WORST_CASE(?, O(1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    eval_easy1_start(Ar_0, Ar_1) -> Com_1(eval_easy1_bb0_in(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy1_bb0_in(Ar_0, Ar_1) -> Com_1(eval_easy1_1(Fresh_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy1_1(Ar_0, Ar_1) -> Com_1(eval_easy1_2(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy1_2(Ar_0, Ar_1) -> Com_1(eval_easy1_3(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy1_3(Ar_0, Ar_1) -> Com_1(eval_easy1_4(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy1_4(Ar_0, Ar_1) -> Com_1(eval_easy1_5(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy1_5(Ar_0, Ar_1) -> Com_1(eval_easy1_6(Ar_0, Ar_1))
		(Comp: ?, Cost: 1)    eval_easy1_6(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, 0))
		(Comp: ?, Cost: 1)    eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb2_in(Ar_0, Ar_1)) [ Ar_1 < 40 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb3_in(Ar_0, Ar_1)) [ Ar_1 >= 40 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 1)) [ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 2)) [ Ar_0 < 0 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy1_stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(eval_easy1_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_easy1_start(Ar_0, Ar_1) -> Com_1(eval_easy1_bb0_in(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_bb0_in(Ar_0, Ar_1) -> Com_1(eval_easy1_1(Fresh_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_1(Ar_0, Ar_1) -> Com_1(eval_easy1_2(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_2(Ar_0, Ar_1) -> Com_1(eval_easy1_3(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_3(Ar_0, Ar_1) -> Com_1(eval_easy1_4(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_4(Ar_0, Ar_1) -> Com_1(eval_easy1_5(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_5(Ar_0, Ar_1) -> Com_1(eval_easy1_6(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_6(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, 0))
		(Comp: ?, Cost: 1)    eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb2_in(Ar_0, Ar_1)) [ Ar_1 < 40 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb3_in(Ar_0, Ar_1)) [ Ar_1 >= 40 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 1)) [ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 2)) [ Ar_0 < 0 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy1_stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(eval_easy1_start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval_easy1_start) = 2
	Pol(eval_easy1_bb0_in) = 2
	Pol(eval_easy1_1) = 2
	Pol(eval_easy1_2) = 2
	Pol(eval_easy1_3) = 2
	Pol(eval_easy1_4) = 2
	Pol(eval_easy1_5) = 2
	Pol(eval_easy1_6) = 2
	Pol(eval_easy1_bb1_in) = 2
	Pol(eval_easy1_bb2_in) = 2
	Pol(eval_easy1_bb3_in) = 1
	Pol(eval_easy1_stop) = 0
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	eval_easy1_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy1_stop(Ar_0, Ar_1))
	eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb3_in(Ar_0, Ar_1)) [ Ar_1 >= 40 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    eval_easy1_start(Ar_0, Ar_1) -> Com_1(eval_easy1_bb0_in(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_bb0_in(Ar_0, Ar_1) -> Com_1(eval_easy1_1(Fresh_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_1(Ar_0, Ar_1) -> Com_1(eval_easy1_2(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_2(Ar_0, Ar_1) -> Com_1(eval_easy1_3(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_3(Ar_0, Ar_1) -> Com_1(eval_easy1_4(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_4(Ar_0, Ar_1) -> Com_1(eval_easy1_5(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_5(Ar_0, Ar_1) -> Com_1(eval_easy1_6(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)    eval_easy1_6(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, 0))
		(Comp: ?, Cost: 1)    eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb2_in(Ar_0, Ar_1)) [ Ar_1 < 40 ]
