WORST_CASE(?, O(n^1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Fresh_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))
		(Comp: ?, Cost: 1)    eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 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_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Fresh_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))
		(Comp: ?, Cost: 1)    eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval_start_start) = 1
	Pol(eval_start_bb0_in) = 1
	Pol(eval_start_0) = 1
	Pol(eval_start_1) = 1
	Pol(eval_start_2) = 1
	Pol(eval_start_3) = 1
	Pol(eval_start_bb1_in) = 1
	Pol(eval_start_bb2_in) = 1
	Pol(eval_start_bb4_in) = 0
	Pol(eval_start_4) = 1
	Pol(eval_start_5) = 1
	Pol(eval_start_bb3_in) = 1
	Pol(eval_start_bb5_in) = 0
	Pol(eval_start_bb6_in) = -1
	Pol(eval_start_stop) = -2
	Pol(koat_start) = 1
orients all transitions weakly and the transitions
	eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_1 ]
	eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 > 0 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]
		(Comp: 1, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Fresh_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))
		(Comp: ?, Cost: 1)    eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval_start_start) = 2
	Pol(eval_start_bb0_in) = 2
	Pol(eval_start_0) = 2
	Pol(eval_start_1) = 2
	Pol(eval_start_2) = 2
	Pol(eval_start_3) = 2
	Pol(eval_start_bb1_in) = 2
	Pol(eval_start_bb2_in) = 2
	Pol(eval_start_bb4_in) = 2
	Pol(eval_start_4) = 2
	Pol(eval_start_5) = 2
	Pol(eval_start_bb3_in) = 2
	Pol(eval_start_bb5_in) = 2
	Pol(eval_start_bb6_in) = 1
	Pol(eval_start_stop) = 0
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))
	eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]
strictly and produces the following problem:
4:	T:
		(Comp: 1, Cost: 1)    eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]
		(Comp: 1, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Fresh_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)    eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))
		(Comp: ?, Cost: 1)    eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_1 ]
		(Comp: 2, Cost: 1)    eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]
		(Comp: ?, Cost: 1)    eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))
		(Comp: 2, Cost: 1)    eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval_start_start) = 5*V_2
	Pol(eval_start_bb0_in) = 5*V_2
	Pol(eval_start_0) = 5*V_2
	Pol(eval_start_1) = 5*V_2
	Pol(eval_start_2) = 5*V_2
	Pol(eval_start_3) = 5*V_2
	Pol(eval_start_bb1_in) = 5*V_2 - 5*V_3
	Pol(eval_start_bb2_in) = 5*V_2 - 5*V_3 - 1
	Pol(eval_start_bb4_in) = 5*V_2 - 5*V_3 - 6
	Pol(eval_start_4) = 5*V_2 - 5*V_3 - 2
	Pol(eval_start_5) = 5*V_2 - 5*V_3 - 3
	Pol(eval_start_bb3_in) = 5*V_2 - 5*V_3 - 4
	Pol(eval_start_bb5_in) = 5*V_2 - 5*V_3 - 6
	Pol(eval_start_bb6_in) = 5*V_2 - 5*V_3 - 6
	Pol(eval_start_stop) = 5*V_2 - 5*V_3 - 6
	Pol(koat_start) = 5*V_2
orients all transitions weakly and the transition
	eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)         eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, Ar_3))
		(Comp: 5*Ar_1, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]
		(Comp: 1, Cost: 1)         eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_1 ]
		(Comp: ?, Cost: 1)         eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: ?, Cost: 1)         eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Fresh_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)         eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)         eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))
		(Comp: ?, Cost: 1)         eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_1 ]
		(Comp: 2, Cost: 1)         eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]
		(Comp: ?, Cost: 1)         eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))
		(Comp: 2, Cost: 1)         eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 0)         koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 5 produces the following problem:
6:	T:
		(Comp: 1, Cost: 1)         eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, Ar_3))
		(Comp: 5*Ar_1, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]
		(Comp: 1, Cost: 1)         eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_1 ]
