NO

### Pre-processing the ITS problem ###

Initial linear ITS problem
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      2: f2 -> f3 : arg1'=arg1P_3, [ arg1>=0 && arg1==arg1P_3 ], cost: 1
      4: f2 -> f5 : arg1'=arg1P_5, [ arg1<0 && arg1==arg1P_5 ], cost: 1
      1: f3 -> f4 : arg1'=arg1P_2, [ arg1P_2==x2_1+arg1 ], cost: 1
      3: f4 -> f2 : arg1'=arg1P_4, [ arg1==arg1P_4 ], cost: 1
      5: __init -> f1 : arg1'=arg1P_6, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: __init -> f1 : arg1'=arg1P_6, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      2: f2 -> f3 : arg1'=arg1P_3, [ arg1>=0 && arg1==arg1P_3 ], cost: 1
      1: f3 -> f4 : arg1'=arg1P_2, [ arg1P_2==x2_1+arg1 ], cost: 1
      3: f4 -> f2 : arg1'=arg1P_4, [ arg1==arg1P_4 ], cost: 1
      5: __init -> f1 : arg1'=arg1P_6, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      2: f2 -> f3 : [ arg1>=0 ], cost: 1
      1: f3 -> f4 : arg1'=x2_1+arg1, [], cost: 1
      3: f4 -> f2 : [], cost: 1
      5: __init -> f1 : arg1'=arg1P_6, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
      8: f2 -> f2 : arg1'=x2_1+arg1, [ arg1>=0 ], cost: 3
      6: __init -> f2 : arg1'=arg1P_1, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      8: f2 -> f2 : arg1'=x2_1+arg1, [ arg1>=0 ], cost: 3

[test] deduced pseudo-invariant -x2_1<=0, also trying x2_1<=-1
   Accelerated rule 8 with non-termination, yielding the new rule 9.
   Accelerated rule 8 with non-termination, yielding the new rule 10.
   Accelerated rule 8 with backward acceleration, yielding the new rule 11.
   Accelerated rule 8 with backward acceleration, yielding the new rule 12.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Also removing duplicate rules: 10.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      8: f2 -> f2 : arg1'=x2_1+arg1, [ arg1>=0 ], cost: 3
      9: f2 -> [6] : [ x2_1==0 && arg1==0 ], cost: NONTERM
     11: f2 -> [6] : [ arg1>=0 && -x2_1<=0 ], cost: NONTERM
     12: f2 -> f2 : arg1'=x2_1*k+arg1, [ x2_1<=-1 && k>=0 && (-1+k)*x2_1+arg1>=0 ], cost: 3*k
      6: __init -> f2 : arg1'=arg1P_1, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
      6: __init -> f2 : arg1'=arg1P_1, [], cost: 2
     13: __init -> f2 : arg1'=x2_1+arg1P_1, [ arg1P_1>=0 ], cost: 5
     14: __init -> [6] : [], cost: NONTERM
     15: __init -> [6] : [], cost: NONTERM
     16: __init -> f2 : arg1'=x2_1*k+arg1P_1, [ x2_1<=-1 && k>=0 && arg1P_1+(-1+k)*x2_1>=0 ], cost: 2+3*k

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     14: __init -> [6] : [], cost: NONTERM
     15: __init -> [6] : [], cost: NONTERM
     16: __init -> f2 : arg1'=x2_1*k+arg1P_1, [ x2_1<=-1 && k>=0 && arg1P_1+(-1+k)*x2_1>=0 ], cost: 2+3*k

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     15: __init -> [6] : [], cost: NONTERM
     16: __init -> f2 : arg1'=x2_1*k+arg1P_1, [ x2_1<=-1 && k>=0 && arg1P_1+(-1+k)*x2_1>=0 ], cost: 2+3*k

Computing asymptotic complexity for rule 15
   Guard is satisfiable, yielding nontermination
   Resulting cost NONTERM has complexity: Nonterm

Found new complexity Nonterm.

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Nonterm
   Cpx degree:  Nonterm
   Solved cost: NONTERM
   Rule cost:   NONTERM
   Rule guard:  []

NO