NO

Initial ITS

Start location: l3
Program variables: __const_1000^0 __const_110^0 __const_3000^0 __const_4000^0 x^0 y^0
   0: l0 -> l1 : __const_1000^0'=__const_1000^post1, __const_110^0'=__const_110^post1, __const_3000^0'=__const_3000^post1, __const_4000^0'=__const_4000^post1, x^0'=x^post1, y^0'=y^post1, (-y^post1+y^0 == 0 /\ __const_3000^0-__const_3000^post1 == 0 /\ -__const_110^post1+__const_110^0 == 0 /\ 1+y^0-__const_4000^0 <= 0 /\ -__const_4000^post1+__const_4000^0 == 0 /\ 1-x^post1+__const_110^0 <= 0 /\ __const_1000^0-__const_1000^post1 == 0 /\ x^post1-__const_1000^0-x^0 == 0), cost: 1
   1: l1 -> l0 : __const_1000^0'=__const_1000^post2, __const_110^0'=__const_110^post2, __const_3000^0'=__const_3000^post2, __const_4000^0'=__const_4000^post2, x^0'=x^post2, y^0'=y^post2, (__const_1000^0-__const_1000^post2 == 0 /\ __const_110^0-__const_110^post2 == 0 /\ -x^post2+x^0 == 0 /\ __const_3000^0-__const_3000^post2 == 0 /\ -__const_4000^post2+__const_4000^0 == 0 /\ -y^post2+y^0 == 0), cost: 1
   2: l2 -> l0 : __const_1000^0'=__const_1000^post3, __const_110^0'=__const_110^post3, __const_3000^0'=__const_3000^post3, __const_4000^0'=__const_4000^post3, x^0'=x^post3, y^0'=y^post3, (__const_110^0-__const_110^post3 == 0 /\ -__const_1000^post3+__const_1000^0 == 0 /\ -__const_3000^0+y^post3 == 0 /\ -__const_4000^post3+__const_4000^0 == 0 /\ -x^post3+x^0 == 0 /\ -__const_3000^post3+__const_3000^0 == 0), cost: 1
   3: l3 -> l2 : __const_1000^0'=__const_1000^post4, __const_110^0'=__const_110^post4, __const_3000^0'=__const_3000^post4, __const_4000^0'=__const_4000^post4, x^0'=x^post4, y^0'=y^post4, (-x^post4+x^0 == 0 /\ -__const_1000^post4+__const_1000^0 == 0 /\ __const_3000^0-__const_3000^post4 == 0 /\ y^0-y^post4 == 0 /\ -__const_4000^post4+__const_4000^0 == 0 /\ __const_110^0-__const_110^post4 == 0), cost: 1

Chained Linear Paths

Start location: l3
Program variables: __const_1000^0 __const_110^0 __const_3000^0 __const_4000^0 x^0 y^0
   5: l0 -> l0 : __const_1000^0'=__const_1000^post2, __const_110^0'=__const_110^post2, __const_3000^0'=__const_3000^post2, __const_4000^0'=__const_4000^post2, x^0'=x^post2, y^0'=y^post2, (-__const_4000^post2+__const_4000^post1 == 0 /\ -y^post1+y^0 == 0 /\ -__const_1000^post2+__const_1000^post1 == 0 /\ __const_3000^0-__const_3000^post1 == 0 /\ -__const_110^post1+__const_110^0 == 0 /\ 1+y^0-__const_4000^0 <= 0 /\ -__const_4000^post1+__const_4000^0 == 0 /\ -y^post2+y^post1 == 0 /\ 1-x^post1+__const_110^0 <= 0 /\ x^post1-x^post2 == 0 /\ __const_1000^0-__const_1000^post1 == 0 /\ x^post1-__const_1000^0-x^0 == 0 /\ __const_110^post1-__const_110^post2 == 0 /\ -__const_3000^post2+__const_3000^post1 == 0), cost: 1
   4: l3 -> l0 : __const_1000^0'=__const_1000^post3, __const_110^0'=__const_110^post3, __const_3000^0'=__const_3000^post3, __const_4000^0'=__const_4000^post3, x^0'=x^post3, y^0'=y^post3, (-x^post4+x^0 == 0 /\ __const_4000^post4-__const_4000^post3 == 0 /\ -__const_1000^post4+__const_1000^0 == 0 /\ -__const_3000^post3+__const_3000^post4 == 0 /\ __const_3000^0-__const_3000^post4 == 0 /\ y^0-y^post4 == 0 /\ __const_1000^post4-__const_1000^post3 == 0 /\ -__const_4000^post4+__const_4000^0 == 0 /\ __const_110^0-__const_110^post4 == 0 /\ -__const_3000^post4+y^post3 == 0 /\ x^post4-x^post3 == 0 /\ __const_110^post4-__const_110^post3 == 0), cost: 1

