f1(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1))", 0-0) = Ar_0
	S("f1(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1))", 0-1) = Ar_1
orients the transitions
	f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
weakly and the transition
	f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)       f1(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f1(Ar_0, Ar_1)) [ 0 <= 0 ] with all transitions in problem 3, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
We thus obtain the following problem:
4:	T:
		(Comp: 1, Cost: 1)       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(f0(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 4:
	f1(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1))
We thus obtain the following problem:
5:	T:
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: 1, Cost: 1)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0, Ar_1)) [ 0 <= 0 ]
	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 transitions are obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
We thus obtain the following problem:
6:	T:
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 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, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ] with all transitions in problem 6, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 2*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 ]
We thus obtain the following problem:
7:	T:
		(Comp: 1, Cost: 3)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 2*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 2*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 ] with all transitions in problem 7, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 3*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 ]
We thus obtain the following problem:
8:	T:
		(Comp: 1, Cost: 4)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 3*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 3*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 ] with all transitions in problem 8, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 4*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 ]
We thus obtain the following problem:
9:	T:
		(Comp: 1, Cost: 5)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 4*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 4*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 ] with all transitions in problem 9, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 5*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 ]
We thus obtain the following problem:
10:	T:
		(Comp: 1, Cost: 6)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 5*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 5*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 ] with all transitions in problem 10, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 6*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 ]
We thus obtain the following problem:
11:	T:
		(Comp: 1, Cost: 7)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 6*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 6*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 ] with all transitions in problem 11, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 7*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 ]
We thus obtain the following problem:
12:	T:
		(Comp: 1, Cost: 8)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 7*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 7*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 ] with all transitions in problem 12, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 8*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 ]
We thus obtain the following problem:
13:	T:
		(Comp: 1, Cost: 9)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 8*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 8*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 ] with all transitions in problem 13, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 9*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 ]
We thus obtain the following problem:
14:	T:
		(Comp: 1, Cost: 10)      koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 9*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 9*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 ] with all transitions in problem 14, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 10*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 ]
We thus obtain the following problem:
15:	T:
		(Comp: 1, Cost: 11)      koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 10*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 10*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 ] with all transitions in problem 15, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 11*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 /\ Ar_0 + 10*Ar_1 >= 1 ]
We thus obtain the following problem:
16:	T:
		(Comp: 1, Cost: 12)      koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 11*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 /\ Ar_0 + 10*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 11*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 /\ Ar_0 + 10*Ar_1 >= 1 ] with all transitions in problem 16, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 12*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 /\ Ar_0 + 10*Ar_1 >= 1 /\ Ar_0 + 11*Ar_1 >= 1 ]
We thus obtain the following problem:
17:	T:
		(Comp: 1, Cost: 13)      koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 12*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 /\ Ar_0 + 10*Ar_1 >= 1 /\ Ar_0 + 11*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 12*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 /\ Ar_0 + 10*Ar_1 >= 1 /\ Ar_0 + 11*Ar_1 >= 1 ] with all transitions in problem 17, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 13*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 /\ Ar_0 + 10*Ar_1 >= 1 /\ Ar_0 + 11*Ar_1 >= 1 /\ Ar_0 + 12*Ar_1 >= 1 ]
We thus obtain the following problem:
18:	T:
		(Comp: 1, Cost: 14)      koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 13*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 /\ Ar_0 + 10*Ar_1 >= 1 /\ Ar_0 + 11*Ar_1 >= 1 /\ Ar_0 + 12*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

By chaining the transition koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 13*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 /\ Ar_0 + 10*Ar_1 >= 1 /\ Ar_0 + 11*Ar_1 >= 1 /\ Ar_0 + 12*Ar_1 >= 1 ] with all transitions in problem 18, the following new transition is obtained:
	koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 14*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 /\ Ar_0 + 10*Ar_1 >= 1 /\ Ar_0 + 11*Ar_1 >= 1 /\ Ar_0 + 12*Ar_1 >= 1 /\ Ar_0 + 13*Ar_1 >= 1 ]
We thus obtain the following problem:
19:	T:
		(Comp: 1, Cost: 15)      koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + 14*Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 /\ Ar_0 + Ar_1 >= 1 /\ Ar_0 + 2*Ar_1 >= 1 /\ Ar_0 + 3*Ar_1 >= 1 /\ Ar_0 + 4*Ar_1 >= 1 /\ Ar_0 + 5*Ar_1 >= 1 /\ Ar_0 + 6*Ar_1 >= 1 /\ Ar_0 + 7*Ar_1 >= 1 /\ Ar_0 + 8*Ar_1 >= 1 /\ Ar_0 + 9*Ar_1 >= 1 /\ Ar_0 + 10*Ar_1 >= 1 /\ Ar_0 + 11*Ar_1 >= 1 /\ Ar_0 + 12*Ar_1 >= 1 /\ Ar_0 + 13*Ar_1 >= 1 ]
		(Comp: 1, Cost: 2)       koat_start(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ 0 <= 0 /\ Ar_0 >= 1 /\ Ar_1 >= 1 ]
		(Comp: Ar_0, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f0(Ar_0, Ar_1) -> Com_1(f0(Ar_0 + Ar_1, Ar_1)) [ Ar_0 >= 1 /\ Ar_1 >= 1 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 0.248 sec (SMT: 0.212 sec)
