WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l7
      0: l0 -> l1 : copied^0'=copied^post_1, e^0'=e^post_1, n^0'=n^post_1, olde^0'=olde^post_1, oldn^0'=oldn^post_1, [ 1<=copied^0 && olde^0<=e^0 && n^0<=oldn^0 && copied^0==copied^post_1 && e^0==e^post_1 && n^0==n^post_1 && olde^0==olde^post_1 && oldn^0==oldn^post_1 ], cost: 1
      1: l0 -> l2 : copied^0'=copied^post_2, e^0'=e^post_2, n^0'=n^post_2, olde^0'=olde^post_2, oldn^0'=oldn^post_2, [ copied^0<=0 && copied^post_2==1 && oldn^post_2==n^0 && olde^post_2==e^0 && 1<=e^0 && n^0<=100 && n^post_2==11+n^0 && e^post_2==1+e^0 ], cost: 1
      3: l0 -> l3 : copied^0'=copied^post_4, e^0'=e^post_4, n^0'=n^post_4, olde^0'=olde^post_4, oldn^0'=oldn^post_4, [ copied^0<=0 && copied^post_4==1 && oldn^post_4==n^0 && olde^post_4==e^0 && 1<=e^0 && 101<=n^0 && n^post_4==-10+n^0 && e^post_4==-1+e^0 ], cost: 1
      5: l0 -> l4 : copied^0'=copied^post_6, e^0'=e^post_6, n^0'=n^post_6, olde^0'=olde^post_6, oldn^0'=oldn^post_6, [ 1<=e^0 && n^0<=100 && n^post_6==11+n^0 && e^post_6==1+e^0 && copied^0==copied^post_6 && olde^0==olde^post_6 && oldn^0==oldn^post_6 ], cost: 1
      7: l0 -> l5 : copied^0'=copied^post_8, e^0'=e^post_8, n^0'=n^post_8, olde^0'=olde^post_8, oldn^0'=oldn^post_8, [ 1<=e^0 && 101<=n^0 && n^post_8==-10+n^0 && e^post_8==-1+e^0 && copied^0==copied^post_8 && olde^0==olde^post_8 && oldn^0==oldn^post_8 ], cost: 1
      2: l2 -> l0 : copied^0'=copied^post_3, e^0'=e^post_3, n^0'=n^post_3, olde^0'=olde^post_3, oldn^0'=oldn^post_3, [ copied^0==copied^post_3 && e^0==e^post_3 && n^0==n^post_3 && olde^0==olde^post_3 && oldn^0==oldn^post_3 ], cost: 1
      4: l3 -> l0 : copied^0'=copied^post_5, e^0'=e^post_5, n^0'=n^post_5, olde^0'=olde^post_5, oldn^0'=oldn^post_5, [ copied^0==copied^post_5 && e^0==e^post_5 && n^0==n^post_5 && olde^0==olde^post_5 && oldn^0==oldn^post_5 ], cost: 1
      6: l4 -> l0 : copied^0'=copied^post_7, e^0'=e^post_7, n^0'=n^post_7, olde^0'=olde^post_7, oldn^0'=oldn^post_7, [ copied^0==copied^post_7 && e^0==e^post_7 && n^0==n^post_7 && olde^0==olde^post_7 && oldn^0==oldn^post_7 ], cost: 1
      8: l5 -> l0 : copied^0'=copied^post_9, e^0'=e^post_9, n^0'=n^post_9, olde^0'=olde^post_9, oldn^0'=oldn^post_9, [ copied^0==copied^post_9 && e^0==e^post_9 && n^0==n^post_9 && olde^0==olde^post_9 && oldn^0==oldn^post_9 ], cost: 1
      9: l6 -> l0 : copied^0'=copied^post_10, e^0'=e^post_10, n^0'=n^post_10, olde^0'=olde^post_10, oldn^0'=oldn^post_10, [ n^post_10==n^post_10 && e^post_10==1 && copied^post_10==0 && olde^0==olde^post_10 && oldn^0==oldn^post_10 ], cost: 1
     10: l7 -> l6 : copied^0'=copied^post_11, e^0'=e^post_11, n^0'=n^post_11, olde^0'=olde^post_11, oldn^0'=oldn^post_11, [ copied^0==copied^post_11 && e^0==e^post_11 && n^0==n^post_11 && olde^0==olde^post_11 && oldn^0==oldn^post_11 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     10: l7 -> l6 : copied^0'=copied^post_11, e^0'=e^post_11, n^0'=n^post_11, olde^0'=olde^post_11, oldn^0'=oldn^post_11, [ copied^0==copied^post_11 && e^0==e^post_11 && n^0==n^post_11 && olde^0==olde^post_11 && oldn^0==oldn^post_11 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l7
