NO

Initial ITS

Start location: l4
Program variables: i^0 j^0 ret_pair5^0
   0: l0 -> l1 : i^0'=i^post1, j^0'=j^post1, ret_pair5^0'=ret_pair5^post1, (0 == 0 /\ -2+j^post1-j^0 == 0 /\ -1-i^0+i^post1 == 0), cost: 1
   1: l0 -> l2 : i^0'=i^post2, j^0'=j^post2, ret_pair5^0'=ret_pair5^post2, (ret_pair5^0-ret_pair5^post2 == 0 /\ -j^post2+j^0 == 0 /\ i^0-i^post2 == 0), cost: 1
   2: l1 -> l0 : i^0'=i^post3, j^0'=j^post3, ret_pair5^0'=ret_pair5^post3, (ret_pair5^0-ret_pair5^post3 == 0 /\ -j^post3+j^0 == 0 /\ i^0-i^post3 == 0), cost: 1
   3: l3 -> l1 : i^0'=i^post4, j^0'=j^post4, ret_pair5^0'=ret_pair5^post4, (j^post4 == 0 /\ ret_pair5^0-ret_pair5^post4 == 0 /\ i^post4 == 0), cost: 1
   4: l4 -> l3 : i^0'=i^post5, j^0'=j^post5, ret_pair5^0'=ret_pair5^post5, (i^0-i^post5 == 0 /\ j^0-j^post5 == 0 /\ ret_pair5^0-ret_pair5^post5 == 0), cost: 1

Chained Linear Paths

Start location: l4
Program variables: i^0 j^0 ret_pair5^0
   0: l0 -> l1 : i^0'=i^post1, j^0'=j^post1, ret_pair5^0'=ret_pair5^post1, (0 == 0 /\ -2+j^post1-j^0 == 0 /\ -1-i^0+i^post1 == 0), cost: 1
   1: l0 -> l2 : i^0'=i^post2, j^0'=j^post2, ret_pair5^0'=ret_pair5^post2, (ret_pair5^0-ret_pair5^post2 == 0 /\ -j^post2+j^0 == 0 /\ i^0-i^post2 == 0), cost: 1
   2: l1 -> l0 : i^0'=i^post3, j^0'=j^post3, ret_pair5^0'=ret_pair5^post3, (ret_pair5^0-ret_pair5^post3 == 0 /\ -j^post3+j^0 == 0 /\ i^0-i^post3 == 0), cost: 1
   5: l4 -> l1 : i^0'=i^post4, j^0'=j^post4, ret_pair5^0'=ret_pair5^post4, (i^0-i^post5 == 0 /\ j^post4 == 0 /\ j^0-j^post5 == 0 /\ ret_pair5^0-ret_pair5^post5 == 0 /\ i^post4 == 0 /\ ret_pair5^post5-ret_pair5^post4 == 0), cost: 1

	Eliminating location l3 by chaining:

	Applied chaining

	First rule:
	l4 -> l3 : i^0'=i^post5, j^0'=j^post5, ret_pair5^0'=ret_pair5^post5, (i^0-i^post5 == 0 /\ j^0-j^post5 == 0 /\ ret_pair5^0-ret_pair5^post5 == 0), cost: 1
	Second rule:
	l3 -> l1 : i^0'=i^post4, j^0'=j^post4, ret_pair5^0'=ret_pair5^post4, (j^post4 == 0 /\ ret_pair5^0-ret_pair5^post4 == 0 /\ i^post4 == 0), cost: 1
	New rule:
	l4 -> l1 : i^0'=i^post4, j^0'=j^post4, ret_pair5^0'=ret_pair5^post4, (i^0-i^post5 == 0 /\ j^post4 == 0 /\ j^0-j^post5 == 0 /\ ret_pair5^0-ret_pair5^post5 == 0 /\ i^post4 == 0 /\ ret_pair5^post5-ret_pair5^post4 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 3 4

