NO

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

Initial linear ITS problem
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg1==arg1P_1 && arg2==arg2P_1 && arg1==arg3P_1 && arg4==arg4P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && arg2==arg2P_2 && arg3==arg3P_2 && arg2==arg4P_2 ], cost: 1
      8: f3 -> f4 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg3<arg4 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1
      9: f3 -> f4 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg3>arg4 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1
     11: f3 -> f10 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg3==arg4 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg4P_3==arg2+arg4 && arg1==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
      6: f8 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg3P_4==arg3+arg1 && arg1==arg1P_4 && arg2==arg2P_4 && arg4==arg4P_4 ], cost: 1
      7: f9 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      4: f4 -> f5 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg3>arg4 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
      5: f4 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3<=arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1
     10: f7 -> f3 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1
     12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg1==arg1P_1 && arg2==arg2P_1 && arg1==arg3P_1 && arg4==arg4P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && arg2==arg2P_2 && arg3==arg3P_2 && arg2==arg4P_2 ], cost: 1
      8: f3 -> f4 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg3<arg4 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1
      9: f3 -> f4 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg3>arg4 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg4P_3==arg2+arg4 && arg1==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
      6: f8 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg3P_4==arg3+arg1 && arg1==arg1P_4 && arg2==arg2P_4 && arg4==arg4P_4 ], cost: 1
      7: f9 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      4: f4 -> f5 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg3>arg4 && arg1==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
      5: f4 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3<=arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1
     10: f7 -> f3 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1
     12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg3'=arg1, [], cost: 1
      1: f2 -> f3 : arg4'=arg2, [], cost: 1
      8: f3 -> f4 : [ arg3<arg4 ], cost: 1
      9: f3 -> f4 : [ arg3>arg4 ], cost: 1
      2: f5 -> f8 : arg4'=arg2+arg4, [], cost: 1
      6: f8 -> f7 : [], cost: 1
      3: f6 -> f9 : arg3'=arg3+arg1, [], cost: 1
      7: f9 -> f7 : [], cost: 1
      4: f4 -> f5 : [ arg3>arg4 ], cost: 1
      5: f4 -> f6 : [ arg3<=arg4 ], cost: 1
     10: f7 -> f3 : [], cost: 1
     12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
      8: f3 -> f4 : [ arg3<arg4 ], cost: 1
      9: f3 -> f4 : [ arg3>arg4 ], cost: 1
     17: f4 -> f7 : arg4'=arg2+arg4, [ arg3>arg4 ], cost: 3
     18: f4 -> f7 : arg3'=arg3+arg1, [ arg3<=arg4 ], cost: 3
     10: f7 -> f3 : [], cost: 1
     14: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg1P_13, arg4'=arg2P_13, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     19: f3 -> f7 : arg3'=arg3+arg1, [ arg3<arg4 ], cost: 4
     20: f3 -> f7 : arg4'=arg2+arg4, [ arg3>arg4 ], cost: 4
     10: f7 -> f3 : [], cost: 1
     14: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg1P_13, arg4'=arg2P_13, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     21: f3 -> f3 : arg3'=arg3+arg1, [ arg3<arg4 ], cost: 5
     22: f3 -> f3 : arg4'=arg2+arg4, [ arg3>arg4 ], cost: 5
     14: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg1P_13, arg4'=arg2P_13, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     21: f3 -> f3 : arg3'=arg3+arg1, [ arg3<arg4 ], cost: 5
     22: f3 -> f3 : arg4'=arg2+arg4, [ arg3>arg4 ], cost: 5