	Eliminating location l2 by chaining:

	Applied chaining

	First rule:
	l3 -> l2 : __const_1000^0'=__const_1000^post4, __const_110^0'=__const_110^post4, __const_3000^0'=__const_3000^post4, __const_4000^0'=__const_4000^post4, x^0'=x^post4, y^0'=y^post4, (-x^post4+x^0 == 0 /\ -__const_1000^post4+__const_1000^0 == 0 /\ __const_3000^0-__const_3000^post4 == 0 /\ y^0-y^post4 == 0 /\ -__const_4000^post4+__const_4000^0 == 0 /\ __const_110^0-__const_110^post4 == 0), cost: 1
	Second rule:
	l2 -> l0 : __const_1000^0'=__const_1000^post3, __const_110^0'=__const_110^post3, __const_3000^0'=__const_3000^post3, __const_4000^0'=__const_4000^post3, x^0'=x^post3, y^0'=y^post3, (__const_110^0-__const_110^post3 == 0 /\ -__const_1000^post3+__const_1000^0 == 0 /\ -__const_3000^0+y^post3 == 0 /\ -__const_4000^post3+__const_4000^0 == 0 /\ -x^post3+x^0 == 0 /\ -__const_3000^post3+__const_3000^0 == 0), cost: 1
	New rule:
	l3 -> l0 : __const_1000^0'=__const_1000^post3, __const_110^0'=__const_110^post3, __const_3000^0'=__const_3000^post3, __const_4000^0'=__const_4000^post3, x^0'=x^post3, y^0'=y^post3, (-x^post4+x^0 == 0 /\ __const_4000^post4-__const_4000^post3 == 0 /\ -__const_1000^post4+__const_1000^0 == 0 /\ -__const_3000^post3+__const_3000^post4 == 0 /\ __const_3000^0-__const_3000^post4 == 0 /\ y^0-y^post4 == 0 /\ __const_1000^post4-__const_1000^post3 == 0 /\ -__const_4000^post4+__const_4000^0 == 0 /\ __const_110^0-__const_110^post4 == 0 /\ -__const_3000^post4+y^post3 == 0 /\ x^post4-x^post3 == 0 /\ __const_110^post4-__const_110^post3 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 2 3
	
	Eliminating location l1 by chaining:

