WORST_CASE(?, O(1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 10 ]
		(Comp: ?, Cost: 1)    f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, 0, Fresh_2, Ar_3, Ar_4)) [ Ar_0 >= 10 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(0, Ar_1, Ar_2, Fresh_0, Fresh_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 1 produces the following problem:
2:	T:
		(Comp: ?, Cost: 1)    f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_1 ]
		(Comp: ?, Cost: 1)    f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 10 ]
		(Comp: ?, Cost: 1)    f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, 0, Fresh_2, Ar_3, Ar_4)) [ Ar_0 >= 10 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(0, Ar_1, Ar_2, Fresh_0, Fresh_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f12) = 2
	Pol(f25) = 1
	Pol(f36) = 0
	Pol(f0) = 2
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 10 ]
	f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, 0, Fresh_2, Ar_3, Ar_4)) [ Ar_0 >= 10 ]
strictly and produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_0 ]
		(Comp: ?, Cost: 1)    f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_1 ]
		(Comp: 2, Cost: 1)    f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 10 ]
		(Comp: 2, Cost: 1)    f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, 0, Fresh_2, Ar_3, Ar_4)) [ Ar_0 >= 10 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(0, Ar_1, Ar_2, Fresh_0, Fresh_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f12) = -V_1 + 10
	Pol(f25) = -V_1 - V_2 - 9
	Pol(f36) = -V_1 - V_2 - 9
	Pol(f0) = 10
	Pol(koat_start) = 10
orients all transitions weakly and the transition
	f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_0 ]
strictly and produces the following problem:
4:	T:
		(Comp: 10, Cost: 1)    f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_0 ]
		(Comp: ?, Cost: 1)     f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_1 ]
		(Comp: 2, Cost: 1)     f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 10 ]
		(Comp: 2, Cost: 1)     f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, 0, Fresh_2, Ar_3, Ar_4)) [ Ar_0 >= 10 ]
		(Comp: 1, Cost: 1)     f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(0, Ar_1, Ar_2, Fresh_0, Fresh_1))
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f12) = 10
	Pol(f25) = -V_2 + 10
	Pol(f36) = -V_2 + 10
	Pol(f0) = 10
	Pol(koat_start) = 10
orients all transitions weakly and the transition
	f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_1 ]
strictly and produces the following problem:
5:	T:
		(Comp: 10, Cost: 1)    f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_0 ]
		(Comp: 10, Cost: 1)    f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ 9 >= Ar_1 ]
		(Comp: 2, Cost: 1)     f25(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= 10 ]
		(Comp: 2, Cost: 1)     f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f25(Ar_0, 0, Fresh_2, Ar_3, Ar_4)) [ Ar_0 >= 10 ]
		(Comp: 1, Cost: 1)     f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(0, Ar_1, Ar_2, Fresh_0, Fresh_1))
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 25

Time: 0.827 sec (SMT: 0.797 sec)