NO

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

Initial linear ITS problem
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
     17: f2 -> f3 : arg1'=arg1P_18, [ arg1<0 && arg1==arg1P_18 ], cost: 1
     18: f2 -> f3 : arg1'=arg1P_19, [ arg1>0 && arg1==arg1P_19 ], cost: 1
     20: f2 -> f17 : arg1'=arg1P_21, [ arg1==0 && arg1==arg1P_21 ], cost: 1
      1: f4 -> f7 : arg1'=arg1P_2, [ arg1P_2==2+arg1 ], cost: 1
      3: f7 -> f8 : arg1'=arg1P_4, [ arg1<0 && arg1==arg1P_4 ], cost: 1
      4: f7 -> f9 : arg1'=arg1P_5, [ arg1>=0 && arg1==arg1P_5 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, [ arg1P_3==-arg1 ], cost: 1
      5: f11 -> f10 : arg1'=arg1P_6, [ arg1==arg1P_6 ], cost: 1
      6: f9 -> f10 : arg1'=arg1P_7, [ arg1==arg1P_7 ], cost: 1
     15: f10 -> f6 : arg1'=arg1P_16, [ arg1==arg1P_16 ], cost: 1
      7: f5 -> f12 : arg1'=arg1P_8, [ arg1P_8==-2+arg1 ], cost: 1
      9: f12 -> f13 : arg1'=arg1P_10, [ arg1>0 && arg1==arg1P_10 ], cost: 1
     10: f12 -> f14 : arg1'=arg1P_11, [ arg1<=0 && arg1==arg1P_11 ], cost: 1
      8: f13 -> f16 : arg1'=arg1P_9, [ arg1P_9==-arg1 ], cost: 1
     11: f16 -> f15 : arg1'=arg1P_12, [ arg1==arg1P_12 ], cost: 1
     12: f14 -> f15 : arg1'=arg1P_13, [ arg1==arg1P_13 ], cost: 1
     16: f15 -> f6 : arg1'=arg1P_17, [ arg1==arg1P_17 ], cost: 1
     13: f3 -> f4 : arg1'=arg1P_14, [ arg1<0 && arg1==arg1P_14 ], cost: 1
     14: f3 -> f5 : arg1'=arg1P_15, [ arg1>=0 && arg1==arg1P_15 ], cost: 1
     19: f6 -> f2 : arg1'=arg1P_20, [ arg1==arg1P_20 ], cost: 1
     21: __init -> f1 : arg1'=arg1P_22, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     21: __init -> f1 : arg1'=arg1P_22, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
     17: f2 -> f3 : arg1'=arg1P_18, [ arg1<0 && arg1==arg1P_18 ], cost: 1
     18: f2 -> f3 : arg1'=arg1P_19, [ arg1>0 && arg1==arg1P_19 ], cost: 1
      1: f4 -> f7 : arg1'=arg1P_2, [ arg1P_2==2+arg1 ], cost: 1
      3: f7 -> f8 : arg1'=arg1P_4, [ arg1<0 && arg1==arg1P_4 ], cost: 1
      4: f7 -> f9 : arg1'=arg1P_5, [ arg1>=0 && arg1==arg1P_5 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, [ arg1P_3==-arg1 ], cost: 1
      5: f11 -> f10 : arg1'=arg1P_6, [ arg1==arg1P_6 ], cost: 1
      6: f9 -> f10 : arg1'=arg1P_7, [ arg1==arg1P_7 ], cost: 1
     15: f10 -> f6 : arg1'=arg1P_16, [ arg1==arg1P_16 ], cost: 1
      7: f5 -> f12 : arg1'=arg1P_8, [ arg1P_8==-2+arg1 ], cost: 1
      9: f12 -> f13 : arg1'=arg1P_10, [ arg1>0 && arg1==arg1P_10 ], cost: 1
     10: f12 -> f14 : arg1'=arg1P_11, [ arg1<=0 && arg1==arg1P_11 ], cost: 1
      8: f13 -> f16 : arg1'=arg1P_9, [ arg1P_9==-arg1 ], cost: 1
     11: f16 -> f15 : arg1'=arg1P_12, [ arg1==arg1P_12 ], cost: 1
     12: f14 -> f15 : arg1'=arg1P_13, [ arg1==arg1P_13 ], cost: 1
     16: f15 -> f6 : arg1'=arg1P_17, [ arg1==arg1P_17 ], cost: 1
     13: f3 -> f4 : arg1'=arg1P_14, [ arg1<0 && arg1==arg1P_14 ], cost: 1
     14: f3 -> f5 : arg1'=arg1P_15, [ arg1>=0 && arg1==arg1P_15 ], cost: 1
     19: f6 -> f2 : arg1'=arg1P_20, [ arg1==arg1P_20 ], cost: 1
