NO

Initial ITS

Start location: l3
Program variables: t^0 x^0 y^0
   0: l0 -> l1 : t^0'=t^post1, x^0'=x^post1, y^0'=y^post1, (x^post1-y^0-x^0 == 0 /\ -x^0 <= 0 /\ -t^post1+t^0 == 0 /\ y^0-y^post1 == 0 /\ -y^0+t^0 <= 0), cost: 1
   1: l1 -> l0 : t^0'=t^post2, x^0'=x^post2, y^0'=y^post2, (-x^post2+x^0 == 0 /\ y^0-y^post2 == 0 /\ -t^post2+t^0 == 0), cost: 1
   2: l2 -> l0 : t^0'=t^post3, x^0'=x^post3, y^0'=y^post3, (x^0-x^post3 == 0 /\ 1-t^9+t^post3 == 0 /\ 1-t^6+t^7 == 0 /\ 1+t^5-t^4 == 0 /\ -y^0+t^post3 <= 0 /\ 1-t^7+t^8 == 0 /\ 1+t^1 == 0 /\ -y^post3+y^0 == 0 /\ 1+t^2-t^1 == 0 /\ 1-t^2+t^3 == 0 /\ 1+t^9-t^8 == 0 /\ -1-x^0 <= 0 /\ 1-t^5+t^6 == 0 /\ 1-t^3+t^4 == 0), cost: 1
   3: l3 -> l2 : t^0'=t^post4, x^0'=x^post4, y^0'=y^post4, (-y^post4+y^0 == 0 /\ x^0-x^post4 == 0 /\ -t^post4+t^0 == 0), cost: 1

Chained Linear Paths

Start location: l3
Program variables: t^0 x^0 y^0
   5: l0 -> l0 : t^0'=t^post2, x^0'=x^post2, y^0'=y^post2, (-x^post2+x^post1 == 0 /\ x^post1-y^0-x^0 == 0 /\ -y^post2+y^post1 == 0 /\ -x^0 <= 0 /\ -t^post2+t^post1 == 0 /\ -t^post1+t^0 == 0 /\ y^0-y^post1 == 0 /\ -y^0+t^0 <= 0), cost: 1
   4: l3 -> l0 : t^0'=t^post3, x^0'=x^post3, y^0'=y^post3, (1-t^9+t^post3 == 0 /\ 1-t^6+t^7 == 0 /\ 1+t^5-t^4 == 0 /\ -y^post4+y^0 == 0 /\ 1-t^7+t^8 == 0 /\ 1+t^1 == 0 /\ x^0-x^post4 == 0 /\ -1-x^post4 <= 0 /\ y^post4-y^post3 == 0 /\ 1+t^2-t^1 == 0 /\ 1-t^2+t^3 == 0 /\ 1+t^9-t^8 == 0 /\ -y^post4+t^post3 <= 0 /\ 1-t^5+t^6 == 0 /\ -t^post4+t^0 == 0 /\ x^post4-x^post3 == 0 /\ 1-t^3+t^4 == 0), cost: 1

	Eliminating location l2 by chaining:

	Applied chaining

	First rule:
	l3 -> l2 : t^0'=t^post4, x^0'=x^post4, y^0'=y^post4, (-y^post4+y^0 == 0 /\ x^0-x^post4 == 0 /\ -t^post4+t^0 == 0), cost: 1
	Second rule:
	l2 -> l0 : t^0'=t^post3, x^0'=x^post3, y^0'=y^post3, (x^0-x^post3 == 0 /\ 1-t^9+t^post3 == 0 /\ 1-t^6+t^7 == 0 /\ 1+t^5-t^4 == 0 /\ -y^0+t^post3 <= 0 /\ 1-t^7+t^8 == 0 /\ 1+t^1 == 0 /\ -y^post3+y^0 == 0 /\ 1+t^2-t^1 == 0 /\ 1-t^2+t^3 == 0 /\ 1+t^9-t^8 == 0 /\ -1-x^0 <= 0 /\ 1-t^5+t^6 == 0 /\ 1-t^3+t^4 == 0), cost: 1
	New rule:
	l3 -> l0 : t^0'=t^post3, x^0'=x^post3, y^0'=y^post3, (1-t^9+t^post3 == 0 /\ 1-t^6+t^7 == 0 /\ 1+t^5-t^4 == 0 /\ -y^post4+y^0 == 0 /\ 1-t^7+t^8 == 0 /\ 1+t^1 == 0 /\ x^0-x^post4 == 0 /\ -1-x^post4 <= 0 /\ y^post4-y^post3 == 0 /\ 1+t^2-t^1 == 0 /\ 1-t^2+t^3 == 0 /\ 1+t^9-t^8 == 0 /\ -y^post4+t^post3 <= 0 /\ 1-t^5+t^6 == 0 /\ -t^post4+t^0 == 0 /\ x^post4-x^post3 == 0 /\ 1-t^3+t^4 == 0), cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	l0 -> l1 : t^0'=t^post1, x^0'=x^post1, y^0'=y^post1, (x^post1-y^0-x^0 == 0 /\ -x^0 <= 0 /\ -t^post1+t^0 == 0 /\ y^0-y^post1 == 0 /\ -y^0+t^0 <= 0), cost: 1
	Second rule:
	l1 -> l0 : t^0'=t^post2, x^0'=x^post2, y^0'=y^post2, (-x^post2+x^0 == 0 /\ y^0-y^post2 == 0 /\ -t^post2+t^0 == 0), cost: 1
	New rule:
	l0 -> l0 : t^0'=t^post2, x^0'=x^post2, y^0'=y^post2, (-x^post2+x^post1 == 0 /\ x^post1-y^0-x^0 == 0 /\ -y^post2+y^post1 == 0 /\ -x^0 <= 0 /\ -t^post2+t^post1 == 0 /\ -t^post1+t^0 == 0 /\ y^0-y^post1 == 0 /\ -y^0+t^0 <= 0), cost: 1
	