	Applied chaining

	First rule:
	l0 -> l1 : __const_1000^0'=__const_1000^post1, __const_110^0'=__const_110^post1, __const_3000^0'=__const_3000^post1, __const_4000^0'=__const_4000^post1, x^0'=x^post1, y^0'=y^post1, (-y^post1+y^0 == 0 /\ __const_3000^0-__const_3000^post1 == 0 /\ -__const_110^post1+__const_110^0 == 0 /\ 1+y^0-__const_4000^0 <= 0 /\ -__const_4000^post1+__const_4000^0 == 0 /\ 1-x^post1+__const_110^0 <= 0 /\ __const_1000^0-__const_1000^post1 == 0 /\ x^post1-__const_1000^0-x^0 == 0), cost: 1
	Second rule:
	l1 -> l0 : __const_1000^0'=__const_1000^post2, __const_110^0'=__const_110^post2, __const_3000^0'=__const_3000^post2, __const_4000^0'=__const_4000^post2, x^0'=x^post2, y^0'=y^post2, (__const_1000^0-__const_1000^post2 == 0 /\ __const_110^0-__const_110^post2 == 0 /\ -x^post2+x^0 == 0 /\ __const_3000^0-__const_3000^post2 == 0 /\ -__const_4000^post2+__const_4000^0 == 0 /\ -y^post2+y^0 == 0), cost: 1
	New rule:
	l0 -> l0 : __const_1000^0'=__const_1000^post2, __const_110^0'=__const_110^post2, __const_3000^0'=__const_3000^post2, __const_4000^0'=__const_4000^post2, x^0'=x^post2, y^0'=y^post2, (-__const_4000^post2+__const_4000^post1 == 0 /\ -y^post1+y^0 == 0 /\ -__const_1000^post2+__const_1000^post1 == 0 /\ __const_3000^0-__const_3000^post1 == 0 /\ -__const_110^post1+__const_110^0 == 0 /\ 1+y^0-__const_4000^0 <= 0 /\ -__const_4000^post1+__const_4000^0 == 0 /\ -y^post2+y^post1 == 0 /\ 1-x^post1+__const_110^0 <= 0 /\ x^post1-x^post2 == 0 /\ __const_1000^0-__const_1000^post1 == 0 /\ x^post1-__const_1000^0-x^0 == 0 /\ __const_110^post1-__const_110^post2 == 0 /\ -__const_3000^post2+__const_3000^post1 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 0 1

Simplified Transitions

Start location: l3
Program variables: __const_1000^0 __const_110^0 __const_3000^0 __const_4000^0 x^0 y^0
   7: l0 -> l0 : x^0'=__const_1000^0+x^0, (1+__const_110^0-__const_1000^0-x^0 <= 0 /\ 1+y^0-__const_4000^0 <= 0), cost: 1
   6: l3 -> l0 : y^0'=__const_3000^0, T, cost: 1

	Propagated Equalities

	Original rule:
	l3 -> l0 : __const_1000^0'=__const_1000^post3, __const_110^0'=__const_110^post3, __const_3000^0'=__const_3000^post3, __const_4000^0'=__const_4000^post3, x^0'=x^post3, y^0'=y^post3, (-x^post4+x^0 == 0 /\ __const_4000^post4-__const_4000^post3 == 0 /\ -__const_1000^post4+__const_1000^0 == 0 /\ -__const_3000^post3+__const_3000^post4 == 0 /\ __const_3000^0-__const_3000^post4 == 0 /\ y^0-y^post4 == 0 /\ __const_1000^post4-__const_1000^post3 == 0 /\ -__const_4000^post4+__const_4000^0 == 0 /\ __const_110^0-__const_110^post4 == 0 /\ -__const_3000^post4+y^post3 == 0 /\ x^post4-x^post3 == 0 /\ __const_110^post4-__const_110^post3 == 0), cost: 1
	New rule:
	l3 -> l0 : __const_1000^0'=__const_1000^post4, __const_110^0'=__const_110^post4, __const_3000^0'=__const_3000^post4, __const_4000^0'=__const_4000^post4, x^0'=x^post4, y^0'=__const_3000^post4, (0 == 0 /\ -x^post4+x^0 == 0 /\ -__const_1000^post4+__const_1000^0 == 0 /\ __const_3000^0-__const_3000^post4 == 0 /\ y^0-y^post4 == 0 /\ -__const_4000^post4+__const_4000^0 == 0 /\ __const_110^0-__const_110^post4 == 0), cost: 1
	