     21: __init -> f1 : arg1'=arg1P_22, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
     17: f2 -> f3 : [ arg1<0 ], cost: 1
     18: f2 -> f3 : [ arg1>0 ], cost: 1
      1: f4 -> f7 : arg1'=2+arg1, [], cost: 1
      3: f7 -> f8 : [ arg1<0 ], cost: 1
      4: f7 -> f9 : [ arg1>=0 ], cost: 1
      2: f8 -> f11 : arg1'=-arg1, [], cost: 1
      5: f11 -> f10 : [], cost: 1
      6: f9 -> f10 : [], cost: 1
     15: f10 -> f6 : [], cost: 1
      7: f5 -> f12 : arg1'=-2+arg1, [], cost: 1
      9: f12 -> f13 : [ arg1>0 ], cost: 1
     10: f12 -> f14 : [ arg1<=0 ], cost: 1
      8: f13 -> f16 : arg1'=-arg1, [], cost: 1
     11: f16 -> f15 : [], cost: 1
     12: f14 -> f15 : [], cost: 1
     16: f15 -> f6 : [], cost: 1
     13: f3 -> f4 : [ arg1<0 ], cost: 1
     14: f3 -> f5 : [ arg1>=0 ], cost: 1
     19: f6 -> f2 : [], cost: 1
     21: __init -> f1 : arg1'=arg1P_22, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     17: f2 -> f3 : [ arg1<0 ], cost: 1
     18: f2 -> f3 : [ arg1>0 ], cost: 1
     26: f7 -> f10 : [ arg1>=0 ], cost: 2
     27: f7 -> f10 : arg1'=-arg1, [ arg1<0 ], cost: 3
     15: f10 -> f6 : [], cost: 1
     29: f12 -> f15 : [ arg1<=0 ], cost: 2
     30: f12 -> f15 : arg1'=-arg1, [ arg1>0 ], cost: 3
     16: f15 -> f6 : [], cost: 1
     23: f3 -> f7 : arg1'=2+arg1, [ arg1<0 ], cost: 2
     24: f3 -> f12 : arg1'=-2+arg1, [ arg1>=0 ], cost: 2
     19: f6 -> f2 : [], cost: 1
     22: __init -> f2 : arg1'=arg1P_1, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     31: f2 -> f7 : arg1'=2+arg1, [ arg1<0 ], cost: 3
     32: f2 -> f12 : arg1'=-2+arg1, [ arg1>0 ], cost: 3
     33: f7 -> f6 : [ arg1>=0 ], cost: 3
     34: f7 -> f6 : arg1'=-arg1, [ arg1<0 ], cost: 4
     35: f12 -> f6 : [ arg1<=0 ], cost: 3
     36: f12 -> f6 : arg1'=-arg1, [ arg1>0 ], cost: 4
     19: f6 -> f2 : [], cost: 1
     22: __init -> f2 : arg1'=arg1P_1, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     37: f2 -> f6 : arg1'=2+arg1, [ arg1<0 && 2+arg1>=0 ], cost: 6
     38: f2 -> f6 : arg1'=-2-arg1, [ 2+arg1<0 ], cost: 7
     39: f2 -> f6 : arg1'=-2+arg1, [ arg1>0 && -2+arg1<=0 ], cost: 6
     40: f2 -> f6 : arg1'=2-arg1, [ -2+arg1>0 ], cost: 7
     19: f6 -> f2 : [], cost: 1
     22: __init -> f2 : arg1'=arg1P_1, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     41: f2 -> f2 : arg1'=2+arg1, [ arg1<0 && 2+arg1>=0 ], cost: 7
     42: f2 -> f2 : arg1'=-2-arg1, [ 2+arg1<0 ], cost: 8
     43: f2 -> f2 : arg1'=-2+arg1, [ arg1>0 && -2+arg1<=0 ], cost: 7
     44: f2 -> f2 : arg1'=2-arg1, [ -2+arg1>0 ], cost: 8
     22: __init -> f2 : arg1'=arg1P_1, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     41: f2 -> f2 : arg1'=2+arg1, [ arg1<0 && 2+arg1>=0 ], cost: 7
     42: f2 -> f2 : arg1'=-2-arg1, [ 2+arg1<0 ], cost: 8
     43: f2 -> f2 : arg1'=-2+arg1, [ arg1>0 && -2+arg1<=0 ], cost: 7
     44: f2 -> f2 : arg1'=2-arg1, [ -2+arg1>0 ], cost: 8

   Failed to prove monotonicity of the guard of rule 41.
   Failed to prove monotonicity of the guard of rule 42.
   Failed to prove monotonicity of the guard of rule 43.
   Failed to prove monotonicity of the guard of rule 44.
