WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1
     21: f3 -> f4 : arg1'=arg1P_22, arg2'=arg2P_22, [ arg1>0 && arg2>0 && arg1==arg1P_22 && arg2==arg2P_22 ], cost: 1
     23: f3 -> f20 : arg1'=arg1P_24, arg2'=arg2P_24, [ arg1<=0 && arg1==arg1P_24 && arg2==arg2P_24 ], cost: 1
     24: f3 -> f20 : arg1'=arg1P_25, arg2'=arg2P_25, [ arg2<=0 && arg1==arg1P_25 && arg2==arg2P_25 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==-1+arg1 && arg1==arg1P_3 ], cost: 1
      6: f11 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      3: f9 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 ], cost: 1
      7: f12 -> f10 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      4: f5 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1<arg2 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f5 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1>=arg2 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      8: f10 -> f13 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg2==arg2P_9 ], cost: 1
     19: f13 -> f7 : arg1'=arg1P_20, arg2'=arg2P_20, [ arg1==arg1P_20 && arg2==arg2P_20 ], cost: 1
      9: f14 -> f17 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1P_10==-1+arg1 && arg2==arg2P_10 ], cost: 1
     13: f17 -> f16 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     10: f15 -> f18 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1P_11==-1+arg2 && arg2==arg2P_11 ], cost: 1
     14: f18 -> f16 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     11: f6 -> f14 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg1<arg2 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     12: f6 -> f15 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1>=arg2 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
     15: f16 -> f19 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg1==arg1P_16 ], cost: 1
     20: f19 -> f7 : arg1'=arg1P_21, arg2'=arg2P_21, [ arg1==arg1P_21 && arg2==arg2P_21 ], cost: 1
     16: f4 -> f5 : arg1'=arg1P_17, arg2'=arg2P_17, [ x36_1<0 && arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     17: f4 -> f5 : arg1'=arg1P_18, arg2'=arg2P_18, [ x61_1>0 && arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
     18: f4 -> f6 : arg1'=arg1P_19, arg2'=arg2P_19, [ x39_1==0 && arg1==arg1P_19 && arg2==arg2P_19 ], cost: 1
     22: f7 -> f3 : arg1'=arg1P_23, arg2'=arg2P_23, [ arg1==arg1P_23 && arg2==arg2P_23 ], cost: 1
     25: __init -> f1 : arg1'=arg1P_26, arg2'=arg2P_26, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     25: __init -> f1 : arg1'=arg1P_26, arg2'=arg2P_26, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1
     21: f3 -> f4 : arg1'=arg1P_22, arg2'=arg2P_22, [ arg1>0 && arg2>0 && arg1==arg1P_22 && arg2==arg2P_22 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==-1+arg1 && arg1==arg1P_3 ], cost: 1
      6: f11 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      3: f9 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 ], cost: 1
      7: f12 -> f10 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      4: f5 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1<arg2 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f5 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1>=arg2 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      8: f10 -> f13 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg2==arg2P_9 ], cost: 1
