MAYBE

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    eval_catmouse_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb0_in(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_catmouse_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_0(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_catmouse_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_1(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_catmouse_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_2(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_catmouse_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_3(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_catmouse_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_4(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_catmouse_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_5(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_catmouse_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, 0))
		(Comp: ?, Cost: 1)    eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= Ar_1 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 > Ar_1 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_2 <= Ar_0 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 > Ar_0 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_stop(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_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_catmouse_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb0_in(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_0(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_1(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_3(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_4(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_5(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, 0))
		(Comp: ?, Cost: 1)    eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= Ar_1 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 > Ar_1 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_2 <= Ar_0 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 > Ar_0 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_stop(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(eval_catmouse_start) = 2
	Pol(eval_catmouse_bb0_in) = 2
	Pol(eval_catmouse_0) = 2
	Pol(eval_catmouse_1) = 2
	Pol(eval_catmouse_2) = 2
	Pol(eval_catmouse_3) = 2
	Pol(eval_catmouse_4) = 2
	Pol(eval_catmouse_5) = 2
	Pol(eval_catmouse_bb1_in) = 2
	Pol(eval_catmouse_bb2_in) = 2
	Pol(eval_catmouse_bb3_in) = 1
	Pol(eval_catmouse_stop) = 0
	Pol(koat_start) = 2
orients all transitions weakly and the transitions
	eval_catmouse_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_stop(Ar_0, Ar_1, Ar_2))
	eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 > Ar_1 ]
strictly and produces the following problem:
3:	T:
		(Comp: 1, Cost: 1)    eval_catmouse_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb0_in(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_0(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_1(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_3(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_4(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_5(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, 0))
		(Comp: ?, Cost: 1)    eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= Ar_1 ]
		(Comp: 2, Cost: 1)    eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 > Ar_1 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_2 <= Ar_0 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_2 > Ar_0 ]
		(Comp: 2, Cost: 1)    eval_catmouse_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_stop(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_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_catmouse_bb2_in: X_2 - X_3 >= 0
  For symbol eval_catmouse_bb3_in: -X_2 + X_3 - 1 >= 0


This yielded the following problem:
4:	T:
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
		(Comp: 2, Cost: 1)    eval_catmouse_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_stop(Ar_0, Ar_1, Ar_2)) [ -Ar_1 + Ar_2 - 1 >= 0 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2 - 1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 > Ar_0 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2 + 1)) [ Ar_1 - Ar_2 >= 0 /\ Ar_2 <= Ar_0 ]
		(Comp: 2, Cost: 1)    eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 > Ar_1 ]
		(Comp: ?, Cost: 1)    eval_catmouse_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_2 <= Ar_1 ]
		(Comp: 1, Cost: 1)    eval_catmouse_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb1_in(Ar_0, Ar_1, 0))
		(Comp: 1, Cost: 1)    eval_catmouse_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_5(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_4(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_3(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_1(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_0(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)    eval_catmouse_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_catmouse_bb0_in(Ar_0, Ar_1, Ar_2))
	start location:	koat_start
	leaf cost:	0

Complexity upper bound ?

Time: 1.960 sec (SMT: 1.877 sec)