WORST_CASE(INF,?)

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

Initial linear ITS problem
   Start location: l4
      0: l0 -> l1 : x^0'=x^post_1, y^0'=y^post_1, [ 1<=y^0 && y^post_1==-1+y^0 && x^0==x^post_1 ], cost: 1
      2: l0 -> l2 : x^0'=x^post_3, y^0'=y^post_3, [ y^0<=0 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1
      1: l1 -> l0 : x^0'=x^post_2, y^0'=y^post_2, [ x^0==x^post_2 && y^0==y^post_2 ], cost: 1
      3: l2 -> l0 : x^0'=x^post_4, y^0'=y^post_4, [ 1<=x^0 && x^post_4==-1+x^0 && y^post_4==y^post_4 ], cost: 1
      4: l3 -> l2 : x^0'=x^post_5, y^0'=y^post_5, [ x^0==x^post_5 && y^0==y^post_5 ], cost: 1
      5: l4 -> l3 : x^0'=x^post_6, y^0'=y^post_6, [ x^0==x^post_6 && y^0==y^post_6 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: l4 -> l3 : x^0'=x^post_6, y^0'=y^post_6, [ x^0==x^post_6 && y^0==y^post_6 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      0: l0 -> l1 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 1
      2: l0 -> l2 : [ y^0<=0 ], cost: 1
      1: l1 -> l0 : [], cost: 1
      3: l2 -> l0 : x^0'=-1+x^0, y^0'=y^post_4, [ 1<=x^0 ], cost: 1
      4: l3 -> l2 : [], cost: 1
      5: l4 -> l3 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      2: l0 -> l2 : [ y^0<=0 ], cost: 1
      7: l0 -> l0 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 2
      3: l2 -> l0 : x^0'=-1+x^0, y^0'=y^post_4, [ 1<=x^0 ], cost: 1
      6: l4 -> l2 : [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
      7: l0 -> l0 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 2

   Accelerated rule 7 with metering function y^0, yielding the new rule 8.
   Removing the simple loops: 7.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
      2: l0 -> l2 : [ y^0<=0 ], cost: 1
      8: l0 -> l0 : y^0'=0, [ 1<=y^0 ], cost: 2*y^0
      3: l2 -> l0 : x^0'=-1+x^0, y^0'=y^post_4, [ 1<=x^0 ], cost: 1
      6: l4 -> l2 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      2: l0 -> l2 : [ y^0<=0 ], cost: 1
      3: l2 -> l0 : x^0'=-1+x^0, y^0'=y^post_4, [ 1<=x^0 ], cost: 1
      9: l2 -> l0 : x^0'=-1+x^0, y^0'=0, [ 1<=x^0 && 1<=y^post_4 ], cost: 1+2*y^post_4
      6: l4 -> l2 : [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l4
     10: l2 -> l2 : x^0'=-1+x^0, y^0'=y^post_4, [ 1<=x^0 && y^post_4<=0 ], cost: 2
     11: l2 -> l2 : x^0'=-1+x^0, y^0'=0, [ 1<=x^0 && 1<=y^post_4 ], cost: 2+2*y^post_4
      6: l4 -> l2 : [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
     10: l2 -> l2 : x^0'=-1+x^0, y^0'=y^post_4, [ 1<=x^0 && y^post_4<=0 ], cost: 2
     11: l2 -> l2 : x^0'=-1+x^0, y^0'=0, [ 1<=x^0 && 1<=y^post_4 ], cost: 2+2*y^post_4

   Accelerated rule 10 with metering function x^0, yielding the new rule 12.
   Accelerated rule 11 with metering function x^0, yielding the new rule 13.
   Removing the simple loops: 10 11.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
     12: l2 -> l2 : x^0'=0, y^0'=y^post_4, [ 1<=x^0 && y^post_4<=0 ], cost: 2*x^0
     13: l2 -> l2 : x^0'=0, y^0'=0, [ 1<=x^0 && 1<=y^post_4 ], cost: 2*x^0*y^post_4+2*x^0
      6: l4 -> l2 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      6: l4 -> l2 : [], cost: 2
     14: l4 -> l2 : x^0'=0, y^0'=y^post_4, [ 1<=x^0 && y^post_4<=0 ], cost: 2+2*x^0
     15: l4 -> l2 : x^0'=0, y^0'=0, [ 1<=x^0 && 1<=y^post_4 ], cost: 2+2*x^0*y^post_4+2*x^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
     14: l4 -> l2 : x^0'=0, y^0'=y^post_4, [ 1<=x^0 && y^post_4<=0 ], cost: 2+2*x^0
     15: l4 -> l2 : x^0'=0, y^0'=0, [ 1<=x^0 && 1<=y^post_4 ], cost: 2+2*x^0*y^post_4+2*x^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
     14: l4 -> l2 : x^0'=0, y^0'=y^post_4, [ 1<=x^0 && y^post_4<=0 ], cost: 2+2*x^0
     15: l4 -> l2 : x^0'=0, y^0'=0, [ 1<=x^0 && 1<=y^post_4 ], cost: 2+2*x^0*y^post_4+2*x^0

Computing asymptotic complexity for rule 14
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      2+2*x^0 (+), 1-y^post_4 (+/+!), x^0 (+/+!) [not solved]

      removing all constraints (solved by SMT)
      resulting limit problem: [solved]

      applying transformation rule (C) using substitution {x^0==n,y^post_4==-n}
      resulting limit problem:
      [solved]

   Solution:
      x^0 / n
      y^post_4 / -n
   Resulting cost 2+2*n has complexity: Poly(n^1)

Found new complexity Poly(n^1).

Computing asymptotic complexity for rule 15
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      2+2*x^0*y^post_4+2*x^0 (+), x^0 (+/+!), y^post_4 (+/+!) [not solved]

      removing all constraints (solved by SMT)
      resulting limit problem: [solved]

      applying transformation rule (C) using substitution {x^0==1,y^post_4==1+n}
      resulting limit problem:
      [solved]

   Solution:
      x^0 / 1
      y^post_4 / 1+n
   Resulting cost 6+2*n has complexity: Unbounded

Found new complexity Unbounded.

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Unbounded
   Cpx degree:  Unbounded
   Solved cost: 6+2*n
   Rule cost:   2+2*x^0*y^post_4+2*x^0
   Rule guard:  [ 1<=x^0 && 1<=y^post_4 ]

WORST_CASE(INF,?)