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
     20: f3 -> f4 : arg1'=arg1P_21, arg2'=arg2P_21, [ arg1<30 && arg1==arg1P_21 && arg2==arg2P_21 ], cost: 1
     22: f3 -> f19 : arg1'=arg1P_23, arg2'=arg2P_23, [ arg1>=30 && arg1==arg1P_23 && arg2==arg2P_23 ], cost: 1
      2: f6 -> f9 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==7+arg2 && arg1==arg1P_3 ], cost: 1
      6: f9 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      3: f7 -> f10 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==2+arg2 && arg1==arg1P_4 ], cost: 1
      7: f10 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2>5 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f5 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2<=5 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
     10: f8 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg2>=10 && arg2<=12 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     11: f8 -> f12 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg2<10 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     12: f8 -> f12 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg2>12 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
      8: f11 -> f14 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1P_9==10+arg1 && arg2==arg2P_9 ], cost: 1
     13: f14 -> f13 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
      9: f12 -> f15 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1P_10==1+arg1 && arg2==arg2P_10 ], cost: 1
     14: f15 -> f13 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     16: f13 -> f4 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     15: f4 -> f5 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg2<arg1 && arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     17: f4 -> f16 : arg1'=arg1P_18, arg2'=arg2P_18, [ arg2>=arg1 && arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
     18: f16 -> f17 : arg1'=arg1P_19, arg2'=arg2P_19, [ arg1P_19==2+arg1 && arg2==arg2P_19 ], cost: 1
     19: f17 -> f18 : arg1'=arg1P_20, arg2'=arg2P_20, [ arg2P_20==-10+arg2 && arg1==arg1P_20 ], cost: 1
     21: f18 -> f3 : arg1'=arg1P_22, arg2'=arg2P_22, [ arg1==arg1P_22 && arg2==arg2P_22 ], cost: 1
     23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, [], 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
     20: f3 -> f4 : arg1'=arg1P_21, arg2'=arg2P_21, [ arg1<30 && arg1==arg1P_21 && arg2==arg2P_21 ], cost: 1
      2: f6 -> f9 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==7+arg2 && arg1==arg1P_3 ], cost: 1
      6: f9 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      3: f7 -> f10 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==2+arg2 && arg1==arg1P_4 ], cost: 1
      7: f10 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      4: f5 -> f6 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2>5 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f5 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2<=5 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
     10: f8 -> f11 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg2>=10 && arg2<=12 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     11: f8 -> f12 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg2<10 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     12: f8 -> f12 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg2>12 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
      8: f11 -> f14 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1P_9==10+arg1 && arg2==arg2P_9 ], cost: 1
     13: f14 -> f13 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
      9: f12 -> f15 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1P_10==1+arg1 && arg2==arg2P_10 ], cost: 1
     14: f15 -> f13 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     16: f13 -> f4 : arg1'=arg1P_17, arg2'=arg2P_17, [ arg1==arg1P_17 && arg2==arg2P_17 ], cost: 1
     15: f4 -> f5 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg2<arg1 && arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     17: f4 -> f16 : arg1'=arg1P_18, arg2'=arg2P_18, [ arg2>=arg1 && arg1==arg1P_18 && arg2==arg2P_18 ], cost: 1
     18: f16 -> f17 : arg1'=arg1P_19, arg2'=arg2P_19, [ arg1P_19==2+arg1 && arg2==arg2P_19 ], cost: 1
     19: f17 -> f18 : arg1'=arg1P_20, arg2'=arg2P_20, [ arg2P_20==-10+arg2 && arg1==arg1P_20 ], cost: 1
     21: f18 -> f3 : arg1'=arg1P_22, arg2'=arg2P_22, [ arg1==arg1P_22 && arg2==arg2P_22 ], cost: 1
     23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, [], 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