     19: f13 -> f7 : arg1'=arg1P_20, arg2'=arg2P_20, [ arg1==arg1P_20 && arg2==arg2P_20 ], cost: 1
      9: f14 -> f17 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1P_10==-1+arg1 && arg2==arg2P_10 ], cost: 1
     13: f17 -> f16 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     10: f15 -> f18 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1P_11==-1+arg2 && arg2==arg2P_11 ], cost: 1
     14: f18 -> f16 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     11: f6 -> f14 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg1<arg2 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     12: f6 -> f15 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1>=arg2 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
     15: f16 -> f19 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg1==arg1P_16 ], cost: 1
     20: f19 -> f7 : arg1'=arg1P_21, arg2'=arg2P_21, [ arg1==arg1P_21 && arg2==arg2P_21 ], cost: 1
     16: f4 -> f5 : arg1'=arg1P_17, arg2'=arg2P_17, [ x36_1<0 && arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     17: f4 -> f5 : arg1'=arg1P_18, arg2'=arg2P_18, [ x61_1>0 && arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
     18: f4 -> f6 : arg1'=arg1P_19, arg2'=arg2P_19, [ x39_1==0 && arg1==arg1P_19 && arg2==arg2P_19 ], cost: 1
     22: f7 -> f3 : arg1'=arg1P_23, arg2'=arg2P_23, [ arg1==arg1P_23 && arg2==arg2P_23 ], cost: 1
     25: __init -> f1 : arg1'=arg1P_26, arg2'=arg2P_26, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      1: f2 -> f3 : arg2'=arg2P_2, [], cost: 1
     21: f3 -> f4 : [ arg1>0 && arg2>0 ], cost: 1
      2: f8 -> f11 : arg2'=-1+arg1, [], cost: 1
      6: f11 -> f10 : [], cost: 1
      3: f9 -> f12 : arg2'=-1+arg2, [], cost: 1
      7: f12 -> f10 : [], cost: 1
      4: f5 -> f8 : [ arg1<arg2 ], cost: 1
      5: f5 -> f9 : [ arg1>=arg2 ], cost: 1
      8: f10 -> f13 : arg1'=arg1P_9, [], cost: 1
     19: f13 -> f7 : [], cost: 1
      9: f14 -> f17 : arg1'=-1+arg1, [], cost: 1
     13: f17 -> f16 : [], cost: 1
     10: f15 -> f18 : arg1'=-1+arg2, [], cost: 1
     14: f18 -> f16 : [], cost: 1
     11: f6 -> f14 : [ arg1<arg2 ], cost: 1
     12: f6 -> f15 : [ arg1>=arg2 ], cost: 1
     15: f16 -> f19 : arg2'=arg2P_16, [], cost: 1
     20: f19 -> f7 : [], cost: 1
     17: f4 -> f5 : [], cost: 1
     18: f4 -> f6 : [], cost: 1
     22: f7 -> f3 : [], cost: 1
     25: __init -> f1 : arg1'=arg1P_26, arg2'=arg2P_26, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     21: f3 -> f4 : [ arg1>0 && arg2>0 ], cost: 1
     30: f5 -> f10 : arg2'=-1+arg1, [ arg1<arg2 ], cost: 3
     31: f5 -> f10 : arg2'=-1+arg2, [ arg1>=arg2 ], cost: 3
     32: f10 -> f7 : arg1'=arg1P_9, [], cost: 2
     35: f6 -> f16 : arg1'=-1+arg1, [ arg1<arg2 ], cost: 3
     36: f6 -> f16 : arg1'=-1+arg2, [ arg1>=arg2 ], cost: 3
     37: f16 -> f7 : arg2'=arg2P_16, [], cost: 2
     17: f4 -> f5 : [], cost: 1
     18: f4 -> f6 : [], cost: 1
     22: f7 -> f3 : [], cost: 1
     27: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     38: f3 -> f5 : [ arg1>0 && arg2>0 ], cost: 2
     39: f3 -> f6 : [ arg1>0 && arg2>0 ], cost: 2
     40: f5 -> f7 : arg1'=arg1P_9, arg2'=-1+arg1, [ arg1<arg2 ], cost: 5
     41: f5 -> f7 : arg1'=arg1P_9, arg2'=-1+arg2, [ arg1>=arg2 ], cost: 5
     42: f6 -> f7 : arg1'=-1+arg1, arg2'=arg2P_16, [ arg1<arg2 ], cost: 5
     43: f6 -> f7 : arg1'=-1+arg2, arg2'=arg2P_16, [ arg1>=arg2 ], cost: 5
     22: f7 -> f3 : [], cost: 1