		propagated equality __const_4000^post3 = __const_4000^post4
		
		propagated equality __const_3000^post3 = __const_3000^post4
		
		propagated equality __const_1000^post3 = __const_1000^post4
		
		propagated equality y^post3 = __const_3000^post4
		
		propagated equality x^post3 = x^post4
		
		propagated equality __const_110^post3 = __const_110^post4
		
	Propagated Equalities

	Original rule:
	l3 -> l0 : __const_1000^0'=__const_1000^post4, __const_110^0'=__const_110^post4, __const_3000^0'=__const_3000^post4, __const_4000^0'=__const_4000^post4, x^0'=x^post4, y^0'=__const_3000^post4, (0 == 0 /\ -x^post4+x^0 == 0 /\ -__const_1000^post4+__const_1000^0 == 0 /\ __const_3000^0-__const_3000^post4 == 0 /\ y^0-y^post4 == 0 /\ -__const_4000^post4+__const_4000^0 == 0 /\ __const_110^0-__const_110^post4 == 0), cost: 1
	New rule:
	l3 -> l0 : __const_1000^0'=__const_1000^0, __const_110^0'=__const_110^0, __const_3000^0'=__const_3000^0, __const_4000^0'=__const_4000^0, x^0'=x^0, y^0'=__const_3000^0, 0 == 0, cost: 1
	
		propagated equality x^post4 = x^0
		
		propagated equality __const_1000^post4 = __const_1000^0
		
		propagated equality __const_3000^post4 = __const_3000^0
		
		propagated equality y^post4 = y^0
		
		propagated equality __const_4000^post4 = __const_4000^0
		
		propagated equality __const_110^post4 = __const_110^0
		
	Simplified Guard

	Original rule:
	l3 -> l0 : __const_1000^0'=__const_1000^0, __const_110^0'=__const_110^0, __const_3000^0'=__const_3000^0, __const_4000^0'=__const_4000^0, x^0'=x^0, y^0'=__const_3000^0, 0 == 0, cost: 1
	New rule:
	l3 -> l0 : __const_1000^0'=__const_1000^0, __const_110^0'=__const_110^0, __const_3000^0'=__const_3000^0, __const_4000^0'=__const_4000^0, x^0'=x^0, y^0'=__const_3000^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l3 -> l0 : __const_1000^0'=__const_1000^0, __const_110^0'=__const_110^0, __const_3000^0'=__const_3000^0, __const_4000^0'=__const_4000^0, x^0'=x^0, y^0'=__const_3000^0, T, cost: 1
	New rule:
	l3 -> l0 : y^0'=__const_3000^0, T, cost: 1
	
	Propagated Equalities

	Original rule:
	l0 -> l0 : __const_1000^0'=__const_1000^post2, __const_110^0'=__const_110^post2, __const_3000^0'=__const_3000^post2, __const_4000^0'=__const_4000^post2, x^0'=x^post2, y^0'=y^post2, (-__const_4000^post2+__const_4000^post1 == 0 /\ -y^post1+y^0 == 0 /\ -__const_1000^post2+__const_1000^post1 == 0 /\ __const_3000^0-__const_3000^post1 == 0 /\ -__const_110^post1+__const_110^0 == 0 /\ 1+y^0-__const_4000^0 <= 0 /\ -__const_4000^post1+__const_4000^0 == 0 /\ -y^post2+y^post1 == 0 /\ 1-x^post1+__const_110^0 <= 0 /\ x^post1-x^post2 == 0 /\ __const_1000^0-__const_1000^post1 == 0 /\ x^post1-__const_1000^0-x^0 == 0 /\ __const_110^post1-__const_110^post2 == 0 /\ -__const_3000^post2+__const_3000^post1 == 0), cost: 1
	New rule:
	l0 -> l0 : __const_1000^0'=__const_1000^post1, __const_110^0'=__const_110^post1, __const_3000^0'=__const_3000^post1, __const_4000^0'=__const_4000^post1, x^0'=x^post1, y^0'=y^post1, (0 == 0 /\ -y^post1+y^0 == 0 /\ __const_3000^0-__const_3000^post1 == 0 /\ -__const_110^post1+__const_110^0 == 0 /\ 1+y^0-__const_4000^0 <= 0 /\ -__const_4000^post1+__const_4000^0 == 0 /\ 1-x^post1+__const_110^0 <= 0 /\ __const_1000^0-__const_1000^post1 == 0 /\ x^post1-__const_1000^0-x^0 == 0), cost: 1
	
