unknown

Initial ITS

Start location: l4
Program variables: x^0 y^0
   0: l0 -> l1 : x^0'=x^post1, y^0'=y^post1, (11-x^0 <= 0 /\ y^0-y^post1 == 0 /\ -x^post1+x^0 == 0), cost: 1
   1: l0 -> l2 : x^0'=x^post2, y^0'=y^post2, (-10+x^0 <= 0 /\ -10+y^post2+x^0 == 0 /\ -1-x^0+x^post2 == 0), cost: 1
   2: l2 -> l0 : x^0'=x^post3, y^0'=y^post3, (-x^post3+x^0 == 0 /\ y^0-y^post3 == 0), cost: 1
   3: l3 -> l2 : x^0'=x^post4, y^0'=y^post4, (-1+x^post4 == 0 /\ y^0-y^post4 == 0), cost: 1
   4: l4 -> l3 : x^0'=x^post5, y^0'=y^post5, (x^0-x^post5 == 0 /\ -y^post5+y^0 == 0), cost: 1

Chained Linear Paths

Start location: l4
Program variables: x^0 y^0
   0: l0 -> l1 : x^0'=x^post1, y^0'=y^post1, (11-x^0 <= 0 /\ y^0-y^post1 == 0 /\ -x^post1+x^0 == 0), cost: 1
   1: l0 -> l2 : x^0'=x^post2, y^0'=y^post2, (-10+x^0 <= 0 /\ -10+y^post2+x^0 == 0 /\ -1-x^0+x^post2 == 0), cost: 1
   2: l2 -> l0 : x^0'=x^post3, y^0'=y^post3, (-x^post3+x^0 == 0 /\ y^0-y^post3 == 0), cost: 1
   5: l4 -> l2 : x^0'=x^post4, y^0'=y^post4, (-1+x^post4 == 0 /\ x^0-x^post5 == 0 /\ y^post5-y^post4 == 0 /\ -y^post5+y^0 == 0), cost: 1

	Eliminating location l3 by chaining:

	Applied chaining

	First rule:
	l4 -> l3 : x^0'=x^post5, y^0'=y^post5, (x^0-x^post5 == 0 /\ -y^post5+y^0 == 0), cost: 1
	Second rule:
	l3 -> l2 : x^0'=x^post4, y^0'=y^post4, (-1+x^post4 == 0 /\ y^0-y^post4 == 0), cost: 1
	New rule:
	l4 -> l2 : x^0'=x^post4, y^0'=y^post4, (-1+x^post4 == 0 /\ x^0-x^post5 == 0 /\ y^post5-y^post4 == 0 /\ -y^post5+y^0 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 3 4

Simplified Transitions

Start location: l4
Program variables: x^0 y^0
   6: l0 -> l1 : 11-x^0 <= 0, cost: 1
   7: l0 -> l2 : x^0'=1+x^0, y^0'=10-x^0, -10+x^0 <= 0, cost: 1
   8: l2 -> l0 : T, cost: 1
   9: l4 -> l2 : x^0'=1, T, cost: 1

	Propagated Equalities

	Original rule:
	l0 -> l1 : x^0'=x^post1, y^0'=y^post1, (11-x^0 <= 0 /\ y^0-y^post1 == 0 /\ -x^post1+x^0 == 0), cost: 1
	New rule:
	l0 -> l1 : x^0'=x^0, y^0'=y^0, (0 == 0 /\ 11-x^0 <= 0), cost: 1
	
		propagated equality y^post1 = y^0
		
		propagated equality x^post1 = x^0
		
	Simplified Guard

	Original rule:
	l0 -> l1 : x^0'=x^0, y^0'=y^0, (0 == 0 /\ 11-x^0 <= 0), cost: 1
	New rule:
	l0 -> l1 : x^0'=x^0, y^0'=y^0, 11-x^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l0 -> l1 : x^0'=x^0, y^0'=y^0, 11-x^0 <= 0, cost: 1
	New rule:
	l0 -> l1 : 11-x^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l0 -> l2 : x^0'=x^post2, y^0'=y^post2, (-10+x^0 <= 0 /\ -10+y^post2+x^0 == 0 /\ -1-x^0+x^post2 == 0), cost: 1
	New rule:
	l0 -> l2 : x^0'=1+x^0, y^0'=10-x^0, (0 == 0 /\ -10+x^0 <= 0), cost: 1
	
		propagated equality y^post2 = 10-x^0
		
		propagated equality x^post2 = 1+x^0
		
	Simplified Guard

	Original rule:
	l0 -> l2 : x^0'=1+x^0, y^0'=10-x^0, (0 == 0 /\ -10+x^0 <= 0), cost: 1
	New rule:
	l0 -> l2 : x^0'=1+x^0, y^0'=10-x^0, -10+x^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l2 -> l0 : x^0'=x^post3, y^0'=y^post3, (-x^post3+x^0 == 0 /\ y^0-y^post3 == 0), cost: 1
	New rule:
	l2 -> l0 : x^0'=x^0, y^0'=y^0, 0 == 0, cost: 1
	
		propagated equality x^post3 = x^0
		
		propagated equality y^post3 = y^0
		
	Simplified Guard

	Original rule:
	l2 -> l0 : x^0'=x^0, y^0'=y^0, 0 == 0, cost: 1
	New rule:
	l2 -> l0 : x^0'=x^0, y^0'=y^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l2 -> l0 : x^0'=x^0, y^0'=y^0, T, cost: 1
	New rule:
	l2 -> l0 : T, cost: 1
	
