WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_Load -> f152_0_gcd_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f152_0_gcd_EQ -> f207_0_mod_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>0 && arg2>arg1 && arg1>0 && arg1==arg1P_2 && arg2==arg2P_2 ], cost: 1
      2: f152_0_gcd_EQ -> f207_0_mod_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2>0 && arg2<arg1 && arg1>0 && arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
      3: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2>0 && 0==arg1 && arg2==arg1P_4 && 0==arg2P_4 ], cost: 1
      4: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>0 && arg1==arg2 && arg1==arg1P_5 && 0==arg2P_5 ], cost: 1
      5: f207_0_mod_LE -> f207_0_mod_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2<arg1 && arg1>0 && arg2>0 && -arg2+arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      6: f207_0_mod_LE -> f152_0_gcd_EQ : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>arg1 && arg2==arg1P_7 && arg1==arg2P_7 ], cost: 1
      7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_Load -> f152_0_gcd_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f152_0_gcd_EQ -> f207_0_mod_LE : [ arg2>arg1 && arg1>0 ], cost: 1
      2: f152_0_gcd_EQ -> f207_0_mod_LE : [ arg2>0 && arg2<arg1 ], cost: 1
      3: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=0, [ arg2>0 && 0==arg1 ], cost: 1
      4: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=0, [ arg1>0 && arg1==arg2 ], cost: 1
      5: f207_0_mod_LE -> f207_0_mod_LE : arg1'=-arg2+arg1, [ arg2<arg1 && arg1>0 && arg2>0 ], cost: 1
      6: f207_0_mod_LE -> f152_0_gcd_EQ : arg1'=arg2, arg2'=arg1, [ arg2>arg1 ], cost: 1
      7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 1.
   Accelerating the following rules:
      3: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=0, [ arg2>0 && 0==arg1 ], cost: 1
      4: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=0, [ arg1>0 && arg1==arg2 ], cost: 1

   Failed to prove monotonicity of the guard of rule 3.
   Failed to prove monotonicity of the guard of rule 4.
[accelerate] Nesting with 2 inner and 2 outer candidates

Accelerating simple loops of location 2.
   Accelerating the following rules:
      5: f207_0_mod_LE -> f207_0_mod_LE : arg1'=-arg2+arg1, [ arg2<arg1 && arg1>0 && arg2>0 ], cost: 1

   Accelerated rule 5 with backward acceleration, yielding the new rule 8.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 5.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_Load -> f152_0_gcd_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f152_0_gcd_EQ -> f207_0_mod_LE : [ arg2>arg1 && arg1>0 ], cost: 1
      2: f152_0_gcd_EQ -> f207_0_mod_LE : [ arg2>0 && arg2<arg1 ], cost: 1
      3: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=0, [ arg2>0 && 0==arg1 ], cost: 1
      4: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg2'=0, [ arg1>0 && arg1==arg2 ], cost: 1
      6: f207_0_mod_LE -> f152_0_gcd_EQ : arg1'=arg2, arg2'=arg1, [ arg2>arg1 ], cost: 1
      8: f207_0_mod_LE -> f207_0_mod_LE : arg1'=-arg2*k+arg1, [ arg1>0 && arg2>0 && k>=0 && arg2<-arg2*(-1+k)+arg1 ], cost: k
      7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
      0: f1_0_main_Load -> f152_0_gcd_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1
      9: f1_0_main_Load -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=0, [ arg2>-1 && arg1>0 && arg2P_1>0 ], cost: 2
     10: f1_0_main_Load -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=0, [ arg2>-1 && arg1>0 && arg2P_1>0 ], cost: 2
      1: f152_0_gcd_EQ -> f207_0_mod_LE : [ arg2>arg1 && arg1>0 ], cost: 1
      2: f152_0_gcd_EQ -> f207_0_mod_LE : [ arg2>0 && arg2<arg1 ], cost: 1
     11: f152_0_gcd_EQ -> f207_0_mod_LE : arg1'=-arg2*k+arg1, [ arg2>arg1 && arg1>0 && arg2>0 && k>=0 && arg2<-arg2*(-1+k)+arg1 ], cost: 1+k
     12: f152_0_gcd_EQ -> f207_0_mod_LE : arg1'=-arg2*k+arg1, [ arg2>0 && arg2<arg1 && arg1>0 && k>=0 && arg2<-arg2*(-1+k)+arg1 ], cost: 1+k
      6: f207_0_mod_LE -> f152_0_gcd_EQ : arg1'=arg2, arg2'=arg1, [ arg2>arg1 ], cost: 1
      7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, [], cost: 1

Eliminated locations (on tree-shaped paths):
   Start location: __init
     16: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=arg1, [ arg2>arg1 && arg1>0 ], cost: 2
     17: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=-arg2*k+arg1, [ arg2>arg1 && arg1>0 && arg2>0 && k>=0 && arg2<-arg2*(-1+k)+arg1 && arg2>-arg2*k+arg1 ], cost: 2+k
     18: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=-arg2*k+arg1, [ arg2>0 && arg2<arg1 && arg1>0 && k>=0 && arg2<-arg2*(-1+k)+arg1 && arg2>-arg2*k+arg1 ], cost: 2+k
     13: __init -> f152_0_gcd_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2P_8>-1 && arg1P_1>-1 && arg1P_8>0 ], cost: 2
     14: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=0, [ arg2P_8>-1 && arg1P_8>0 && arg2P_1>0 ], cost: 3
     15: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=0, [ arg2P_8>-1 && arg1P_8>0 && arg2P_1>0 ], cost: 3