[test] deduced pseudo-invariant arg1<=0, also trying -arg1<=-1
   Accelerated rule 21 with non-termination, yielding the new rule 23.
   Accelerated rule 21 with non-termination, yielding the new rule 24.
   Accelerated rule 21 with backward acceleration, yielding the new rule 25.
   Accelerated rule 21 with backward acceleration, yielding the new rule 26.
[test] deduced pseudo-invariant arg2<=0, also trying -arg2<=-1
   Accelerated rule 22 with non-termination, yielding the new rule 27.
   Accelerated rule 22 with non-termination, yielding the new rule 28.
   Accelerated rule 22 with backward acceleration, yielding the new rule 29.
   Accelerated rule 22 with backward acceleration, yielding the new rule 30.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Also removing duplicate rules: 24 28.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     21: f3 -> f3 : arg3'=arg3+arg1, [ arg3<arg4 ], cost: 5
     22: f3 -> f3 : arg4'=arg2+arg4, [ arg3>arg4 ], cost: 5
     23: f3 -> [11] : [ arg3<arg4 && arg3==0 && arg4==1 && arg1==0 ], cost: NONTERM
     25: f3 -> [11] : [ arg3<arg4 && arg1<=0 ], cost: NONTERM
     26: f3 -> f3 : arg3'=arg3+k*arg1, [ -arg1<=-1 && k>=0 && (-1+k)*arg1+arg3<arg4 ], cost: 5*k
     27: f3 -> [11] : [ arg3>arg4 && arg2==0 && arg3==1 && arg4==0 ], cost: NONTERM
     29: f3 -> [11] : [ arg3>arg4 && arg2<=0 ], cost: NONTERM
     30: f3 -> f3 : arg4'=arg2*k_2+arg4, [ -arg2<=-1 && k_2>=0 && arg3>arg4+arg2*(-1+k_2) ], cost: 5*k_2
     14: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg1P_13, arg4'=arg2P_13, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     14: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg1P_13, arg4'=arg2P_13, [], cost: 3
     31: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=2*arg1P_13, arg4'=arg2P_13, [ arg1P_13<arg2P_13 ], cost: 8
     32: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg1P_13, arg4'=2*arg2P_13, [ arg1P_13>arg2P_13 ], cost: 8
     33: __init -> [11] : [], cost: NONTERM
     34: __init -> [11] : [], cost: NONTERM
     35: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=k*arg1P_13+arg1P_13, arg4'=arg2P_13, [ -arg1P_13<=-1 && k>=0 && arg1P_13+(-1+k)*arg1P_13<arg2P_13 ], cost: 3+5*k
     36: __init -> [11] : [], cost: NONTERM
     37: __init -> [11] : [], cost: NONTERM
     38: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg1P_13, arg4'=arg2P_13+arg2P_13*k_2, [ -arg2P_13<=-1 && k_2>=0 && arg1P_13>arg2P_13*(-1+k_2)+arg2P_13 ], cost: 3+5*k_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     33: __init -> [11] : [], cost: NONTERM
     34: __init -> [11] : [], cost: NONTERM
     35: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=k*arg1P_13+arg1P_13, arg4'=arg2P_13, [ -arg1P_13<=-1 && k>=0 && arg1P_13+(-1+k)*arg1P_13<arg2P_13 ], cost: 3+5*k
     36: __init -> [11] : [], cost: NONTERM
     37: __init -> [11] : [], cost: NONTERM
     38: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg1P_13, arg4'=arg2P_13+arg2P_13*k_2, [ -arg2P_13<=-1 && k_2>=0 && arg1P_13>arg2P_13*(-1+k_2)+arg2P_13 ], cost: 3+5*k_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     35: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=k*arg1P_13+arg1P_13, arg4'=arg2P_13, [ -arg1P_13<=-1 && k>=0 && arg1P_13+(-1+k)*arg1P_13<arg2P_13 ], cost: 3+5*k
     37: __init -> [11] : [], cost: NONTERM
     38: __init -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg1P_13, arg4'=arg2P_13+arg2P_13*k_2, [ -arg2P_13<=-1 && k_2>=0 && arg1P_13>arg2P_13*(-1+k_2)+arg2P_13 ], cost: 3+5*k_2

Computing asymptotic complexity for rule 37
   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