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, arg3'=arg3P_1, [ arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
     16: f3 -> f4 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ 0<=arg1 && arg1<arg2 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 ], cost: 1
     17: f3 -> f5 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [ 0>arg1 && arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 ], cost: 1
     18: f3 -> f5 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, [ arg1>=arg2 && arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 ], cost: 1
      2: f4 -> f7 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg3P_3==1+arg1 && arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
      9: f7 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg3<arg1 && x28_1<0 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     10: f7 -> f8 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg3<arg1 && x55_1>0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     11: f7 -> f8 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg3>arg1 && x59_1<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     12: f7 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg3>arg1 && x63_1>0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
     14: f7 -> f14 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg3==arg1 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
     15: f7 -> f14 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ x67_1==0 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
      3: f9 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg3P_4==1+arg3 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1
      7: f12 -> f11 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      4: f10 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1==arg1P_5 && arg2==arg2P_5 && 0==arg3P_5 ], cost: 1
      8: f13 -> f11 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      5: f8 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg3<=arg2 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f8 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3>arg2 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
     13: f11 -> f7 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     19: f14 -> f6 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, [ arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 ], cost: 1
     20: f5 -> f6 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, [ arg1==arg1P_21 && arg2==arg2P_21 && arg3==arg3P_21 ], cost: 1
     21: __init -> f1 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_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, arg3'=arg3P_22, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
     16: f3 -> f4 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ 0<=arg1 && arg1<arg2 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 ], cost: 1
      2: f4 -> f7 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg3P_3==1+arg1 && arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
      9: f7 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg3<arg1 && x28_1<0 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     10: f7 -> f8 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg3<arg1 && x55_1>0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     11: f7 -> f8 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg3>arg1 && x59_1<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     12: f7 -> f8 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg3>arg1 && x63_1>0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
      3: f9 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg3P_4==1+arg3 && arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1
      7: f12 -> f11 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      4: f10 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1==arg1P_5 && arg2==arg2P_5 && 0==arg3P_5 ], cost: 1
      8: f13 -> f11 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      5: f8 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg3<=arg2 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f8 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3>arg2 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
     13: f11 -> f7 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     21: __init -> f1 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, [], 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
     16: f3 -> f4 : [ 0<=arg1 && arg1<arg2 ], cost: 1
      2: f4 -> f7 : arg3'=1+arg1, [], cost: 1
     10: f7 -> f8 : [ arg3<arg1 ], cost: 1
     12: f7 -> f8 : [ arg3>arg1 ], cost: 1
      3: f9 -> f12 : arg3'=1+arg3, [], cost: 1
      7: f12 -> f11 : [], cost: 1
      4: f10 -> f13 : arg3'=0, [], cost: 1
      8: f13 -> f11 : [], cost: 1
      5: f8 -> f9 : [ arg3<=arg2 ], cost: 1
      6: f8 -> f10 : [ arg3>arg2 ], cost: 1
     13: f11 -> f7 : [], cost: 1
     21: __init -> f1 : arg1'=arg1P_22, arg2'=arg2P_22, arg3'=arg3P_22, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     10: f7 -> f8 : [ arg3<arg1 ], cost: 1
     12: f7 -> f8 : [ arg3>arg1 ], cost: 1
     28: f8 -> f11 : arg3'=1+arg3, [ arg3<=arg2 ], cost: 3
     29: f8 -> f11 : arg3'=0, [ arg3>arg2 ], cost: 3
     13: f11 -> f7 : [], cost: 1
     25: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=1+arg1P_1, [ 0<=arg1P_1 && arg1P_1<arg2P_2 ], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     30: f7 -> f11 : arg3'=1+arg3, [ arg3<arg1 && arg3<=arg2 ], cost: 4
     31: f7 -> f11 : arg3'=0, [ arg3<arg1 && arg3>arg2 ], cost: 4
     32: f7 -> f11 : arg3'=1+arg3, [ arg3>arg1 && arg3<=arg2 ], cost: 4
     33: f7 -> f11 : arg3'=0, [ arg3>arg1 && arg3>arg2 ], cost: 4
     13: f11 -> f7 : [], cost: 1
     25: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=1+arg1P_1, [ 0<=arg1P_1 && arg1P_1<arg2P_2 ], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     34: f7 -> f7 : arg3'=1+arg3, [ arg3<arg1 && arg3<=arg2 ], cost: 5
     35: f7 -> f7 : arg3'=0, [ arg3<arg1 && arg3>arg2 ], cost: 5
     36: f7 -> f7 : arg3'=1+arg3, [ arg3>arg1 && arg3<=arg2 ], cost: 5
     37: f7 -> f7 : arg3'=0, [ arg3>arg1 && arg3>arg2 ], cost: 5
     25: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=1+arg1P_1, [ 0<=arg1P_1 && arg1P_1<arg2P_2 ], cost: 5

