
Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 + 2 >= Ar_2 /\ Ar_2 >= 0 /\ Ar_2 + 2 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 3 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 3 /\ Ar_2 >= 0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 3 /\ Ar_0 >= 0 /\ Ar_3 + 2 = Ar_2 /\ Ar_1 = Ar_2 ]
		(Comp: ?, Cost: 1)    lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 + 3 /\ Ar_3 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 + 2 /\ Ar_1 = Ar_2 ]
		(Comp: ?, Cost: 1)    lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 /\ Ar_3 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 + 2 /\ Ar_1 = Ar_2 ]
		(Comp: ?, Cost: 1)    lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 3 /\ Ar_2 >= 0 /\ Ar_1 + 2 = Ar_0 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_1 >= Ar_0 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_1 >= Ar_2 + 1 /\ Ar_2 >= 0 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_1 >= Ar_2 + 1 /\ Ar_2 >= 0 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transitions from problem 1:
	lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_3 >= Ar_2 + 3 /\ Ar_3 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 + 2 /\ Ar_1 = Ar_2 ]
	lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_1 >= Ar_0 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_1 >= Ar_2 + 1 /\ Ar_2 >= 0 /\ Ar_3 = Ar_0 ]
We thus obtain the following problem:
2:	T:
		(Comp: ?, Cost: 1)    lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_1 >= Ar_2 + 1 /\ Ar_2 >= 0 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 3 /\ Ar_2 >= 0 /\ Ar_1 + 2 = Ar_0 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 + 3 /\ Ar_3 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 + 2 /\ Ar_1 = Ar_2 ]
		(Comp: ?, Cost: 1)    lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 3 /\ Ar_0 >= 0 /\ Ar_3 + 2 = Ar_2 /\ Ar_1 = Ar_2 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 3 /\ Ar_2 >= 0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 3 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 + 2 >= Ar_2 /\ Ar_2 >= 0 /\ Ar_2 + 2 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_1 >= Ar_2 + 1 /\ Ar_2 >= 0 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 3 /\ Ar_2 >= 0 /\ Ar_1 + 2 = Ar_0 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 + 3 /\ Ar_3 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 + 2 /\ Ar_1 = Ar_2 ]
		(Comp: ?, Cost: 1)    lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 3 /\ Ar_0 >= 0 /\ Ar_3 + 2 = Ar_2 /\ Ar_1 = Ar_2 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 3 /\ Ar_2 >= 0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 3 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 + 2 >= Ar_2 /\ Ar_2 >= 0 /\ Ar_2 + 2 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(lbl91) = 1
	Pol(stop) = 0
	Pol(lbl81) = 1
	Pol(start) = 1
	Pol(start0) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transitions
	lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 3 /\ Ar_2 >= 0 /\ Ar_1 + 2 = Ar_0 /\ Ar_3 = Ar_0 ]
	lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 3 /\ Ar_0 >= 0 /\ Ar_3 + 2 = Ar_2 /\ Ar_1 = Ar_2 ]
strictly and produces the following problem:
4:	T:
		(Comp: ?, Cost: 1)    lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_1 >= Ar_2 + 1 /\ Ar_2 >= 0 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 3 /\ Ar_2 >= 0 /\ Ar_1 + 2 = Ar_0 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 + 3 /\ Ar_3 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 + 2 /\ Ar_1 = Ar_2 ]
		(Comp: 1, Cost: 1)    lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 3 /\ Ar_0 >= 0 /\ Ar_3 + 2 = Ar_2 /\ Ar_1 = Ar_2 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 3 /\ Ar_2 >= 0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 3 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 + 2 >= Ar_2 /\ Ar_2 >= 0 /\ Ar_2 + 2 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(lbl91) = 2*V_1 - V_2 + 2*V_3 - V_4
	Pol(stop) = 2*V_1 - V_2 + 2*V_3 - V_4
	Pol(lbl81) = 2*V_1 + V_2 - V_4
	Pol(start) = -V_2 + 2*V_3 + V_4
	Pol(start0) = V_1 + V_3
	Pol(koat_start) = V_1 + V_3
orients all transitions weakly and the transitions
	lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_1 >= Ar_2 + 1 /\ Ar_2 >= 0 /\ Ar_3 = Ar_0 ]
	lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 + 3 /\ Ar_3 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 + 2 /\ Ar_1 = Ar_2 ]
strictly and produces the following problem:
5:	T:
		(Comp: Ar_0 + Ar_2, Cost: 1)    lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= Ar_1 + 3 /\ Ar_0 >= Ar_1 + 2 /\ Ar_1 >= Ar_2 + 1 /\ Ar_2 >= 0 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)              lbl91(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 3 /\ Ar_2 >= 0 /\ Ar_1 + 2 = Ar_0 /\ Ar_3 = Ar_0 ]
		(Comp: Ar_0 + Ar_2, Cost: 1)    lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_2 >= Ar_3 + 3 /\ Ar_3 >= Ar_0 + 1 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_3 + 2 /\ Ar_1 = Ar_2 ]
		(Comp: 1, Cost: 1)              lbl81(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= Ar_0 + 3 /\ Ar_0 >= 0 /\ Ar_3 + 2 = Ar_2 /\ Ar_1 = Ar_2 ]
		(Comp: 1, Cost: 1)              start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl91(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ Ar_0 >= Ar_2 + 3 /\ Ar_2 >= 0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)              start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(lbl81(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ Ar_0 >= 0 /\ Ar_2 >= Ar_0 + 3 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)              start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 0 /\ Ar_0 + 2 >= Ar_2 /\ Ar_2 >= 0 /\ Ar_2 + 2 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)              start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_2 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)              start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)              start0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0))
		(Comp: 1, Cost: 0)              koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 2*Ar_0 + 2*Ar_2 + 8

Time: 0.082 sec (SMT: 0.070 sec)