Simplified Transitions

Start location: l4
Program variables: i^0 j^0 ret_pair5^0
   6: l0 -> l1 : i^0'=1+i^0, j^0'=2+j^0, ret_pair5^0'=ret_pair5^post1, T, cost: 1
   7: l0 -> l2 : T, cost: 1
   8: l1 -> l0 : T, cost: 1
   9: l4 -> l1 : i^0'=0, j^0'=0, T, cost: 1

	Propagated Equalities

	Original rule:
	l0 -> l1 : i^0'=i^post1, j^0'=j^post1, ret_pair5^0'=ret_pair5^post1, (0 == 0 /\ -2+j^post1-j^0 == 0 /\ -1-i^0+i^post1 == 0), cost: 1
	New rule:
	l0 -> l1 : i^0'=1+i^0, j^0'=2+j^0, ret_pair5^0'=ret_pair5^post1, 0 == 0, cost: 1
	
		propagated equality j^post1 = 2+j^0
		
		propagated equality i^post1 = 1+i^0
		
	Simplified Guard

	Original rule:
	l0 -> l1 : i^0'=1+i^0, j^0'=2+j^0, ret_pair5^0'=ret_pair5^post1, 0 == 0, cost: 1
	New rule:
	l0 -> l1 : i^0'=1+i^0, j^0'=2+j^0, ret_pair5^0'=ret_pair5^post1, T, cost: 1
	
	Propagated Equalities

	Original rule:
	l0 -> l2 : i^0'=i^post2, j^0'=j^post2, ret_pair5^0'=ret_pair5^post2, (ret_pair5^0-ret_pair5^post2 == 0 /\ -j^post2+j^0 == 0 /\ i^0-i^post2 == 0), cost: 1
	New rule:
	l0 -> l2 : i^0'=i^0, j^0'=j^0, ret_pair5^0'=ret_pair5^0, 0 == 0, cost: 1
	
		propagated equality ret_pair5^post2 = ret_pair5^0
		
		propagated equality j^post2 = j^0
		
		propagated equality i^post2 = i^0
		
	Simplified Guard

	Original rule:
	l0 -> l2 : i^0'=i^0, j^0'=j^0, ret_pair5^0'=ret_pair5^0, 0 == 0, cost: 1
	New rule:
	l0 -> l2 : i^0'=i^0, j^0'=j^0, ret_pair5^0'=ret_pair5^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l0 -> l2 : i^0'=i^0, j^0'=j^0, ret_pair5^0'=ret_pair5^0, T, cost: 1
	New rule:
	l0 -> l2 : T, cost: 1
	
	Propagated Equalities

	Original rule:
	l1 -> l0 : i^0'=i^post3, j^0'=j^post3, ret_pair5^0'=ret_pair5^post3, (ret_pair5^0-ret_pair5^post3 == 0 /\ -j^post3+j^0 == 0 /\ i^0-i^post3 == 0), cost: 1
	New rule:
	l1 -> l0 : i^0'=i^0, j^0'=j^0, ret_pair5^0'=ret_pair5^0, 0 == 0, cost: 1
	
		propagated equality ret_pair5^post3 = ret_pair5^0
		
		propagated equality j^post3 = j^0
		
		propagated equality i^post3 = i^0
		
	Simplified Guard

	Original rule:
	l1 -> l0 : i^0'=i^0, j^0'=j^0, ret_pair5^0'=ret_pair5^0, 0 == 0, cost: 1
	New rule:
	l1 -> l0 : i^0'=i^0, j^0'=j^0, ret_pair5^0'=ret_pair5^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l1 -> l0 : i^0'=i^0, j^0'=j^0, ret_pair5^0'=ret_pair5^0, T, cost: 1
	New rule:
	l1 -> l0 : T, cost: 1
	