		(Comp: 2, Cost: 1)    eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb3_in(Ar_0, Ar_1)) [ Ar_1 >= 40 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 1)) [ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 2)) [ Ar_0 < 0 ]
		(Comp: ?, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 2)) [ Ar_0 > 0 ]
		(Comp: 2, Cost: 1)    eval_easy1_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy1_stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1) -> Com_1(eval_easy1_start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval_easy1_start) = 79
	Pol(eval_easy1_bb0_in) = 79
	Pol(eval_easy1_1) = 79
	Pol(eval_easy1_2) = 79
	Pol(eval_easy1_3) = 79
	Pol(eval_easy1_4) = 79
	Pol(eval_easy1_5) = 79
	Pol(eval_easy1_6) = 79
	Pol(eval_easy1_bb1_in) = -2*V_2 + 79
	Pol(eval_easy1_bb2_in) = -2*V_2 + 78
	Pol(eval_easy1_bb3_in) = -2*V_2 + 79
	Pol(eval_easy1_stop) = -2*V_2 + 79
	Pol(koat_start) = 79
orients all transitions weakly and the transition
	eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb2_in(Ar_0, Ar_1)) [ Ar_1 < 40 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)     eval_easy1_start(Ar_0, Ar_1) -> Com_1(eval_easy1_bb0_in(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_bb0_in(Ar_0, Ar_1) -> Com_1(eval_easy1_1(Fresh_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_1(Ar_0, Ar_1) -> Com_1(eval_easy1_2(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_2(Ar_0, Ar_1) -> Com_1(eval_easy1_3(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_3(Ar_0, Ar_1) -> Com_1(eval_easy1_4(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_4(Ar_0, Ar_1) -> Com_1(eval_easy1_5(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_5(Ar_0, Ar_1) -> Com_1(eval_easy1_6(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_6(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, 0))
		(Comp: 79, Cost: 1)    eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb2_in(Ar_0, Ar_1)) [ Ar_1 < 40 ]
		(Comp: 2, Cost: 1)     eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb3_in(Ar_0, Ar_1)) [ Ar_1 >= 40 ]
		(Comp: ?, Cost: 1)     eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 1)) [ Ar_0 = 0 ]
		(Comp: ?, Cost: 1)     eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 2)) [ Ar_0 < 0 ]
		(Comp: ?, Cost: 1)     eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 2)) [ Ar_0 > 0 ]
		(Comp: 2, Cost: 1)     eval_easy1_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy1_stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1) -> Com_1(eval_easy1_start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 4 produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)     eval_easy1_start(Ar_0, Ar_1) -> Com_1(eval_easy1_bb0_in(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_bb0_in(Ar_0, Ar_1) -> Com_1(eval_easy1_1(Fresh_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_1(Ar_0, Ar_1) -> Com_1(eval_easy1_2(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_2(Ar_0, Ar_1) -> Com_1(eval_easy1_3(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_3(Ar_0, Ar_1) -> Com_1(eval_easy1_4(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_4(Ar_0, Ar_1) -> Com_1(eval_easy1_5(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_5(Ar_0, Ar_1) -> Com_1(eval_easy1_6(Ar_0, Ar_1))
		(Comp: 1, Cost: 1)     eval_easy1_6(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, 0))
		(Comp: 79, Cost: 1)    eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb2_in(Ar_0, Ar_1)) [ Ar_1 < 40 ]
		(Comp: 2, Cost: 1)     eval_easy1_bb1_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb3_in(Ar_0, Ar_1)) [ Ar_1 >= 40 ]
		(Comp: 79, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 1)) [ Ar_0 = 0 ]
		(Comp: 79, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 2)) [ Ar_0 < 0 ]
		(Comp: 79, Cost: 1)    eval_easy1_bb2_in(Ar_0, Ar_1) -> Com_1(eval_easy1_bb1_in(Ar_0, Ar_1 + 2)) [ Ar_0 > 0 ]
		(Comp: 2, Cost: 1)     eval_easy1_bb3_in(Ar_0, Ar_1) -> Com_1(eval_easy1_stop(Ar_0, Ar_1))
		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1) -> Com_1(eval_easy1_start(Ar_0, Ar_1)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 328

Time: 0.895 sec (SMT: 0.870 sec)