	Propagated Equalities

	Original rule:
	l4 -> l2 : x^0'=x^post4, y^0'=y^post4, (-1+x^post4 == 0 /\ x^0-x^post5 == 0 /\ y^post5-y^post4 == 0 /\ -y^post5+y^0 == 0), cost: 1
	New rule:
	l4 -> l2 : x^0'=1, y^0'=y^post5, (0 == 0 /\ x^0-x^post5 == 0 /\ -y^post5+y^0 == 0), cost: 1
	
		propagated equality x^post4 = 1
		
		propagated equality y^post4 = y^post5
		
	Propagated Equalities

	Original rule:
	l4 -> l2 : x^0'=1, y^0'=y^post5, (0 == 0 /\ x^0-x^post5 == 0 /\ -y^post5+y^0 == 0), cost: 1
	New rule:
	l4 -> l2 : x^0'=1, y^0'=y^0, 0 == 0, cost: 1
	
		propagated equality x^post5 = x^0
		
		propagated equality y^post5 = y^0
		
	Simplified Guard

	Original rule:
	l4 -> l2 : x^0'=1, y^0'=y^0, 0 == 0, cost: 1
	New rule:
	l4 -> l2 : x^0'=1, y^0'=y^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l4 -> l2 : x^0'=1, y^0'=y^0, T, cost: 1
	New rule:
	l4 -> l2 : x^0'=1, T, cost: 1

Step with 9

	Trace

	9[T]
	
	Blocked

	[{}, {}]

Step with 8

	Trace

	9[T], 8[T]
	
	Blocked

	[{}, {}, {}]

Step with 7

	Trace

	9[T], 8[T], 7[(-10+x^0 <= 0)]
	
	Blocked

	[{}, {}, {6[T]}, {}]

Accelerate

Start location: l4
Program variables: x^0 y^0
   6: l0 -> l1 : 11-x^0 <= 0, cost: 1
   7: l0 -> l2 : x^0'=1+x^0, y^0'=10-x^0, -10+x^0 <= 0, cost: 1
   8: l2 -> l0 : T, cost: 1
  10: l2 -> l2 : x^0'=n+x^0, y^0'=11-n-x^0, (-1+n >= 0 /\ 11-n-x^0 >= 0), cost: 1
   9: l4 -> l2 : x^0'=1, T, cost: 1

	Loop Acceleration

	Original rule:
	l2 -> l2 : x^0'=1+x^0, y^0'=10-x^0, -10+x^0 <= 0, cost: 1
	New rule:
	l2 -> l2 : x^0'=n+x^0, y^0'=11-n-x^0, (-1+n >= 0 /\ 11-n-x^0 >= 0), cost: 1

		10-x^0 >= 0 [0]: montonic decrease yields 11-n-x^0 >= 0
		
		10-x^0 >= 0 [1]: eventual increase yields (1 <= 0 /\ 10-x^0 >= 0)
		
		Replacement map: {10-x^0 >= 0 -> 11-n-x^0 >= 0}

	Trace

	9[T], 10[(-1+n >= 0 /\ 11-n-x^0 >= 0)]
	
	Blocked

	[{}, {}, {10[T]}]

Step with 8

	Trace

	9[T], 10[(-1+n >= 0 /\ 11-n-x^0 >= 0)], 8[T]
	
	Blocked

	[{}, {}, {10[T]}, {}]

Step with 7

	Trace

	9[T], 10[(-1+n >= 0 /\ 11-n-x^0 >= 0)], 8[T], 7[(-10+x^0 <= 0)]
	
	Blocked

	[{}, {}, {10[T]}, {}, {}]

Covered

	Trace

	9[T], 10[(-1+n >= 0 /\ 11-n-x^0 >= 0)], 8[T]
	
	Blocked

	[{}, {}, {10[T]}, {7[T]}]

Step with 6

	Trace

	9[T], 10[(-1+n >= 0 /\ 11-n-x^0 >= 0)], 8[T], 6[(11-x^0 <= 0)]
	
	Blocked

	[{}, {}, {10[T]}, {7[T]}, {}]

Backtrack

	Trace

	9[T], 10[(-1+n >= 0 /\ 11-n-x^0 >= 0)], 8[T]
	
	Blocked

	[{}, {}, {10[T]}, {6[T], 7[T]}]

Backtrack

	Trace

	9[T], 10[(-1+n >= 0 /\ 11-n-x^0 >= 0)]
	
	Blocked

	[{}, {}, {8[T], 10[T]}]

Backtrack

	Trace

	9[T]
	
	Blocked

	[{}, {10[T]}]

Step with 8

	Trace

	9[T], 8[T]
	
	Blocked

	[{}, {10[T]}, {}]

Step with 7

	Trace

	9[T], 8[T], 7[(-10+x^0 <= 0)]
	
	Blocked

	[{}, {10[T]}, {6[T]}, {}]

Covered

	Trace

	9[T], 8[T]
	
	Blocked

	[{}, {10[T]}, {6[T], 7[T]}]

Backtrack

	Trace

	9[T]
	
	Blocked

	[{}, {8[T], 10[T]}]

Backtrack

	Trace

	Blocked

	[{9[T]}]

Accept

unknown

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b