WORST_CASE(?, O(1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 ]
		(Comp: ?, Cost: 1)    f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)    f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, 999, Ar_3)) [ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, 999, Ar_2, 1))
		(Comp: ?, Cost: 1)    f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, 999, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transitions from problem 1:
	f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f8(Ar_0 - 1, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 ]
	f8(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, 999, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 ]
We thus obtain the following problem:
2:	T:
		(Comp: ?, Cost: 1)    f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)    f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, 999, Ar_3)) [ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 >= 0 ]
		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, 999, Ar_2, 1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ]
		(Comp: ?, Cost: 1)    f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, 999, Ar_3)) [ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, 999, Ar_2, 1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f28) = 1
	Pol(f36) = 0
	Pol(f19) = 2
	Pol(f0) = 2
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]
	f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, 999, Ar_3)) [ 0 >= Ar_1 + 1 ]
strictly and produces the following problem:
4:	T:
		(Comp: 2, Cost: 1)    f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]
		(Comp: ?, Cost: 1)    f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ]
		(Comp: 2, Cost: 1)    f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, 999, Ar_3)) [ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)    f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, 999, Ar_2, 1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f28) = V_3 + 1
	Pol(f36) = V_3 + 1
	Pol(f19) = 1000
	Pol(f0) = 1000
	Pol(koat_start) = 1000
orients all transitions weakly and the transition
	f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ]
strictly and produces the following problem:
5:	T:
		(Comp: 2, Cost: 1)       f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]
		(Comp: 1000, Cost: 1)    f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ]
		(Comp: 2, Cost: 1)       f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, 999, Ar_3)) [ 0 >= Ar_1 + 1 ]
		(Comp: ?, Cost: 1)       f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)       f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, 999, Ar_2, 1))
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f28) = V_2 + 1
	Pol(f36) = V_2 + 1
	Pol(f19) = V_2 + 1
	Pol(f0) = 1000
	Pol(koat_start) = 1000
orients all transitions weakly and the transition
	f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 >= 0 ]
strictly and produces the following problem:
6:	T:
		(Comp: 2, Cost: 1)       f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 ]
		(Comp: 1000, Cost: 1)    f28(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 0 ]
		(Comp: 2, Cost: 1)       f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f28(Ar_0, Ar_1, 999, Ar_3)) [ 0 >= Ar_1 + 1 ]
		(Comp: 1000, Cost: 1)    f19(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, Ar_1 - 1, Ar_2, Ar_3)) [ Ar_1 >= 0 ]
		(Comp: 1, Cost: 1)       f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f19(Ar_0, 999, Ar_2, 1))
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 2005

Time: 0.836 sec (SMT: 0.808 sec)