unknown

Initial ITS

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

Chained Linear Paths

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

	Eliminating location l2 by chaining:

	Applied chaining

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

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

	Applied chaining

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

	Removed the following rules: 0 1

Simplified Transitions

Start location: l3
Program variables: x^0 y^0
   7: l0 -> l0 : x^0'=-y^0+x^0, y^0'=1+y^0, 1-x^0 <= 0, cost: 1
   6: l3 -> l0 : 1-y^0 <= 0, cost: 1

	Propagated Equalities

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

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

	Original rule:
	l3 -> l0 : x^0'=x^0, y^0'=y^0, (0 == 0 /\ 1-y^0 <= 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^0, y^0'=y^0, 1-y^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l3 -> l0 : x^0'=x^0, y^0'=y^0, 1-y^0 <= 0, cost: 1
	New rule:
	l3 -> l0 : 1-y^0 <= 0, cost: 1
	
	Propagated Equalities

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

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

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

Step with 6

	Trace

	6[(1-y^0 <= 0)]
	
	Blocked

	[{}, {}]

Step with 7

	Trace

	6[(1-y^0 <= 0)], 7[(1-x^0 <= 0)]
	
	Blocked

	[{}, {}, {}]

Accelerate

Start location: l3
Program variables: x^0 y^0
   7: l0 -> l0 : x^0'=-y^0+x^0, y^0'=1+y^0, 1-x^0 <= 0, cost: 1
   8: l0 -> l0 : x^0'=-y^0*n+1/2*n-1/2*n^2+x^0, y^0'=y^0+n, (-3/2+1/2*n-1/2*(-1+n)^2+x^0-y^0*(-1+n) >= 0 /\ -1+x^0 >= 0 /\ -1+n >= 0), cost: 1
   6: l3 -> l0 : 1-y^0 <= 0, cost: 1

	Loop Acceleration

	Original rule:
	l0 -> l0 : x^0'=-y^0+x^0, y^0'=1+y^0, (1-x^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=-y^0*n+1/2*n-1/2*n^2+x^0, y^0'=y^0+n, (-3/2+1/2*n-1/2*(-1+n)^2+x^0-y^0*(-1+n) >= 0 /\ -1+x^0 >= 0 /\ -1+n >= 0), cost: 1

		-1+x^0 >= 0 [0]: eventual decrease yields (-3/2+1/2*n-1/2*(-1+n)^2+x^0-y^0*(-1+n) >= 0 /\ -1+x^0 >= 0)
		
		Replacement map: {-1+x^0 >= 0 -> (-3/2+1/2*n-1/2*(-1+n)^2+x^0-y^0*(-1+n) >= 0 /\ -1+x^0 >= 0)}

	Trace

	6[(1-y^0 <= 0)], 8[(-3/2+1/2*n-1/2*(-1+n)^2+x^0-y^0*(-1+n) >= 0 /\ -1+x^0 >= 0 /\ -1+n >= 0)]
	
	Blocked

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

Backtrack

	Trace

	6[(1-y^0 <= 0)]
	
	Blocked

	[{}, {8[T]}]

Step with 7

	Trace

	6[(1-y^0 <= 0)], 7[(1-x^0 <= 0)]
	
	Blocked

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

Covered

	Trace

	6[(1-y^0 <= 0)]
	
	Blocked

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

Backtrack

	Trace

	Blocked

	[{6[T]}]

Accept

unknown

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b