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 && 20==arg2P_2 ], cost: 1
     17: f3 -> f4 : arg1'=arg1P_18, arg2'=arg2P_18, [ 0<=arg1 && arg1<=arg2 && arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
     19: f3 -> f14 : arg1'=arg1P_20, arg2'=arg2P_20, [ 0>arg1 && arg1==arg1P_20 && arg2==arg2P_20 ], cost: 1
     20: f3 -> f14 : arg1'=arg1P_21, arg2'=arg2P_21, [ arg1>arg2 && arg1==arg1P_21 && arg2==arg2P_21 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, arg2'=arg2P_3, [ 0==arg1P_3 && arg2==arg2P_3 ], cost: 1
      3: f11 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 ], cost: 1
      8: f12 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      4: f9 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1P_5==1+arg1 && arg2==arg2P_5 ], cost: 1
      9: f13 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
      5: f5 -> f8 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg2 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      6: f5 -> f9 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1<arg2 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      7: f5 -> f9 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1>arg2 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
     15: f10 -> f7 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     10: f4 -> f5 : arg1'=arg1P_11, arg2'=arg2P_11, [ 0<arg1 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     11: f4 -> f5 : arg1'=arg1P_12, arg2'=arg2P_12, [ 0>arg1 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     12: f4 -> f5 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1<arg2 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
     13: f4 -> f5 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1>arg2 && arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     14: f4 -> f6 : arg1'=arg1P_15, arg2'=arg2P_15, [ 0==arg1 && arg1==arg2 && arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     16: f6 -> f7 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     18: f7 -> f3 : arg1'=arg1P_19, arg2'=arg2P_19, [ arg1==arg1P_19 && arg2==arg2P_19 ], cost: 1
     21: __init -> f1 : arg1'=arg1P_22, arg2'=arg2P_22, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     21: __init -> f1 : arg1'=arg1P_22, arg2'=arg2P_22, [], 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 && 20==arg2P_2 ], cost: 1
     17: f3 -> f4 : arg1'=arg1P_18, arg2'=arg2P_18, [ 0<=arg1 && arg1<=arg2 && arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, arg2'=arg2P_3, [ 0==arg1P_3 && arg2==arg2P_3 ], cost: 1
      3: f11 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 ], cost: 1
      8: f12 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      4: f9 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1P_5==1+arg1 && arg2==arg2P_5 ], cost: 1
      9: f13 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
      5: f5 -> f8 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg2 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      6: f5 -> f9 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1<arg2 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      7: f5 -> f9 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1>arg2 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
     15: f10 -> f7 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     10: f4 -> f5 : arg1'=arg1P_11, arg2'=arg2P_11, [ 0<arg1 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     11: f4 -> f5 : arg1'=arg1P_12, arg2'=arg2P_12, [ 0>arg1 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     12: f4 -> f5 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1<arg2 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
     13: f4 -> f5 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1>arg2 && arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
     14: f4 -> f6 : arg1'=arg1P_15, arg2'=arg2P_15, [ 0==arg1 && arg1==arg2 && arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     16: f6 -> f7 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     18: f7 -> f3 : arg1'=arg1P_19, arg2'=arg2P_19, [ arg1==arg1P_19 && arg2==arg2P_19 ], cost: 1
     21: __init -> f1 : arg1'=arg1P_22, arg2'=arg2P_22, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      1: f2 -> f3 : arg2'=20, [], cost: 1
     17: f3 -> f4 : [ 0<=arg1 && arg1<=arg2 ], cost: 1
      2: f8 -> f11 : arg1'=0, [], cost: 1
      3: f11 -> f12 : arg2'=-1+arg2, [], cost: 1
      8: f12 -> f10 : [], cost: 1
      4: f9 -> f13 : arg1'=1+arg1, [], cost: 1
      9: f13 -> f10 : [], cost: 1
      5: f5 -> f8 : [ arg1==arg2 ], cost: 1
      6: f5 -> f9 : [ arg1<arg2 ], cost: 1
      7: f5 -> f9 : [ arg1>arg2 ], cost: 1
     15: f10 -> f7 : [], cost: 1
     10: f4 -> f5 : [ 0<arg1 ], cost: 1
     11: f4 -> f5 : [ 0>arg1 ], cost: 1
     12: f4 -> f5 : [ arg1<arg2 ], cost: 1
     13: f4 -> f5 : [ arg1>arg2 ], cost: 1
     14: f4 -> f6 : [ 0==arg1 && arg1==arg2 ], cost: 1
     16: f6 -> f7 : [], cost: 1
     18: f7 -> f3 : [], cost: 1
     21: __init -> f1 : arg1'=arg1P_22, arg2'=arg2P_22, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     17: f3 -> f4 : [ 0<=arg1 && arg1<=arg2 ], cost: 1
     28: f9 -> f10 : arg1'=1+arg1, [], cost: 2
      6: f5 -> f9 : [ arg1<arg2 ], cost: 1
      7: f5 -> f9 : [ arg1>arg2 ], cost: 1
     27: f5 -> f10 : arg1'=0, arg2'=-1+arg2, [ arg1==arg2 ], cost: 4
     15: f10 -> f7 : [], cost: 1
     10: f4 -> f5 : [ 0<arg1 ], cost: 1
     11: f4 -> f5 : [ 0>arg1 ], cost: 1
     12: f4 -> f5 : [ arg1<arg2 ], cost: 1
     13: f4 -> f5 : [ arg1>arg2 ], cost: 1
     24: f4 -> f7 : [ 0==arg1 && arg1==arg2 ], cost: 2
     18: f7 -> f3 : [], cost: 1
     23: __init -> f3 : arg1'=arg1P_1, arg2'=20, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     29: f3 -> f5 : [ arg1<=arg2 && 0<arg1 ], cost: 2
     30: f3 -> f5 : [ 0<=arg1 && arg1<arg2 ], cost: 2
     31: f3 -> f7 : [ 0==arg1 && arg1==arg2 ], cost: 3
     34: f5 -> f7 : arg1'=0, arg2'=-1+arg2, [ arg1==arg2 ], cost: 5
     35: f5 -> f7 : arg1'=1+arg1, [ arg1<arg2 ], cost: 4
     36: f5 -> f7 : arg1'=1+arg1, [ arg1>arg2 ], cost: 4
     18: f7 -> f3 : [], cost: 1
     23: __init -> f3 : arg1'=arg1P_1, arg2'=20, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     40: f3 -> f3 : [ 0==arg1 && arg1==arg2 ], cost: 4
     41: f3 -> f3 : arg1'=0, arg2'=-1+arg2, [ 0<arg1 && arg1==arg2 ], cost: 8
     42: f3 -> f3 : arg1'=1+arg1, [ 0<arg1 && arg1<arg2 ], cost: 7
     43: f3 -> f3 : arg1'=1+arg1, [ 0<=arg1 && arg1<arg2 ], cost: 7
     23: __init -> f3 : arg1'=arg1P_1, arg2'=20, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     40: f3 -> f3 : [ 0==arg1 && arg1==arg2 ], cost: 4
     41: f3 -> f3 : arg1'=0, arg2'=-1+arg2, [ 0<arg1 && arg1==arg2 ], cost: 8
     42: f3 -> f3 : arg1'=1+arg1, [ 0<arg1 && arg1<arg2 ], cost: 7
     43: f3 -> f3 : arg1'=1+arg1, [ 0<=arg1 && arg1<arg2 ], cost: 7