Accelerating simple loops of location 4.
   Accelerating the following rules:
     34: f7 -> f7 : arg3'=1+arg3, [ arg3<arg1 && arg3<=arg2 ], cost: 5
     35: f7 -> f7 : arg3'=0, [ arg3<arg1 && arg3>arg2 ], cost: 5
     36: f7 -> f7 : arg3'=1+arg3, [ arg3>arg1 && arg3<=arg2 ], cost: 5
     37: f7 -> f7 : arg3'=0, [ arg3>arg1 && arg3>arg2 ], cost: 5

   Accelerated rule 34 with backward acceleration, yielding the new rule 38.
   Accelerated rule 34 with backward acceleration, yielding the new rule 39.
   Accelerated rule 35 with non-termination, yielding the new rule 40.
   Accelerated rule 36 with backward acceleration, yielding the new rule 41.
   Accelerated rule 37 with non-termination, yielding the new rule 42.
[accelerate] Nesting with 3 inner and 4 outer candidates
   Nested simple loops 35 (outer loop) and 39 (inner loop) with Rule(4 | arg3<arg1, arg3>arg2, 1+arg2>=0, arg2<arg1, | NONTERM || 15 | ), resulting in the new rules: 43, 44.
   Nested simple loops 37 (outer loop) and 41 (inner loop) with Rule(4 | arg3>arg1, arg3>arg2, 0>arg1, 1+arg2>=0, | NONTERM || 15 | ), resulting in the new rules: 45, 46.
   Removing the simple loops: 34 35 36 37.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     38: f7 -> f7 : arg3'=arg1, [ -arg3+arg1>=0 && -1+arg1<=arg2 ], cost: -5*arg3+5*arg1
     39: f7 -> f7 : arg3'=1+arg2, [ 1+arg2-arg3>=0 && arg2<arg1 ], cost: 5+5*arg2-5*arg3
     40: f7 -> [15] : [ arg3<arg1 && arg3>arg2 && 0<arg1 && 0>arg2 ], cost: NONTERM
     41: f7 -> f7 : arg3'=1+arg2, [ arg3>arg1 && 1+arg2-arg3>=0 ], cost: 5+5*arg2-5*arg3
     42: f7 -> [15] : [ arg3>arg1 && arg3>arg2 && 0>arg1 && 0>arg2 ], cost: NONTERM
     43: f7 -> [15] : [ arg3<arg1 && arg3>arg2 && 1+arg2>=0 && arg2<arg1 ], cost: NONTERM
     44: f7 -> [15] : [ 1+arg2-arg3>=0 && 1+arg2<arg1 && 1+arg2>=0 ], cost: NONTERM
     45: f7 -> [15] : [ arg3>arg1 && arg3>arg2 && 0>arg1 && 1+arg2>=0 ], cost: NONTERM
     46: f7 -> [15] : [ arg3>arg1 && 1+arg2-arg3>=0 && 1+arg2>arg1 && 0>arg1 && 1+arg2>=0 ], cost: NONTERM
     25: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=1+arg1P_1, [ 0<=arg1P_1 && arg1P_1<arg2P_2 ], cost: 5

Chained accelerated rules (with incoming rules):
   Start location: __init
     25: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=1+arg1P_1, [ 0<=arg1P_1 && arg1P_1<arg2P_2 ], cost: 5
     47: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=1+arg2P_2, [ 0<=arg1P_1 && arg1P_1<arg2P_2 ], cost: 5-5*arg1P_1+5*arg2P_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     47: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=1+arg2P_2, [ 0<=arg1P_1 && arg1P_1<arg2P_2 ], cost: 5-5*arg1P_1+5*arg2P_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     47: __init -> f7 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=1+arg2P_2, [ 0<=arg1P_1 && arg1P_1<arg2P_2 ], cost: 5-5*arg1P_1+5*arg2P_2

Computing asymptotic complexity for rule 47
   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),?)