MAYBE

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    eval_ex3_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb0_in(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_ex3_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_0(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_ex3_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_1(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_ex3_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_2(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_ex3_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_3(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_ex3_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_4(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_ex3_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_2, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2)) [ 0 < Ar_0 /\ Ar_0 < 255 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 255 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 < 0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_1 = 0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_stop(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_start(Ar_0, Ar_1, Ar_2)) [ 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_ex3_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb0_in(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_0(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_1(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_3(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_4(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_2, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2)) [ 0 < Ar_0 /\ Ar_0 < 255 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 255 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 < 0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_1 = 0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_stop(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval_ex3_start) = 2
	Pol(eval_ex3_bb0_in) = 2
	Pol(eval_ex3_0) = 2
	Pol(eval_ex3_1) = 2
	Pol(eval_ex3_2) = 2
	Pol(eval_ex3_3) = 2
	Pol(eval_ex3_4) = 2
	Pol(eval_ex3_bb1_in) = 2
	Pol(eval_ex3_bb2_in) = 2
	Pol(eval_ex3_bb3_in) = 1
	Pol(eval_ex3_stop) = 0
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_stop(Ar_0, Ar_1, Ar_2))
	eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 255 ]
	eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    eval_ex3_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb0_in(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_0(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_1(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_3(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_4(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_2, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2)) [ 0 < Ar_0 /\ Ar_0 < 255 ]
		(Comp: 2, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]
		(Comp: 2, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 255 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 < 0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 - 1, Ar_1, Ar_2)) [ Ar_1 = 0 ]
		(Comp: 2, Cost: 1)    eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_stop(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Applied AI with 'oct' on problem 3 to obtain the following invariants:
  For symbol eval_ex3_bb2_in: -X_1 + 254 >= 0 /\ X_1 - 1 >= 0


This yielded the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)    eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_stop(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 - 1, Ar_1, Ar_2)) [ -Ar_0 + 254 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 = 0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_0 + 254 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_0 + 1, Ar_1, Ar_2)) [ -Ar_0 + 254 >= 0 /\ Ar_0 - 1 >= 0 /\ Ar_1 < 0 ]
		(Comp: 2, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 255 ]
		(Comp: 2, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb3_in(Ar_0, Ar_1, Ar_2)) [ 0 >= Ar_0 ]
		(Comp: ?, Cost: 1)    eval_ex3_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb2_in(Ar_0, Ar_1, Ar_2)) [ 0 < Ar_0 /\ Ar_0 < 255 ]
		(Comp: 1, Cost: 1)    eval_ex3_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb1_in(Ar_2, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_4(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_3(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_1(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_0(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_ex3_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_ex3_bb0_in(Ar_0, Ar_1, Ar_2))
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 3.042 sec (SMT: 2.963 sec)