   Accelerated rule 40 with non-termination, yielding the new rule 44.
   Failed to prove monotonicity of the guard of rule 41.
   Accelerated rule 42 with backward acceleration, yielding the new rule 45.
   Accelerated rule 43 with backward acceleration, yielding the new rule 46.
[accelerate] Nesting with 3 inner and 3 outer candidates
   Nested simple loops 41 (outer loop) and 46 (inner loop) with Rule(2 | 0<=arg1, arg2-arg1>=0, arg2>=1, 0<1, | 23/2*arg2+7/2*arg2^2 || 2 | 0=0, 1=0, ), resulting in the new rules: 47, 48.
   Removing the simple loops: 40 41 42 43.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     44: f3 -> [15] : [ 0==arg1 && arg1==arg2 ], cost: NONTERM
     45: f3 -> f3 : arg1'=arg2, [ 0<arg1 && arg2-arg1>=0 ], cost: 7*arg2-7*arg1
     46: f3 -> f3 : arg1'=arg2, [ 0<=arg1 && arg2-arg1>=0 ], cost: 7*arg2-7*arg1
     47: f3 -> f3 : arg1'=0, arg2'=0, [ 0<=arg1 && arg2-arg1>=0 && arg2>=1 ], cost: 23/2*arg2+7/2*arg2^2
     48: f3 -> f3 : arg1'=0, arg2'=0, [ 0<arg1 && arg1==arg2 && -1+arg2>=1 ], cost: -7/2+23/2*arg2+7/2*(-1+arg2)^2
     23: __init -> f3 : arg1'=arg1P_1, arg2'=20, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     23: __init -> f3 : arg1'=arg1P_1, arg2'=20, [], cost: 3
     49: __init -> f3 : arg1'=20, arg2'=20, [ 0<arg1P_1 && 20-arg1P_1>=0 ], cost: 143-7*arg1P_1
     50: __init -> f3 : arg1'=20, arg2'=20, [ 0<=arg1P_1 && 20-arg1P_1>=0 ], cost: 143-7*arg1P_1
     51: __init -> f3 : arg1'=0, arg2'=0, [], cost: 1633
     52: __init -> f3 : arg1'=0, arg2'=0, [], cost: 1493

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     49: __init -> f3 : arg1'=20, arg2'=20, [ 0<arg1P_1 && 20-arg1P_1>=0 ], cost: 143-7*arg1P_1
     50: __init -> f3 : arg1'=20, arg2'=20, [ 0<=arg1P_1 && 20-arg1P_1>=0 ], cost: 143-7*arg1P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     49: __init -> f3 : arg1'=20, arg2'=20, [ 0<arg1P_1 && 20-arg1P_1>=0 ], cost: 143-7*arg1P_1
     50: __init -> f3 : arg1'=20, arg2'=20, [ 0<=arg1P_1 && 20-arg1P_1>=0 ], cost: 143-7*arg1P_1

Computing asymptotic complexity for rule 49
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 50
   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),?)