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

A polynomial rank function with
	Pol(eval) = V_2
	Pol(start) = V_2
	Pol(koat_start) = V_2
orients all transitions weakly and the transitions
	eval(Ar_0, Ar_1) -> Com_1(eval(Ar_0, 0)) [ Ar_0 >= 1 /\ Ar_1 = 1 ]
	eval(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Ar_1 - 1)) [ Ar_1 >= 1 /\ Ar_1 + 1 >= 0 /\ Ar_0 >= Ar_1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)       eval(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Ar_0)) [ 0 >= Ar_0 /\ Ar_1 = 1 ]
		(Comp: 1, Cost: 1)       eval(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Ar_0)) [ Ar_1 >= 1 /\ Ar_1 + 1 >= 0 /\ Ar_1 >= Ar_0 + 1 ]
		(Comp: Ar_1, Cost: 1)    eval(Ar_0, Ar_1) -> Com_1(eval(Ar_0, 0)) [ Ar_0 >= 1 /\ Ar_1 = 1 ]
		(Comp: Ar_1, Cost: 1)    eval(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Ar_1 - 1)) [ Ar_1 >= 1 /\ Ar_1 + 1 >= 0 /\ Ar_0 >= Ar_1 ]
		(Comp: 1, Cost: 1)       start(Ar_0, Ar_1) -> Com_1(eval(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1) -> Com_1(start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 2*Ar_1 + 3

Time: 0.031 sec (SMT: 0.028 sec)