	Applied deletion

	Removed the following rules: 0 1

Simplified Transitions

Start location: l3
Program variables: t^0 x^0 y^0
   7: l0 -> l0 : x^0'=y^0+x^0, (-x^0 <= 0 /\ -y^0+t^0 <= 0), cost: 1
   6: l3 -> l0 : t^0'=-10, (-10-y^0 <= 0 /\ -1-x^0 <= 0), cost: 1

	Propagated Equalities

	Original rule:
	l3 -> l0 : t^0'=t^post3, x^0'=x^post3, y^0'=y^post3, (1-t^9+t^post3 == 0 /\ 1-t^6+t^7 == 0 /\ 1+t^5-t^4 == 0 /\ -y^post4+y^0 == 0 /\ 1-t^7+t^8 == 0 /\ 1+t^1 == 0 /\ x^0-x^post4 == 0 /\ -1-x^post4 <= 0 /\ y^post4-y^post3 == 0 /\ 1+t^2-t^1 == 0 /\ 1-t^2+t^3 == 0 /\ 1+t^9-t^8 == 0 /\ -y^post4+t^post3 <= 0 /\ 1-t^5+t^6 == 0 /\ -t^post4+t^0 == 0 /\ x^post4-x^post3 == 0 /\ 1-t^3+t^4 == 0), cost: 1
	New rule:
	l3 -> l0 : t^0'=-1+t^9, x^0'=x^post4, y^0'=y^post4, (0 == 0 /\ 1-t^6+t^7 == 0 /\ 1+t^5-t^4 == 0 /\ -y^post4+y^0 == 0 /\ 1-t^7+t^8 == 0 /\ 1+t^1 == 0 /\ x^0-x^post4 == 0 /\ -1-x^post4 <= 0 /\ 1+t^2-t^1 == 0 /\ 1-t^2+t^3 == 0 /\ 1+t^9-t^8 == 0 /\ 1-t^5+t^6 == 0 /\ -t^post4+t^0 == 0 /\ 1-t^3+t^4 == 0 /\ -1-y^post4+t^9 <= 0), cost: 1
	
		propagated equality t^post3 = -1+t^9
		
		propagated equality y^post3 = y^post4
		
		propagated equality x^post3 = x^post4
		
	Propagated Equalities

	Original rule:
	l3 -> l0 : t^0'=-1+t^9, x^0'=x^post4, y^0'=y^post4, (0 == 0 /\ 1-t^6+t^7 == 0 /\ 1+t^5-t^4 == 0 /\ -y^post4+y^0 == 0 /\ 1-t^7+t^8 == 0 /\ 1+t^1 == 0 /\ x^0-x^post4 == 0 /\ -1-x^post4 <= 0 /\ 1+t^2-t^1 == 0 /\ 1-t^2+t^3 == 0 /\ 1+t^9-t^8 == 0 /\ 1-t^5+t^6 == 0 /\ -t^post4+t^0 == 0 /\ 1-t^3+t^4 == 0 /\ -1-y^post4+t^9 <= 0), cost: 1
	New rule:
	l3 -> l0 : t^0'=-10, x^0'=x^0, y^0'=y^0, (0 == 0 /\ -10-y^0 <= 0 /\ -1-x^0 <= 0), cost: 1
	
		propagated equality t^6 = 1+t^7
		
		propagated equality t^4 = 1+t^5
		
		propagated equality y^post4 = y^0
		
		propagated equality t^7 = 1+t^8
		
		propagated equality t^1 = -1
		
		propagated equality x^post4 = x^0
		
		propagated equality t^2 = -2
		
		propagated equality t^3 = -3
		
		propagated equality t^8 = 1+t^9
		
		propagated equality t^5 = 4+t^9
		
		propagated equality t^post4 = t^0
		
		propagated equality t^9 = -9
		
	Simplified Guard

	Original rule:
	l3 -> l0 : t^0'=-10, x^0'=x^0, y^0'=y^0, (0 == 0 /\ -10-y^0 <= 0 /\ -1-x^0 <= 0), cost: 1
	New rule:
	l3 -> l0 : t^0'=-10, x^0'=x^0, y^0'=y^0, (-10-y^0 <= 0 /\ -1-x^0 <= 0), cost: 1
	