Merged rules:
   Start location: __init
     16: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=arg1, [ arg2>arg1 && arg1>0 ], cost: 2
     17: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=-arg2*k+arg1, [ arg2>arg1 && arg1>0 && arg2>0 && k>=0 && arg2<-arg2*(-1+k)+arg1 && arg2>-arg2*k+arg1 ], cost: 2+k
     18: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=-arg2*k+arg1, [ arg2>0 && arg2<arg1 && arg1>0 && k>=0 && arg2<-arg2*(-1+k)+arg1 && arg2>-arg2*k+arg1 ], cost: 2+k
     13: __init -> f152_0_gcd_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2P_8>-1 && arg1P_1>-1 && arg1P_8>0 ], cost: 2
     19: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=0, [ arg2P_8>-1 && arg1P_8>0 && arg2P_1>0 ], cost: 3

Accelerating simple loops of location 1.
   Accelerating the following rules:
     16: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=arg1, [ arg2>arg1 && arg1>0 ], cost: 2
     17: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=-arg2*k+arg1, [ arg2>arg1 && arg1>0 && arg2>0 && k>=0 && arg2<-arg2*(-1+k)+arg1 && arg2>-arg2*k+arg1 ], cost: 2+k
     18: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=-arg2*k+arg1, [ arg2>0 && arg2<arg1 && arg1>0 && k>=0 && arg2<-arg2*(-1+k)+arg1 && arg2>-arg2*k+arg1 ], cost: 2+k

   Failed to prove monotonicity of the guard of rule 16.
   Failed to prove monotonicity of the guard of rule 17.
   Found no closed form for 18.
[accelerate] Nesting with 2 inner and 3 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     16: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=arg1, [ arg2>arg1 && arg1>0 ], cost: 2
     17: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=-arg2*k+arg1, [ arg2>arg1 && arg1>0 && arg2>0 && k>=0 && arg2<-arg2*(-1+k)+arg1 && arg2>-arg2*k+arg1 ], cost: 2+k
     18: f152_0_gcd_EQ -> f152_0_gcd_EQ : arg1'=arg2, arg2'=-arg2*k+arg1, [ arg2>0 && arg2<arg1 && arg1>0 && k>=0 && arg2<-arg2*(-1+k)+arg1 && arg2>-arg2*k+arg1 ], cost: 2+k
     13: __init -> f152_0_gcd_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2P_8>-1 && arg1P_1>-1 && arg1P_8>0 ], cost: 2
     19: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=0, [ arg2P_8>-1 && arg1P_8>0 && arg2P_1>0 ], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     13: __init -> f152_0_gcd_EQ : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_1>-1 && arg2P_8>-1 && arg1P_1>-1 && arg1P_8>0 ], cost: 2
     19: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=0, [ arg2P_8>-1 && arg1P_8>0 && arg2P_1>0 ], cost: 3
     20: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=arg1P_1, [ arg2P_1>-1 && arg2P_1>arg1P_1 && arg1P_1>0 ], cost: 4
     21: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=arg1P_1-k*arg2P_1, [ arg2P_1>arg1P_1 && arg1P_1>0 && arg2P_1>0 && k>=0 && arg2P_1<arg1P_1-arg2P_1*(-1+k) && arg2P_1>arg1P_1-k*arg2P_1 ], cost: 4+k
     22: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=arg1P_1-k*arg2P_1, [ arg2P_1>0 && arg2P_1<arg1P_1 && arg1P_1>0 && k>=0 && arg2P_1<arg1P_1-arg2P_1*(-1+k) && arg2P_1>arg1P_1-k*arg2P_1 ], cost: 4+k

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     21: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=arg1P_1-k*arg2P_1, [ arg2P_1>arg1P_1 && arg1P_1>0 && arg2P_1>0 && k>=0 && arg2P_1<arg1P_1-arg2P_1*(-1+k) && arg2P_1>arg1P_1-k*arg2P_1 ], cost: 4+k
     22: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=arg1P_1-k*arg2P_1, [ arg2P_1>0 && arg2P_1<arg1P_1 && arg1P_1>0 && k>=0 && arg2P_1<arg1P_1-arg2P_1*(-1+k) && arg2P_1>arg1P_1-k*arg2P_1 ], cost: 4+k

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     21: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=arg1P_1-k*arg2P_1, [ arg2P_1>arg1P_1 && arg1P_1>0 && arg2P_1>0 && k>=0 && arg2P_1<arg1P_1-arg2P_1*(-1+k) && arg2P_1>arg1P_1-k*arg2P_1 ], cost: 4+k
     22: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=arg1P_1-k*arg2P_1, [ arg2P_1>0 && arg2P_1<arg1P_1 && arg1P_1>0 && k>=0 && arg2P_1<arg1P_1-arg2P_1*(-1+k) && arg2P_1>arg1P_1-k*arg2P_1 ], cost: 4+k

Computing asymptotic complexity for rule 21
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 22
   Simplified the guard:
     22: __init -> f152_0_gcd_EQ : arg1'=arg2P_1, arg2'=arg1P_1-k*arg2P_1, [ arg2P_1<arg1P_1 && k>=0 && arg2P_1<arg1P_1-arg2P_1*(-1+k) && arg2P_1>arg1P_1-k*arg2P_1 ], cost: 4+k
   Resulting cost 0 has complexity: Unknown

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Constant
   Cpx degree:  0
   Solved cost: 1
   Rule cost:   1
   Rule guard:  []

WORST_CASE(Omega(1),?)