		propagated equality __const_4000^post2 = __const_4000^post1
		
		propagated equality __const_1000^post2 = __const_1000^post1
		
		propagated equality y^post2 = y^post1
		
		propagated equality x^post2 = x^post1
		
		propagated equality __const_110^post2 = __const_110^post1
		
		propagated equality __const_3000^post2 = __const_3000^post1
		
	Propagated Equalities

	Original rule:
	l0 -> l0 : __const_1000^0'=__const_1000^post1, __const_110^0'=__const_110^post1, __const_3000^0'=__const_3000^post1, __const_4000^0'=__const_4000^post1, x^0'=x^post1, y^0'=y^post1, (0 == 0 /\ -y^post1+y^0 == 0 /\ __const_3000^0-__const_3000^post1 == 0 /\ -__const_110^post1+__const_110^0 == 0 /\ 1+y^0-__const_4000^0 <= 0 /\ -__const_4000^post1+__const_4000^0 == 0 /\ 1-x^post1+__const_110^0 <= 0 /\ __const_1000^0-__const_1000^post1 == 0 /\ x^post1-__const_1000^0-x^0 == 0), cost: 1
	New rule:
	l0 -> l0 : __const_1000^0'=__const_1000^0, __const_110^0'=__const_110^0, __const_3000^0'=__const_3000^0, __const_4000^0'=__const_4000^0, x^0'=__const_1000^0+x^0, y^0'=y^0, (0 == 0 /\ 1+__const_110^0-__const_1000^0-x^0 <= 0 /\ 1+y^0-__const_4000^0 <= 0), cost: 1
	
		propagated equality y^post1 = y^0
		
		propagated equality __const_3000^post1 = __const_3000^0
		
		propagated equality __const_110^post1 = __const_110^0
		
		propagated equality __const_4000^post1 = __const_4000^0
		
		propagated equality __const_1000^post1 = __const_1000^0
		
		propagated equality x^post1 = __const_1000^0+x^0
		
	Simplified Guard

	Original rule:
	l0 -> l0 : __const_1000^0'=__const_1000^0, __const_110^0'=__const_110^0, __const_3000^0'=__const_3000^0, __const_4000^0'=__const_4000^0, x^0'=__const_1000^0+x^0, y^0'=y^0, (0 == 0 /\ 1+__const_110^0-__const_1000^0-x^0 <= 0 /\ 1+y^0-__const_4000^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : __const_1000^0'=__const_1000^0, __const_110^0'=__const_110^0, __const_3000^0'=__const_3000^0, __const_4000^0'=__const_4000^0, x^0'=__const_1000^0+x^0, y^0'=y^0, (1+__const_110^0-__const_1000^0-x^0 <= 0 /\ 1+y^0-__const_4000^0 <= 0), cost: 1
	
	Removed Trivial Updates

	Original rule:
	l0 -> l0 : __const_1000^0'=__const_1000^0, __const_110^0'=__const_110^0, __const_3000^0'=__const_3000^0, __const_4000^0'=__const_4000^0, x^0'=__const_1000^0+x^0, y^0'=y^0, (1+__const_110^0-__const_1000^0-x^0 <= 0 /\ 1+y^0-__const_4000^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=__const_1000^0+x^0, (1+__const_110^0-__const_1000^0-x^0 <= 0 /\ 1+y^0-__const_4000^0 <= 0), cost: 1

Step with 6

	Trace

	6[T]
	
	Blocked

	[{}, {}]

Step with 7

	Trace

	6[T], 7[(1+__const_110^0-__const_1000^0-x^0 <= 0 /\ 1+y^0-__const_4000^0 <= 0)]
	
	Blocked

	[{}, {}, {}]

Nonterm

Start location: l3
Program variables: __const_1000^0 __const_110^0 __const_3000^0 __const_4000^0 x^0 y^0
   7: l0 -> l0 : x^0'=__const_1000^0+x^0, (1+__const_110^0-__const_1000^0-x^0 <= 0 /\ 1+y^0-__const_4000^0 <= 0), cost: 1
   8: l0 -> LoAT_sink : (-__const_1000^0 <= 0 /\ -1-__const_110^0+__const_1000^0+x^0 >= 0 /\ -1-y^0+__const_4000^0 >= 0), cost: NONTERM
   9: l0 -> l0 : x^0'=n*__const_1000^0+x^0, (-1+n >= 0 /\ -1-__const_110^0+__const_1000^0+x^0 >= 0 /\ -1-y^0+__const_4000^0 >= 0 /\ -1-__const_110^0+__const_1000^0+(-1+n)*__const_1000^0+x^0 >= 0), cost: 1
   6: l3 -> l0 : y^0'=__const_3000^0, T, cost: 1

