WORST_CASE(?, O(EXP))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    f(Ar_0, Ar_1) -> Com_1(g(Ar_0, 1))
		(Comp: ?, Cost: 1)    g(Ar_0, Ar_1) -> Com_1(g(Ar_0 - 1, 2*Ar_1)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    g(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    h(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1 - 1)) [ Ar_1 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f(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)    f(Ar_0, Ar_1) -> Com_1(g(Ar_0, 1))
		(Comp: ?, Cost: 1)    g(Ar_0, Ar_1) -> Com_1(g(Ar_0 - 1, 2*Ar_1)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    g(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    h(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1 - 1)) [ Ar_1 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f) = 1
	Pol(g) = 1
	Pol(h) = 0
	Pol(koat_start) = 1
orients all transitions weakly and the transition
	g(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    f(Ar_0, Ar_1) -> Com_1(g(Ar_0, 1))
		(Comp: ?, Cost: 1)    g(Ar_0, Ar_1) -> Com_1(g(Ar_0 - 1, 2*Ar_1)) [ Ar_0 > 0 ]
		(Comp: 1, Cost: 1)    g(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    h(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1 - 1)) [ Ar_1 > 0 ]
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(f(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(f) = V_1
	Pol(g) = V_1
	Pol(h) = V_1
	Pol(koat_start) = V_1
orients all transitions weakly and the transition
	g(Ar_0, Ar_1) -> Com_1(g(Ar_0 - 1, 2*Ar_1)) [ Ar_0 > 0 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)       f(Ar_0, Ar_1) -> Com_1(g(Ar_0, 1))
		(Comp: Ar_0, Cost: 1)    g(Ar_0, Ar_1) -> Com_1(g(Ar_0 - 1, 2*Ar_1)) [ Ar_0 > 0 ]
		(Comp: 1, Cost: 1)       g(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)       h(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1 - 1)) [ Ar_1 > 0 ]
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1) -> Com_1(f(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(h) = V_2
and size complexities
	S("koat_start(Ar_0, Ar_1) -> Com_1(f(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-0) = Ar_0
	S("koat_start(Ar_0, Ar_1) -> Com_1(f(Ar_0, Ar_1)) [ 0 <= 0 ]", 0-1) = Ar_1
	S("h(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1 - 1)) [ Ar_1 > 0 ]", 0-0) = Ar_0
	S("h(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1 - 1)) [ Ar_1 > 0 ]", 0-1) = pow(2, Ar_0)
	S("g(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1)) [ Ar_0 <= 0 ]", 0-0) = Ar_0
	S("g(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1)) [ Ar_0 <= 0 ]", 0-1) = pow(2, Ar_0)
	S("g(Ar_0, Ar_1) -> Com_1(g(Ar_0 - 1, 2*Ar_1)) [ Ar_0 > 0 ]", 0-0) = Ar_0
	S("g(Ar_0, Ar_1) -> Com_1(g(Ar_0 - 1, 2*Ar_1)) [ Ar_0 > 0 ]", 0-1) = pow(2, Ar_0)
	S("f(Ar_0, Ar_1) -> Com_1(g(Ar_0, 1))", 0-0) = Ar_0
	S("f(Ar_0, Ar_1) -> Com_1(g(Ar_0, 1))", 0-1) = 1
orients the transitions
	h(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1 - 1)) [ Ar_1 > 0 ]
weakly and the transition
	h(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1 - 1)) [ Ar_1 > 0 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)               f(Ar_0, Ar_1) -> Com_1(g(Ar_0, 1))
		(Comp: Ar_0, Cost: 1)            g(Ar_0, Ar_1) -> Com_1(g(Ar_0 - 1, 2*Ar_1)) [ Ar_0 > 0 ]
		(Comp: 1, Cost: 1)               g(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1)) [ Ar_0 <= 0 ]
		(Comp: pow(2, Ar_0), Cost: 1)    h(Ar_0, Ar_1) -> Com_1(h(Ar_0, Ar_1 - 1)) [ Ar_1 > 0 ]
		(Comp: 1, Cost: 0)               koat_start(Ar_0, Ar_1) -> Com_1(f(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound pow(2, Ar_0) + Ar_0 + 2

Time: 0.972 sec (SMT: 0.944 sec)