     20: f3 -> f4 : [ arg1<30 ], cost: 1
      2: f6 -> f9 : arg2'=7+arg2, [], cost: 1
      6: f9 -> f8 : [], cost: 1
      3: f7 -> f10 : arg2'=2+arg2, [], cost: 1
      7: f10 -> f8 : [], cost: 1
      4: f5 -> f6 : [ arg2>5 ], cost: 1
      5: f5 -> f7 : [ arg2<=5 ], cost: 1
     10: f8 -> f11 : [ arg2>=10 && arg2<=12 ], cost: 1
     11: f8 -> f12 : [ arg2<10 ], cost: 1
     12: f8 -> f12 : [ arg2>12 ], cost: 1
      8: f11 -> f14 : arg1'=10+arg1, [], cost: 1
     13: f14 -> f13 : [], cost: 1
      9: f12 -> f15 : arg1'=1+arg1, [], cost: 1
     14: f15 -> f13 : [], cost: 1
     16: f13 -> f4 : [], cost: 1
     15: f4 -> f5 : [ arg2<arg1 ], cost: 1
     17: f4 -> f16 : [ arg2>=arg1 ], cost: 1
     18: f16 -> f17 : arg1'=2+arg1, [], cost: 1
     19: f17 -> f18 : arg2'=-10+arg2, [], cost: 1
     21: f18 -> f3 : [], cost: 1
     23: __init -> f1 : arg1'=arg1P_24, arg2'=arg2P_24, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     20: f3 -> f4 : [ arg1<30 ], cost: 1
     31: f5 -> f8 : arg2'=7+arg2, [ arg2>5 ], cost: 3
     32: f5 -> f8 : arg2'=2+arg2, [ arg2<=5 ], cost: 3
     11: f8 -> f12 : [ arg2<10 ], cost: 1
     12: f8 -> f12 : [ arg2>12 ], cost: 1
     34: f8 -> f13 : arg1'=10+arg1, [ arg2>=10 && arg2<=12 ], cost: 3
     35: f12 -> f13 : arg1'=1+arg1, [], cost: 2
     16: f13 -> f4 : [], cost: 1
     15: f4 -> f5 : [ arg2<arg1 ], cost: 1
     28: f4 -> f3 : arg1'=2+arg1, arg2'=-10+arg2, [ arg2>=arg1 ], cost: 4
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     20: f3 -> f4 : [ arg1<30 ], cost: 1
     40: f8 -> f4 : arg1'=10+arg1, [ arg2>=10 && arg2<=12 ], cost: 4
     41: f8 -> f4 : arg1'=1+arg1, [ arg2<10 ], cost: 4
     42: f8 -> f4 : arg1'=1+arg1, [ arg2>12 ], cost: 4
     28: f4 -> f3 : arg1'=2+arg1, arg2'=-10+arg2, [ arg2>=arg1 ], cost: 4
     36: f4 -> f8 : arg2'=7+arg2, [ arg2<arg1 && arg2>5 ], cost: 4
     37: f4 -> f8 : arg2'=2+arg2, [ arg2<arg1 && arg2<=5 ], cost: 4
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     20: f3 -> f4 : [ arg1<30 ], cost: 1
     28: f4 -> f3 : arg1'=2+arg1, arg2'=-10+arg2, [ arg2>=arg1 ], cost: 4
     43: f4 -> f4 : arg1'=1+arg1, arg2'=7+arg2, [ arg2<arg1 && arg2>5 ], cost: 8
     44: f4 -> f4 : arg1'=1+arg1, arg2'=2+arg2, [ arg2<arg1 && arg2<=5 ], cost: 8
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 14.
   Accelerating the following rules:
     43: f4 -> f4 : arg1'=1+arg1, arg2'=7+arg2, [ arg2<arg1 && arg2>5 ], cost: 8
     44: f4 -> f4 : arg1'=1+arg1, arg2'=2+arg2, [ arg2<arg1 && arg2<=5 ], cost: 8

   Accelerated rule 43 with backward acceleration, yielding the new rule 45.
   Accelerated rule 44 with backward acceleration, yielding the new rule 46.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 43 44.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     20: f3 -> f4 : [ arg1<30 ], cost: 1
     28: f4 -> f3 : arg1'=2+arg1, arg2'=-10+arg2, [ arg2>=arg1 ], cost: 4
     45: f4 -> f4 : arg1'=k+arg1, arg2'=7*k+arg2, [ arg2>5 && k>=0 && -7+7*k+arg2<-1+k+arg1 ], cost: 8*k
     46: f4 -> f4 : arg1'=arg1+k_1, arg2'=arg2+2*k_1, [ k_1>=0 && -2+arg2+2*k_1<-1+arg1+k_1 && -2+arg2+2*k_1<=5 ], cost: 8*k_1
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     20: f3 -> f4 : [ arg1<30 ], cost: 1
     47: f3 -> f4 : arg1'=k+arg1, arg2'=7*k+arg2, [ arg1<30 && arg2>5 && k>=0 && -7+7*k+arg2<-1+k+arg1 ], cost: 1+8*k
     48: f3 -> f4 : arg1'=arg1+k_1, arg2'=arg2+2*k_1, [ arg1<30 && k_1>=0 && -2+arg2+2*k_1<-1+arg1+k_1 && -2+arg2+2*k_1<=5 ], cost: 1+8*k_1
     28: f4 -> f3 : arg1'=2+arg1, arg2'=-10+arg2, [ arg2>=arg1 ], cost: 4
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     49: f3 -> f3 : arg1'=2+arg1, arg2'=-10+arg2, [ arg1<30 && arg2>=arg1 ], cost: 5
     50: f3 -> f3 : arg1'=2+k+arg1, arg2'=-10+7*k+arg2, [ arg1<30 && arg2>5 && k>=0 && -7+7*k+arg2<-1+k+arg1 && 7*k+arg2>=k+arg1 ], cost: 5+8*k
     51: f3 -> f3 : arg1'=2+arg1+k_1, arg2'=-10+arg2+2*k_1, [ arg1<30 && k_1>=0 && -2+arg2+2*k_1<-1+arg1+k_1 && -2+arg2+2*k_1<=5 && arg2+2*k_1>=arg1+k_1 ], cost: 5+8*k_1
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 2.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     49: f3 -> f3 : arg1'=2+arg1, arg2'=-10+arg2, [ arg1<30 && arg2>=arg1 ], cost: 5
     50: f3 -> f3 : arg1'=2+k+arg1, arg2'=-10+7*k+arg2, [ arg1<30 && arg2>5 && k>=0 && -7+7*k+arg2<-1+k+arg1 && 7*k+arg2>=k+arg1 ], cost: 5+8*k
     51: f3 -> f3 : arg1'=2-arg2+2*arg1, arg2'=-10-arg2+2*arg1, [ arg1<30 && -arg2+arg1>=0 && -2-arg2+2*arg1<=5 ], cost: 5-8*arg2+8*arg1

   Accelerated rule 49 with backward acceleration, yielding the new rule 52.