	Certificate of Non-Termination

	Original rule:
	l0 -> l0 : x^0'=__const_1000^0+x^0, (1+__const_110^0-__const_1000^0-x^0 <= 0 /\ 1+y^0-__const_4000^0 <= 0), cost: 1
	New rule:
	l0 -> LoAT_sink : (-__const_1000^0 <= 0 /\ -1-__const_110^0+__const_1000^0+x^0 >= 0 /\ -1-y^0+__const_4000^0 >= 0), cost: NONTERM

		-1-__const_110^0+__const_1000^0+x^0 >= 0 [0]: eventual decrease yields (-1-__const_110^0+__const_1000^0+x^0 >= 0 /\ -1-__const_110^0+__const_1000^0+(-1+n)*__const_1000^0+x^0 >= 0)
		
		-1-__const_110^0+__const_1000^0+x^0 >= 0 [1]: eventual increase yields (-__const_1000^0 <= 0 /\ -1-__const_110^0+__const_1000^0+x^0 >= 0)
		
		-1-y^0+__const_4000^0 >= 0 [0]: monotonic increase yields -1-y^0+__const_4000^0 >= 0
		
		Replacement map: {-1-__const_110^0+__const_1000^0+x^0 >= 0 -> (-__const_1000^0 <= 0 /\ -1-__const_110^0+__const_1000^0+x^0 >= 0), -1-y^0+__const_4000^0 >= 0 -> -1-y^0+__const_4000^0 >= 0}

	Loop Acceleration

	Original rule:
	l0 -> l0 : x^0'=__const_1000^0+x^0, (1+__const_110^0-__const_1000^0-x^0 <= 0 /\ 1+y^0-__const_4000^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=n*__const_1000^0+x^0, (-1+n >= 0 /\ -1-__const_110^0+__const_1000^0+x^0 >= 0 /\ -1-y^0+__const_4000^0 >= 0 /\ -1-__const_110^0+__const_1000^0+(-1+n)*__const_1000^0+x^0 >= 0), cost: 1

		-1-__const_110^0+__const_1000^0+x^0 >= 0 [0]: eventual decrease yields (-1-__const_110^0+__const_1000^0+x^0 >= 0 /\ -1-__const_110^0+__const_1000^0+(-1+n)*__const_1000^0+x^0 >= 0)
		
		-1-__const_110^0+__const_1000^0+x^0 >= 0 [1]: eventual increase yields (-__const_1000^0 <= 0 /\ -1-__const_110^0+__const_1000^0+x^0 >= 0)
		
		-1-y^0+__const_4000^0 >= 0 [0]: monotonic increase yields -1-y^0+__const_4000^0 >= 0
		
		Replacement map: {-1-__const_110^0+__const_1000^0+x^0 >= 0 -> (-1-__const_110^0+__const_1000^0+x^0 >= 0 /\ -1-__const_110^0+__const_1000^0+(-1+n)*__const_1000^0+x^0 >= 0), -1-y^0+__const_4000^0 >= 0 -> -1-y^0+__const_4000^0 >= 0}

Step with 8

	Trace

	6[T], 8[(-__const_1000^0 <= 0 /\ -1-__const_110^0+__const_1000^0+x^0 >= 0 /\ -1-y^0+__const_4000^0 >= 0)]
	
	Blocked

	[{}, {}, {8[T]}]

Refute

	Counterexample

	[ __const_1000^0=0 __const_110^0=-1 __const_3000^0=0 __const_4000^0=1 x^0=0 y^0=0 ] 6 [ __const_1000^0=0 __const_110^0=-1 __const_3000^0=0 __const_4000^0=1 x^0=0 y^0=y^0 ] 8
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b