	Propagated Equalities

	Original rule:
	l4 -> l1 : i^0'=i^post4, j^0'=j^post4, ret_pair5^0'=ret_pair5^post4, (i^0-i^post5 == 0 /\ j^post4 == 0 /\ j^0-j^post5 == 0 /\ ret_pair5^0-ret_pair5^post5 == 0 /\ i^post4 == 0 /\ ret_pair5^post5-ret_pair5^post4 == 0), cost: 1
	New rule:
	l4 -> l1 : i^0'=0, j^0'=0, ret_pair5^0'=ret_pair5^post5, (0 == 0 /\ i^0-i^post5 == 0 /\ j^0-j^post5 == 0 /\ ret_pair5^0-ret_pair5^post5 == 0), cost: 1
	
		propagated equality j^post4 = 0
		
		propagated equality i^post4 = 0
		
		propagated equality ret_pair5^post4 = ret_pair5^post5
		
	Propagated Equalities

	Original rule:
	l4 -> l1 : i^0'=0, j^0'=0, ret_pair5^0'=ret_pair5^post5, (0 == 0 /\ i^0-i^post5 == 0 /\ j^0-j^post5 == 0 /\ ret_pair5^0-ret_pair5^post5 == 0), cost: 1
	New rule:
	l4 -> l1 : i^0'=0, j^0'=0, ret_pair5^0'=ret_pair5^0, 0 == 0, cost: 1
	
		propagated equality i^post5 = i^0
		
		propagated equality j^post5 = j^0
		
		propagated equality ret_pair5^post5 = ret_pair5^0
		
	Simplified Guard

	Original rule:
	l4 -> l1 : i^0'=0, j^0'=0, ret_pair5^0'=ret_pair5^0, 0 == 0, cost: 1
	New rule:
	l4 -> l1 : i^0'=0, j^0'=0, ret_pair5^0'=ret_pair5^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l4 -> l1 : i^0'=0, j^0'=0, ret_pair5^0'=ret_pair5^0, T, cost: 1
	New rule:
	l4 -> l1 : i^0'=0, j^0'=0, 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[T]
	
	Blocked

	[{}, {}, {}, {}]

Backtrack

	Trace

	9[T], 8[T]
	
	Blocked

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

Step with 6

	Trace

	9[T], 8[T], 6[T]
	
	Blocked

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

Nonterm

Start location: l4
Program variables: i^0 j^0 ret_pair5^0
   6: l0 -> l1 : i^0'=1+i^0, j^0'=2+j^0, ret_pair5^0'=ret_pair5^post1, T, cost: 1
   7: l0 -> l2 : T, cost: 1
   8: l1 -> l0 : T, cost: 1
  10: l1 -> LoAT_sink : -1+n >= 0, cost: NONTERM
  11: l1 -> l1 : i^0'=n+i^0, j^0'=2*n+j^0, ret_pair5^0'=ret_pair5^post1, -1+n >= 0, cost: 1
   9: l4 -> l1 : i^0'=0, j^0'=0, T, cost: 1

	Certificate of Non-Termination

	Original rule:
	l1 -> l1 : i^0'=1+i^0, j^0'=2+j^0, ret_pair5^0'=ret_pair5^post1, T, cost: 1
	New rule:
	l1 -> LoAT_sink : -1+n >= 0, cost: NONTERM

		Replacement map: {}

	Loop Acceleration

	Original rule:
	l1 -> l1 : i^0'=1+i^0, j^0'=2+j^0, ret_pair5^0'=ret_pair5^post1, T, cost: 1
	New rule:
	l1 -> l1 : i^0'=n+i^0, j^0'=2*n+j^0, ret_pair5^0'=ret_pair5^post1, -1+n >= 0, cost: 1

		Replacement map: {}

Step with 10

	Trace

	9[T], 10[-1+n >= 0]
	
	Blocked

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

Refute

	Counterexample

	[ i^0=0 j^0=0 ret_pair5^0=0 ] 9 [ i^0=i^0 j^0=j^0 ret_pair5^0=0 ] 10
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b