   Failed to prove monotonicity of the guard of rule 50.
   Found no closed form for 51.
[accelerate] Nesting with 2 inner and 3 outer candidates
   Removing the simple loops: 49.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     50: f3 -> f3 : arg1'=2+k+arg1, arg2'=-10+7*k+arg2, [ arg1<30 && arg2>5 && k>=0 && -7+7*k+arg2<-1+k+arg1 && 7*k+arg2>=k+arg1 ], cost: 5+8*k
     51: f3 -> f3 : arg1'=2-arg2+2*arg1, arg2'=-10-arg2+2*arg1, [ arg1<30 && -arg2+arg1>=0 && -2-arg2+2*arg1<=5 ], cost: 5-8*arg2+8*arg1
     52: f3 -> f3 : arg1'=2*k_2+arg1, arg2'=arg2-10*k_2, [ k_2>=0 && -2+2*k_2+arg1<30 && 10+arg2-10*k_2>=-2+2*k_2+arg1 ], cost: 5*k_2
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     25: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3
     53: __init -> f3 : arg1'=2+arg1P_1+k, arg2'=-10+arg2P_2+7*k, [ arg1P_1<30 && arg2P_2>5 && k>=0 && -7+arg2P_2+7*k<-1+arg1P_1+k && arg2P_2+7*k>=arg1P_1+k ], cost: 8+8*k
     54: __init -> f3 : arg1'=2-arg2P_2+2*arg1P_1, arg2'=-10-arg2P_2+2*arg1P_1, [ arg1P_1<30 && -arg2P_2+arg1P_1>=0 && -2-arg2P_2+2*arg1P_1<=5 ], cost: 8-8*arg2P_2+8*arg1P_1
     55: __init -> f3 : arg1'=arg1P_1+2*k_2, arg2'=arg2P_2-10*k_2, [ k_2>=0 && -2+arg1P_1+2*k_2<30 && 10+arg2P_2-10*k_2>=-2+arg1P_1+2*k_2 ], cost: 3+5*k_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     53: __init -> f3 : arg1'=2+arg1P_1+k, arg2'=-10+arg2P_2+7*k, [ arg1P_1<30 && arg2P_2>5 && k>=0 && -7+arg2P_2+7*k<-1+arg1P_1+k && arg2P_2+7*k>=arg1P_1+k ], cost: 8+8*k
     54: __init -> f3 : arg1'=2-arg2P_2+2*arg1P_1, arg2'=-10-arg2P_2+2*arg1P_1, [ arg1P_1<30 && -arg2P_2+arg1P_1>=0 && -2-arg2P_2+2*arg1P_1<=5 ], cost: 8-8*arg2P_2+8*arg1P_1
     55: __init -> f3 : arg1'=arg1P_1+2*k_2, arg2'=arg2P_2-10*k_2, [ k_2>=0 && -2+arg1P_1+2*k_2<30 && 10+arg2P_2-10*k_2>=-2+arg1P_1+2*k_2 ], cost: 3+5*k_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     53: __init -> f3 : arg1'=2+arg1P_1+k, arg2'=-10+arg2P_2+7*k, [ arg1P_1<30 && arg2P_2>5 && k>=0 && -7+arg2P_2+7*k<-1+arg1P_1+k && arg2P_2+7*k>=arg1P_1+k ], cost: 8+8*k
     54: __init -> f3 : arg1'=2-arg2P_2+2*arg1P_1, arg2'=-10-arg2P_2+2*arg1P_1, [ arg1P_1<30 && -arg2P_2+arg1P_1>=0 && -2-arg2P_2+2*arg1P_1<=5 ], cost: 8-8*arg2P_2+8*arg1P_1
     55: __init -> f3 : arg1'=arg1P_1+2*k_2, arg2'=arg2P_2-10*k_2, [ k_2>=0 && -2+arg1P_1+2*k_2<30 && 10+arg2P_2-10*k_2>=-2+arg1P_1+2*k_2 ], cost: 3+5*k_2

Computing asymptotic complexity for rule 54
   Simplified the guard:
     54: __init -> f3 : arg1'=2-arg2P_2+2*arg1P_1, arg2'=-10-arg2P_2+2*arg1P_1, [ -arg2P_2+arg1P_1>=0 && -2-arg2P_2+2*arg1P_1<=5 ], cost: 8-8*arg2P_2+8*arg1P_1
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 55
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 53
   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),?)