[accelerate] Nesting with 4 inner and 4 outer candidates
   Nested simple loops 43 (outer loop) and 41 (inner loop) with Rule(1 | 1+arg1==0, | NONTERM || 18 | ), resulting in the new rules: 45, 46.
   Nested simple loops 44 (outer loop) and 42 (inner loop) with Rule(1 | k>=0, -4*k-arg1>0, | 16*k || 1 | 0=4*k+arg1, ), resulting in the new rules: 47, 48.
   Nested simple loops 41 (outer loop) and 43 (inner loop) with Rule(1 | 1-arg1==0, | NONTERM || 18 | ), resulting in the new rules: 49, 50.
   Nested simple loops 42 (outer loop) and 44 (inner loop) with Rule(1 | k_1>=0, 4*k_1-arg1<0, | 16*k_1 || 1 | 0=-4*k_1+arg1, ), resulting in the new rules: 51, 52.
   Removing the simple loops: 41 42 43 44.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     45: f2 -> [18] : [ 1+arg1==0 ], cost: NONTERM
     46: f2 -> [18] : [ -1+arg1==0 ], cost: NONTERM
     47: f2 -> f2 : arg1'=4*k+arg1, [ k>=0 && -4*k-arg1>0 ], cost: 16*k
     48: f2 -> f2 : arg1'=2+4*k-arg1, [ -2+arg1>0 && k>=0 && -2-4*k+arg1>0 ], cost: 8+16*k
     49: f2 -> [18] : [ 1-arg1==0 ], cost: NONTERM
     50: f2 -> [18] : [ -1-arg1==0 ], cost: NONTERM
     51: f2 -> f2 : arg1'=-4*k_1+arg1, [ k_1>=0 && 4*k_1-arg1<0 ], cost: 16*k_1
     52: f2 -> f2 : arg1'=-2-4*k_1-arg1, [ 2+arg1<0 && k_1>=0 && 2+4*k_1+arg1<0 ], cost: 8+16*k_1
     22: __init -> f2 : arg1'=arg1P_1, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
     22: __init -> f2 : arg1'=arg1P_1, [], cost: 2
     53: __init -> [18] : [], cost: NONTERM
     54: __init -> [18] : [], cost: NONTERM
     55: __init -> f2 : arg1'=arg1P_1+4*k, [ k>=0 && -arg1P_1-4*k>0 ], cost: 2+16*k
     56: __init -> f2 : arg1'=2-arg1P_1+4*k, [ -2+arg1P_1>0 && k>=0 && -2+arg1P_1-4*k>0 ], cost: 10+16*k
     57: __init -> [18] : [], cost: NONTERM
     58: __init -> [18] : [], cost: NONTERM
     59: __init -> f2 : arg1'=-4*k_1+arg1P_1, [ k_1>=0 && 4*k_1-arg1P_1<0 ], cost: 2+16*k_1
     60: __init -> f2 : arg1'=-2-4*k_1-arg1P_1, [ 2+arg1P_1<0 && k_1>=0 && 2+4*k_1+arg1P_1<0 ], cost: 10+16*k_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     53: __init -> [18] : [], cost: NONTERM
     54: __init -> [18] : [], cost: NONTERM
     55: __init -> f2 : arg1'=arg1P_1+4*k, [ k>=0 && -arg1P_1-4*k>0 ], cost: 2+16*k
     56: __init -> f2 : arg1'=2-arg1P_1+4*k, [ -2+arg1P_1>0 && k>=0 && -2+arg1P_1-4*k>0 ], cost: 10+16*k
     57: __init -> [18] : [], cost: NONTERM
     58: __init -> [18] : [], cost: NONTERM
     59: __init -> f2 : arg1'=-4*k_1+arg1P_1, [ k_1>=0 && 4*k_1-arg1P_1<0 ], cost: 2+16*k_1
     60: __init -> f2 : arg1'=-2-4*k_1-arg1P_1, [ 2+arg1P_1<0 && k_1>=0 && 2+4*k_1+arg1P_1<0 ], cost: 10+16*k_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     55: __init -> f2 : arg1'=arg1P_1+4*k, [ k>=0 && -arg1P_1-4*k>0 ], cost: 2+16*k
     56: __init -> f2 : arg1'=2-arg1P_1+4*k, [ -2+arg1P_1>0 && k>=0 && -2+arg1P_1-4*k>0 ], cost: 10+16*k
     58: __init -> [18] : [], cost: NONTERM
     59: __init -> f2 : arg1'=-4*k_1+arg1P_1, [ k_1>=0 && 4*k_1-arg1P_1<0 ], cost: 2+16*k_1
     60: __init -> f2 : arg1'=-2-4*k_1-arg1P_1, [ 2+arg1P_1<0 && k_1>=0 && 2+4*k_1+arg1P_1<0 ], cost: 10+16*k_1

Computing asymptotic complexity for rule 58
   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