NO

Initial ITS
Start location: l4
   0: l0 -> l1 : i^0'=i^post0, ret_pair5^0'=ret_pair5^post0, j^0'=j^post0, (0 == 0 /\ -1-i^0+i^post0 == 0 /\ -2+j^post0-j^0 == 0), cost: 1
   1: l0 -> l2 : i^0'=i^post1, ret_pair5^0'=ret_pair5^post1, j^0'=j^post1, (ret_pair5^0-ret_pair5^post1 == 0 /\ i^0-i^post1 == 0 /\ j^0-j^post1 == 0), cost: 1
   2: l1 -> l0 : i^0'=i^post2, ret_pair5^0'=ret_pair5^post2, j^0'=j^post2, (ret_pair5^0-ret_pair5^post2 == 0 /\ j^0-j^post2 == 0 /\ i^0-i^post2 == 0), cost: 1
   3: l3 -> l1 : i^0'=i^post3, ret_pair5^0'=ret_pair5^post3, j^0'=j^post3, (i^post3 == 0 /\ j^post3 == 0 /\ ret_pair5^0-ret_pair5^post3 == 0), cost: 1
   4: l4 -> l3 : i^0'=i^post4, ret_pair5^0'=ret_pair5^post4, j^0'=j^post4, (ret_pair5^0-ret_pair5^post4 == 0 /\ j^0-j^post4 == 0 /\ i^0-i^post4 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l4
   0: l0 -> l1 : i^0'=i^post0, ret_pair5^0'=ret_pair5^post0, j^0'=j^post0, (0 == 0 /\ -1-i^0+i^post0 == 0 /\ -2+j^post0-j^0 == 0), cost: 1
   2: l1 -> l0 : i^0'=i^post2, ret_pair5^0'=ret_pair5^post2, j^0'=j^post2, (ret_pair5^0-ret_pair5^post2 == 0 /\ j^0-j^post2 == 0 /\ i^0-i^post2 == 0), cost: 1
   3: l3 -> l1 : i^0'=i^post3, ret_pair5^0'=ret_pair5^post3, j^0'=j^post3, (i^post3 == 0 /\ j^post3 == 0 /\ ret_pair5^0-ret_pair5^post3 == 0), cost: 1
   4: l4 -> l3 : i^0'=i^post4, ret_pair5^0'=ret_pair5^post4, j^0'=j^post4, (ret_pair5^0-ret_pair5^post4 == 0 /\ j^0-j^post4 == 0 /\ i^0-i^post4 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : i^0'=i^post0, ret_pair5^0'=ret_pair5^post0, j^0'=j^post0, (0 == 0 /\ -1-i^0+i^post0 == 0 /\ -2+j^post0-j^0 == 0), cost: 1
New rule:
l0 -> l1 : i^0'=1+i^0, ret_pair5^0'=ret_pair5^post0, j^0'=2+j^0, 0 == 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l0 : i^0'=i^post2, ret_pair5^0'=ret_pair5^post2, j^0'=j^post2, (ret_pair5^0-ret_pair5^post2 == 0 /\ j^0-j^post2 == 0 /\ i^0-i^post2 == 0), cost: 1
New rule:
l1 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l1 : i^0'=i^post3, ret_pair5^0'=ret_pair5^post3, j^0'=j^post3, (i^post3 == 0 /\ j^post3 == 0 /\ ret_pair5^0-ret_pair5^post3 == 0), cost: 1
New rule:
l3 -> l1 : i^0'=0, j^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : i^0'=i^post4, ret_pair5^0'=ret_pair5^post4, j^0'=j^post4, (ret_pair5^0-ret_pair5^post4 == 0 /\ j^0-j^post4 == 0 /\ i^0-i^post4 == 0), cost: 1
New rule:
l4 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l4
   5: l0 -> l1 : i^0'=1+i^0, ret_pair5^0'=ret_pair5^post0, j^0'=2+j^0, 0 == 0, cost: 1
   6: l1 -> l0 : TRUE, cost: 1
   7: l3 -> l1 : i^0'=0, j^0'=0, TRUE, cost: 1
   8: l4 -> l3 : TRUE, cost: 1


Eliminating location l3 by chaining:

Applied chaining
First rule:
l4 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l1 : i^0'=0, j^0'=0, TRUE, cost: 1
New rule:
l4 -> l1 : i^0'=0, j^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 7 8

Eliminating location l0 by chaining:

Applied chaining
First rule:
l1 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l1 : i^0'=1+i^0, ret_pair5^0'=ret_pair5^post0, j^0'=2+j^0, 0 == 0, cost: 1
New rule:
l1 -> l1 : i^0'=1+i^0, ret_pair5^0'=ret_pair5^post0, j^0'=2+j^0, 0 == 0, cost: 2

Applied deletion
Removed the following rules: 5 6

Eliminated locations on linear paths
Start location: l4
  10: l1 -> l1 : i^0'=1+i^0, ret_pair5^0'=ret_pair5^post0, j^0'=2+j^0, 0 == 0, cost: 2
   9: l4 -> l1 : i^0'=0, j^0'=0, TRUE, cost: 2


Applied nonterm
Original rule:
l1 -> l1 : i^0'=1+i^0, ret_pair5^0'=ret_pair5^post0, j^0'=2+j^0, 0 == 0, cost: 2
New rule:
l1 -> [5] : 0 >= 0, cost: NONTERM

Applied acceleration
Original rule:
l1 -> l1 : i^0'=1+i^0, ret_pair5^0'=ret_pair5^post0, j^0'=2+j^0, 0 == 0, cost: 2
New rule:
l1 -> l1 : i^0'=i^0+n0, ret_pair5^0'=ret_pair5^post0, j^0'=j^0+2*n0, 0 >= 0, cost: 2*n0

Applied deletion
Removed the following rules: 10

Accelerated simple loops
Start location: l4
  11: l1 -> [5] : 0 >= 0, cost: NONTERM
  12: l1 -> l1 : i^0'=i^0+n0, ret_pair5^0'=ret_pair5^post0, j^0'=j^0+2*n0, 0 >= 0, cost: 2*n0
   9: l4 -> l1 : i^0'=0, j^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l4 -> l1 : i^0'=0, j^0'=0, TRUE, cost: 2
Second rule:
l1 -> [5] : 0 >= 0, cost: NONTERM
New rule:
l4 -> [5] : 0 >= 0, cost: NONTERM

Applied chaining
First rule:
l4 -> l1 : i^0'=0, j^0'=0, TRUE, cost: 2
Second rule:
l1 -> l1 : i^0'=i^0+n0, ret_pair5^0'=ret_pair5^post0, j^0'=j^0+2*n0, 0 >= 0, cost: 2*n0
New rule:
l4 -> l1 : i^0'=n0, ret_pair5^0'=ret_pair5^post0, j^0'=2*n0, 0 >= 0, cost: 2+2*n0

Applied deletion
Removed the following rules: 11 12

Chained accelerated rules with incoming rules
Start location: l4
   9: l4 -> l1 : i^0'=0, j^0'=0, TRUE, cost: 2
  13: l4 -> [5] : 0 >= 0, cost: NONTERM
  14: l4 -> l1 : i^0'=n0, ret_pair5^0'=ret_pair5^post0, j^0'=2*n0, 0 >= 0, cost: 2+2*n0


Removed unreachable locations and irrelevant leafs
Start location: l4
  13: l4 -> [5] : 0 >= 0, cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 13 via SMT.

Proved the following lower bound
Complexity:  Nonterm
Cpx degree: Nonterm

Solved cost: NONTERM
Rule cost:   NONTERM
Rule guard:  0 >= 0