	Removed Trivial Updates

	Original rule:
	l3 -> l0 : t^0'=-10, x^0'=x^0, y^0'=y^0, (-10-y^0 <= 0 /\ -1-x^0 <= 0), cost: 1
	New rule:
	l3 -> l0 : t^0'=-10, (-10-y^0 <= 0 /\ -1-x^0 <= 0), cost: 1
	
	Propagated Equalities

	Original rule:
	l0 -> l0 : t^0'=t^post2, x^0'=x^post2, y^0'=y^post2, (-x^post2+x^post1 == 0 /\ x^post1-y^0-x^0 == 0 /\ -y^post2+y^post1 == 0 /\ -x^0 <= 0 /\ -t^post2+t^post1 == 0 /\ -t^post1+t^0 == 0 /\ y^0-y^post1 == 0 /\ -y^0+t^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : t^0'=t^post1, x^0'=x^post1, y^0'=y^post1, (0 == 0 /\ x^post1-y^0-x^0 == 0 /\ -x^0 <= 0 /\ -t^post1+t^0 == 0 /\ y^0-y^post1 == 0 /\ -y^0+t^0 <= 0), cost: 1
	
		propagated equality x^post2 = x^post1
		
		propagated equality y^post2 = y^post1
		
		propagated equality t^post2 = t^post1
		
	Propagated Equalities

	Original rule:
	l0 -> l0 : t^0'=t^post1, x^0'=x^post1, y^0'=y^post1, (0 == 0 /\ x^post1-y^0-x^0 == 0 /\ -x^0 <= 0 /\ -t^post1+t^0 == 0 /\ y^0-y^post1 == 0 /\ -y^0+t^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : t^0'=t^0, x^0'=y^0+x^0, y^0'=y^0, (0 == 0 /\ -x^0 <= 0 /\ -y^0+t^0 <= 0), cost: 1
	
		propagated equality x^post1 = y^0+x^0
		
		propagated equality t^post1 = t^0
		
		propagated equality y^post1 = y^0
		
	Simplified Guard

	Original rule:
	l0 -> l0 : t^0'=t^0, x^0'=y^0+x^0, y^0'=y^0, (0 == 0 /\ -x^0 <= 0 /\ -y^0+t^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : t^0'=t^0, x^0'=y^0+x^0, y^0'=y^0, (-x^0 <= 0 /\ -y^0+t^0 <= 0), cost: 1
	
	Removed Trivial Updates

	Original rule:
	l0 -> l0 : t^0'=t^0, x^0'=y^0+x^0, y^0'=y^0, (-x^0 <= 0 /\ -y^0+t^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=y^0+x^0, (-x^0 <= 0 /\ -y^0+t^0 <= 0), cost: 1

Step with 6

	Trace

	6[(-10-y^0 <= 0 /\ -1-x^0 <= 0)]
	
	Blocked

	[{}, {}]

Step with 7

	Trace

	6[(-10-y^0 <= 0 /\ -1-x^0 <= 0)], 7[(-x^0 <= 0 /\ -y^0+t^0 <= 0)]
	
	Blocked

	[{}, {}, {}]

Nonterm

Start location: l3
Program variables: t^0 x^0 y^0
   7: l0 -> l0 : x^0'=y^0+x^0, (-x^0 <= 0 /\ -y^0+t^0 <= 0), cost: 1
   8: l0 -> LoAT_sink : (-y^0 <= 0 /\ x^0 >= 0 /\ y^0-t^0 >= 0), cost: NONTERM
   9: l0 -> l0 : x^0'=n*y^0+x^0, (-1+n >= 0 /\ y^0*(-1+n)+x^0 >= 0 /\ x^0 >= 0 /\ y^0-t^0 >= 0), cost: 1
   6: l3 -> l0 : t^0'=-10, (-10-y^0 <= 0 /\ -1-x^0 <= 0), cost: 1

	Certificate of Non-Termination

	Original rule:
	l0 -> l0 : x^0'=y^0+x^0, (-x^0 <= 0 /\ -y^0+t^0 <= 0), cost: 1
	New rule:
	l0 -> LoAT_sink : (-y^0 <= 0 /\ x^0 >= 0 /\ y^0-t^0 >= 0), cost: NONTERM

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

	Loop Acceleration

	Original rule:
	l0 -> l0 : x^0'=y^0+x^0, (-x^0 <= 0 /\ -y^0+t^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=n*y^0+x^0, (-1+n >= 0 /\ y^0*(-1+n)+x^0 >= 0 /\ x^0 >= 0 /\ y^0-t^0 >= 0), cost: 1

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

Step with 8

	Trace

	6[(-10-y^0 <= 0 /\ -1-x^0 <= 0)], 8[(-y^0 <= 0 /\ x^0 >= 0 /\ y^0-t^0 >= 0)]
	
	Blocked

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

Refute

	Counterexample

	[ t^0=-10 x^0=0 y^0=0 ] 6 [ t^0=t^0 x^0=0 y^0=0 ] 8
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b