
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f4(0, Ar_1))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0 + 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f10(Ar_0, Ar_1 + 1)) [ 1 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 /\ 0 >= C + 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f10(Ar_0, 0)) [ Ar_0 >= 2 ]
		(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(f4(0, Ar_1))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0 + 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f10(Ar_0, Ar_1 + 1)) [ 1 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 /\ 0 >= C + 1 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 ]
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f10(Ar_0, 0)) [ Ar_0 >= 2 ]
		(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) = 2
	Pol(f4) = 2
	Pol(f10) = 1
	Pol(f18) = 0
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	f4(Ar_0, Ar_1) -> Com_1(f10(Ar_0, 0)) [ Ar_0 >= 2 ]
	f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 /\ 0 >= C + 1 ]
	f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f4(0, Ar_1))
		(Comp: ?, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0 + 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f10(Ar_0, Ar_1 + 1)) [ 1 >= Ar_1 ]
		(Comp: 2, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 /\ 0 >= C + 1 ]
		(Comp: 2, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 ]
		(Comp: 2, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f10(Ar_0, 0)) [ Ar_0 >= 2 ]
		(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) = 2
	Pol(f4) = -V_1 + 2
	Pol(f10) = -V_1 - V_2 + 2
	Pol(f18) = -V_1 - V_2
	Pol(koat_start) = 2
orients all transitions weakly and the transition
	f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0 + 1, Ar_1)) [ 1 >= Ar_0 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f4(0, Ar_1))
		(Comp: 2, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0 + 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f10(Ar_0, Ar_1 + 1)) [ 1 >= Ar_1 ]
		(Comp: 2, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 /\ 0 >= C + 1 ]
		(Comp: 2, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 ]
		(Comp: 2, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f10(Ar_0, 0)) [ Ar_0 >= 2 ]
		(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) = 2
	Pol(f4) = 2
	Pol(f10) = -V_2 + 2
	Pol(f18) = -V_2
	Pol(koat_start) = 2
orients all transitions weakly and the transition
	f10(Ar_0, Ar_1) -> Com_1(f10(Ar_0, Ar_1 + 1)) [ 1 >= Ar_1 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1) -> Com_1(f4(0, Ar_1))
		(Comp: 2, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f4(Ar_0 + 1, Ar_1)) [ 1 >= Ar_0 ]
		(Comp: 2, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f10(Ar_0, Ar_1 + 1)) [ 1 >= Ar_1 ]
		(Comp: 2, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 /\ 0 >= C + 1 ]
		(Comp: 2, Cost: 1)    f10(Ar_0, Ar_1) -> Com_1(f18(Ar_0, Ar_1)) [ Ar_1 >= 2 ]
		(Comp: 2, Cost: 1)    f4(Ar_0, Ar_1) -> Com_1(f10(Ar_0, 0)) [ Ar_0 >= 2 ]
		(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

Complexity upper bound 11

Time: 0.032 sec (SMT: 0.027 sec)
