WORST_CASE(?, O(n^1))

Initial complexity problem:
1:	T:
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, 0, Ar_2, Ar_3, 1, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, 0, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_4 >= 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_4 >= 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ 1 >= Ar_4 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ 1 >= Ar_4 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_4, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_4 + 1 >= Ar_0 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= 2 /\ Ar_6 = 1 /\ Ar_4 + 1 = Ar_0 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Testing for reachability in the complexity graph removes the following transition from problem 1:
	cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_4, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_4 + 1 >= Ar_0 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
We thus obtain the following problem:
2:	T:
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_4 >= 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_4 >= 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= 2 /\ Ar_6 = 1 /\ Ar_4 + 1 = Ar_0 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ 1 >= Ar_4 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ 1 >= Ar_4 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, 0, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, 0, Ar_2, Ar_3, 1, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: ?, Cost: 1)    start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Repeatedly propagating knowledge in problem 2 produces the following problem:
3:	T:
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_4 >= 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_4 >= 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= 2 /\ Ar_6 = 1 /\ Ar_4 + 1 = Ar_0 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ 1 >= Ar_4 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ 1 >= Ar_4 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, 0, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, 0, Ar_2, Ar_3, 1, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(cut) = 1
	Pol(stop) = 0
	Pol(start) = 1
	Pol(start0) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transitions
	cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
	cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= 2 /\ Ar_6 = 1 /\ Ar_4 + 1 = Ar_0 /\ Ar_3 = Ar_0 ]
strictly and produces the following problem:
4:	T:
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_4 >= 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_4 >= 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= 2 /\ Ar_6 = 1 /\ Ar_4 + 1 = Ar_0 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ 1 >= Ar_4 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ 1 >= Ar_4 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, 0, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, 0, Ar_2, Ar_3, 1, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(cut) = 1
	Pol(stop) = 0
	Pol(start) = 1
	Pol(start0) = 1
	Pol(koat_start) = 1
orients all transitions weakly and the transitions
	cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ 1 >= Ar_4 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
	cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_4 >= 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
strictly and produces the following problem:
5:	T:
		(Comp: 1, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_4 >= 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_4 >= 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= 2 /\ Ar_6 = 1 /\ Ar_4 + 1 = Ar_0 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ 1 >= Ar_4 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: ?, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ 1 >= Ar_4 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, 0, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, 0, Ar_2, Ar_3, 1, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)    start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))
		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

A polynomial rank function with
	Pol(cut) = V_7
	Pol(stop) = V_7
	Pol(start) = V_4
	Pol(start0) = V_1
	Pol(koat_start) = V_1
orients all transitions weakly and the transitions
	cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
	cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ 1 >= Ar_4 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
	cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_4 >= 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
strictly and produces the following problem:
6:	T:
		(Comp: 1, Cost: 1)       cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_4 >= 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: Ar_0, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 - 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_4 >= 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)       cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= 2 /\ Ar_6 = 1 /\ Ar_4 + 1 = Ar_0 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)       cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_0 >= Ar_4 + 2 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: Ar_0, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_4, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ Ar_0 >= Ar_4 + 2 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)       cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ 1 >= Ar_4 /\ Ar_4 >= 0 /\ Ar_0 >= 2 /\ Ar_0 >= Ar_4 + 1 /\ Ar_6 = 1 /\ Ar_3 = Ar_0 ]
		(Comp: Ar_0, Cost: 1)    cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 - 1, Ar_7)) [ Ar_6 >= 2 /\ 1 >= Ar_4 /\ Ar_6 >= 1 /\ Ar_4 >= 0 /\ Ar_0 >= Ar_6 + 1 /\ Ar_0 >= Ar_6 + Ar_4 /\ Ar_3 = Ar_0 ]
		(Comp: 1, Cost: 1)       start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, 0, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)       start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, 0, Ar_2, Ar_3, 1, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)       start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_3 = 1 /\ Ar_1 = Ar_2 /\ Ar_0 = 1 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)       start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3 - 1, Ar_7)) [ Ar_0 >= 2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)       start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_3, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ]
		(Comp: 1, Cost: 1)       start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))
		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]
	start location:	koat_start
	leaf cost:	0

Complexity upper bound 3*Ar_0 + 10

Time: 4.716 sec (SMT: 4.522 sec)