		(Comp: 5*Ar_1, Cost: 1)    eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 5*Ar_1, Cost: 1)    eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Fresh_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)         eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 > 0 ]
		(Comp: 5*Ar_1, Cost: 1)    eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: 5*Ar_1, Cost: 1)    eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))
		(Comp: ?, Cost: 1)         eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_1 ]
		(Comp: 2, Cost: 1)         eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]
		(Comp: ?, Cost: 1)         eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))
		(Comp: 2, Cost: 1)         eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 0)         koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval_start_start) = 2*V_2 + 2
	Pol(eval_start_bb0_in) = 2*V_2 + 2
	Pol(eval_start_0) = 2*V_2 + 2
	Pol(eval_start_1) = 2*V_2 + 2
	Pol(eval_start_2) = 2*V_2 + 2
	Pol(eval_start_3) = 2*V_2 + 2
	Pol(eval_start_bb1_in) = 2*V_2 - 2*V_3 + 2
	Pol(eval_start_bb2_in) = 2*V_2 - 2*V_3 + 2
	Pol(eval_start_bb4_in) = 2*V_2 - 2*V_4 + 2
	Pol(eval_start_4) = 2*V_2 - 2*V_3 + 2
	Pol(eval_start_5) = 2*V_2 - 2*V_3 + 2
	Pol(eval_start_bb3_in) = 2*V_2 - 2*V_3
	Pol(eval_start_bb5_in) = 2*V_2 - 2*V_4 + 1
	Pol(eval_start_bb6_in) = 2*V_2 - 2*V_4 + 2
	Pol(eval_start_stop) = 2*V_2 - 2*V_4 + 2
	Pol(koat_start) = 2*V_2 + 2
orients all transitions weakly and the transition
	eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_1 ]
strictly and produces the following problem:
7:	T:
		(Comp: 1, Cost: 1)             eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, Ar_3))
		(Comp: 5*Ar_1, Cost: 1)        eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]
		(Comp: 1, Cost: 1)             eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_1 ]
		(Comp: 5*Ar_1, Cost: 1)        eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 5*Ar_1, Cost: 1)        eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Fresh_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 > 0 ]
		(Comp: 5*Ar_1, Cost: 1)        eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: 5*Ar_1, Cost: 1)        eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))
		(Comp: 2*Ar_1 + 2, Cost: 1)    eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_1 ]
		(Comp: 2, Cost: 1)             eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]
		(Comp: ?, Cost: 1)             eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))
		(Comp: 2, Cost: 1)             eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 0)             koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 7 produces the following problem:
8:	T:
		(Comp: 1, Cost: 1)             eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_bb0_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_2(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, 0, Ar_3))
		(Comp: 5*Ar_1, Cost: 1)        eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 < Ar_1 ]
		(Comp: 1, Cost: 1)             eval_start_bb1_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_2 >= Ar_1 ]
		(Comp: 5*Ar_1, Cost: 1)        eval_start_bb2_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 5*Ar_1, Cost: 1)        eval_start_4(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_5(Fresh_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 1)             eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_2)) [ Ar_0 > 0 ]
		(Comp: 5*Ar_1, Cost: 1)        eval_start_5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 <= 0 ]
		(Comp: 5*Ar_1, Cost: 1)        eval_start_bb3_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb1_in(Ar_0, Ar_1, Ar_2 + 1, Ar_3))
		(Comp: 2*Ar_1 + 2, Cost: 1)    eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 < Ar_1 ]
		(Comp: 2, Cost: 1)             eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_3 >= Ar_1 ]
		(Comp: 2*Ar_1 + 2, Cost: 1)    eval_start_bb5_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_bb4_in(Ar_0, Ar_1, Ar_2, Ar_3 + 1))
		(Comp: 2, Cost: 1)             eval_start_bb6_in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2, Ar_3))
		(Comp: 1, Cost: 0)             koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 29*Ar_1 + 16

Time: 1.430 sec (SMT: 1.372 sec)