     27: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     44: f3 -> f7 : arg1'=arg1P_9, arg2'=-1+arg1, [ arg1>0 && arg2>0 && arg1<arg2 ], cost: 7
     45: f3 -> f7 : arg1'=arg1P_9, arg2'=-1+arg2, [ arg1>0 && arg2>0 && arg1>=arg2 ], cost: 7
     46: f3 -> f7 : arg1'=-1+arg1, arg2'=arg2P_16, [ arg1>0 && arg2>0 && arg1<arg2 ], cost: 7
     47: f3 -> f7 : arg1'=-1+arg2, arg2'=arg2P_16, [ arg1>0 && arg2>0 && arg1>=arg2 ], cost: 7
     22: f7 -> f3 : [], cost: 1
     27: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     48: f3 -> f3 : arg1'=arg1P_9, arg2'=-1+arg1, [ arg1>0 && arg2>0 && arg1<arg2 ], cost: 8
     49: f3 -> f3 : arg1'=arg1P_9, arg2'=-1+arg2, [ arg1>0 && arg2>0 && arg1>=arg2 ], cost: 8
     50: f3 -> f3 : arg1'=-1+arg1, arg2'=arg2P_16, [ arg1>0 && arg2>0 && arg1<arg2 ], cost: 8
     51: f3 -> f3 : arg1'=-1+arg2, arg2'=arg2P_16, [ arg1>0 && arg2>0 && arg1>=arg2 ], cost: 8
     27: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     48: f3 -> f3 : arg1'=arg1P_9, arg2'=-1+arg1, [ arg1>0 && arg2>0 && arg1<arg2 ], cost: 8
     49: f3 -> f3 : arg1'=arg1P_9, arg2'=-1+arg2, [ arg1>0 && arg2>0 && arg1>=arg2 ], cost: 8
     50: f3 -> f3 : arg1'=-1+arg1, arg2'=arg2P_16, [ arg1>0 && arg2>0 && arg1<arg2 ], cost: 8
     51: f3 -> f3 : arg1'=-1+arg2, arg2'=arg2P_16, [ arg1>0 && arg2>0 && arg1>=arg2 ], cost: 8

   Failed to prove monotonicity of the guard of rule 48.
[test] deduced pseudo-invariant -1+arg1P_9-arg1<=0, also trying 1-arg1P_9+arg1<=-1
[test] deduced pseudo-invariant 5+4*arg1P_9+2*arg2+arg1<=0, also trying -5-4*arg1P_9-2*arg2-arg1<=-1
   Failed to prove monotonicity of the guard of rule 49.
[test] deduced pseudo-invariant -1+arg2-arg2P_16<=0, also trying 1-arg2+arg2P_16<=-1
   Accelerated rule 50 with backward acceleration, yielding the new rule 52.
   Failed to prove monotonicity of the guard of rule 51.
[accelerate] Nesting with 4 inner and 4 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     48: f3 -> f3 : arg1'=arg1P_9, arg2'=-1+arg1, [ arg1>0 && arg2>0 && arg1<arg2 ], cost: 8
     49: f3 -> f3 : arg1'=arg1P_9, arg2'=-1+arg2, [ arg1>0 && arg2>0 && arg1>=arg2 ], cost: 8
     50: f3 -> f3 : arg1'=-1+arg1, arg2'=arg2P_16, [ arg1>0 && arg2>0 && arg1<arg2 ], cost: 8
     51: f3 -> f3 : arg1'=-1+arg2, arg2'=arg2P_16, [ arg1>0 && arg2>0 && arg1>=arg2 ], cost: 8
     52: f3 -> f3 : arg1'=0, arg2'=arg2P_16, [ arg2>0 && arg1<arg2 && -1+arg2-arg2P_16<=0 && arg1>=1 ], cost: 8*arg1
     27: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     27: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3
     53: __init -> f3 : arg1'=arg1P_9, arg2'=-1+arg1P_1, [ arg1P_1>0 ], cost: 11
     54: __init -> f3 : arg1'=arg1P_9, arg2'=-1+arg2P_2, [ arg2P_2>0 ], cost: 11
     55: __init -> f3 : arg1'=-1+arg1P_1, arg2'=arg2P_16, [ arg1P_1>0 ], cost: 11
     56: __init -> f3 : arg1'=-1+arg2P_2, arg2'=arg2P_16, [ arg2P_2>0 ], cost: 11
     57: __init -> f3 : arg1'=0, arg2'=arg2P_16, [ arg1P_1>=1 && 1<=1+arg2P_16 && 1+arg1P_1<=1+arg2P_16 ], cost: 3+8*arg1P_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     57: __init -> f3 : arg1'=0, arg2'=arg2P_16, [ arg1P_1>=1 && 1<=1+arg2P_16 && 1+arg1P_1<=1+arg2P_16 ], cost: 3+8*arg1P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     57: __init -> f3 : arg1'=0, arg2'=arg2P_16, [ arg1P_1>=1 && 1<=1+arg2P_16 && 1+arg1P_1<=1+arg2P_16 ], cost: 3+8*arg1P_1

Computing asymptotic complexity for rule 57
   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),?)