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

Testing for reachability in the complexity graph removes the following transitions from problem 1:
	eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 1, Ar_2)) [ Ar_0 > 0 /\ Ar_0 <= 0 ]
	eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0 - 1, 0, Ar_2)) [ Ar_0 <= 0 /\ Ar_0 > 0 ]
We thus obtain the following problem:
2:	T:
		(Comp: ?, Cost: 1)    eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 <= 0 ]
		(Comp: ?, Cost: 1)    eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, Ar_2)) [ Ar_0 <= 0 ]
		(Comp: ?, Cost: 1)    eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0 - 1, 1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)    eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 > 0 ]
		(Comp: ?, Cost: 1)    eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_2, 1, Ar_2))
		(Comp: ?, Cost: 1)    eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2))
		(Comp: ?, Cost: 1)    eval_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

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

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

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

A polynomial rank function with
	Pol(eval_start_bb3_in) = V_1
	Pol(eval_start_stop) = V_1
	Pol(eval_start_bb1_in) = V_1
	Pol(eval_start_bb2_in) = V_1
	Pol(eval_start_5) = V_3
	Pol(eval_start_4) = V_3
	Pol(eval_start_3) = V_3
	Pol(eval_start_2) = V_3
	Pol(eval_start_1) = V_3
	Pol(eval_start_0) = V_3
	Pol(eval_start_bb0_in) = V_3
	Pol(eval_start_start) = V_3
	Pol(koat_start) = V_3
orients all transitions weakly and the transition
	eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0 - 1, 1, Ar_2)) [ Ar_0 > 0 ]
strictly and produces the following problem:
6:	T:
		(Comp: 2, Cost: 1)       eval_start_bb3_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_stop(Ar_0, Ar_1, Ar_2))
		(Comp: 2, Cost: 1)       eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb3_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 <= 0 ]
		(Comp: 1, Cost: 1)       eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0, 0, Ar_2)) [ Ar_0 <= 0 ]
		(Comp: Ar_2, Cost: 1)    eval_start_bb2_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_0 - 1, 1, Ar_2)) [ Ar_0 > 0 ]
		(Comp: ?, Cost: 1)       eval_start_bb1_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb2_in(Ar_0, Ar_1, Ar_2)) [ Ar_1 > 0 ]
		(Comp: 1, Cost: 1)       eval_start_5(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb1_in(Ar_2, 1, Ar_2))
		(Comp: 1, Cost: 1)       eval_start_4(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_5(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)       eval_start_3(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_4(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)       eval_start_2(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_3(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)       eval_start_1(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_2(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)       eval_start_0(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_1(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)       eval_start_bb0_in(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_0(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 1)       eval_start_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_bb0_in(Ar_0, Ar_1, Ar_2))
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval_start_start(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

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

Complexity upper bound 2*Ar_2 + 14

Time: 0.058 sec (SMT: 0.044 sec)