      1: l0 -> l2 : copied^0'=copied^post_2, e^0'=e^post_2, n^0'=n^post_2, olde^0'=olde^post_2, oldn^0'=oldn^post_2, [ copied^0<=0 && copied^post_2==1 && oldn^post_2==n^0 && olde^post_2==e^0 && 1<=e^0 && n^0<=100 && n^post_2==11+n^0 && e^post_2==1+e^0 ], cost: 1
      3: l0 -> l3 : copied^0'=copied^post_4, e^0'=e^post_4, n^0'=n^post_4, olde^0'=olde^post_4, oldn^0'=oldn^post_4, [ copied^0<=0 && copied^post_4==1 && oldn^post_4==n^0 && olde^post_4==e^0 && 1<=e^0 && 101<=n^0 && n^post_4==-10+n^0 && e^post_4==-1+e^0 ], cost: 1
      5: l0 -> l4 : copied^0'=copied^post_6, e^0'=e^post_6, n^0'=n^post_6, olde^0'=olde^post_6, oldn^0'=oldn^post_6, [ 1<=e^0 && n^0<=100 && n^post_6==11+n^0 && e^post_6==1+e^0 && copied^0==copied^post_6 && olde^0==olde^post_6 && oldn^0==oldn^post_6 ], cost: 1
      7: l0 -> l5 : copied^0'=copied^post_8, e^0'=e^post_8, n^0'=n^post_8, olde^0'=olde^post_8, oldn^0'=oldn^post_8, [ 1<=e^0 && 101<=n^0 && n^post_8==-10+n^0 && e^post_8==-1+e^0 && copied^0==copied^post_8 && olde^0==olde^post_8 && oldn^0==oldn^post_8 ], cost: 1
      2: l2 -> l0 : copied^0'=copied^post_3, e^0'=e^post_3, n^0'=n^post_3, olde^0'=olde^post_3, oldn^0'=oldn^post_3, [ copied^0==copied^post_3 && e^0==e^post_3 && n^0==n^post_3 && olde^0==olde^post_3 && oldn^0==oldn^post_3 ], cost: 1
      4: l3 -> l0 : copied^0'=copied^post_5, e^0'=e^post_5, n^0'=n^post_5, olde^0'=olde^post_5, oldn^0'=oldn^post_5, [ copied^0==copied^post_5 && e^0==e^post_5 && n^0==n^post_5 && olde^0==olde^post_5 && oldn^0==oldn^post_5 ], cost: 1
      6: l4 -> l0 : copied^0'=copied^post_7, e^0'=e^post_7, n^0'=n^post_7, olde^0'=olde^post_7, oldn^0'=oldn^post_7, [ copied^0==copied^post_7 && e^0==e^post_7 && n^0==n^post_7 && olde^0==olde^post_7 && oldn^0==oldn^post_7 ], cost: 1
      8: l5 -> l0 : copied^0'=copied^post_9, e^0'=e^post_9, n^0'=n^post_9, olde^0'=olde^post_9, oldn^0'=oldn^post_9, [ copied^0==copied^post_9 && e^0==e^post_9 && n^0==n^post_9 && olde^0==olde^post_9 && oldn^0==oldn^post_9 ], cost: 1
      9: l6 -> l0 : copied^0'=copied^post_10, e^0'=e^post_10, n^0'=n^post_10, olde^0'=olde^post_10, oldn^0'=oldn^post_10, [ n^post_10==n^post_10 && e^post_10==1 && copied^post_10==0 && olde^0==olde^post_10 && oldn^0==oldn^post_10 ], cost: 1
     10: l7 -> l6 : copied^0'=copied^post_11, e^0'=e^post_11, n^0'=n^post_11, olde^0'=olde^post_11, oldn^0'=oldn^post_11, [ copied^0==copied^post_11 && e^0==e^post_11 && n^0==n^post_11 && olde^0==olde^post_11 && oldn^0==oldn^post_11 ], cost: 1

Simplified all rules, resulting in:
   Start location: l7
      1: l0 -> l2 : copied^0'=1, e^0'=1+e^0, n^0'=11+n^0, olde^0'=e^0, oldn^0'=n^0, [ copied^0<=0 && 1<=e^0 && n^0<=100 ], cost: 1
      3: l0 -> l3 : copied^0'=1, e^0'=-1+e^0, n^0'=-10+n^0, olde^0'=e^0, oldn^0'=n^0, [ copied^0<=0 && 1<=e^0 && 101<=n^0 ], cost: 1
      5: l0 -> l4 : e^0'=1+e^0, n^0'=11+n^0, [ 1<=e^0 && n^0<=100 ], cost: 1
      7: l0 -> l5 : e^0'=-1+e^0, n^0'=-10+n^0, [ 1<=e^0 && 101<=n^0 ], cost: 1
      2: l2 -> l0 : [], cost: 1
      4: l3 -> l0 : [], cost: 1
      6: l4 -> l0 : [], cost: 1
      8: l5 -> l0 : [], cost: 1
      9: l6 -> l0 : copied^0'=0, e^0'=1, n^0'=n^post_10, [], cost: 1
     10: l7 -> l6 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l7
     12: l0 -> l0 : copied^0'=1, e^0'=1+e^0, n^0'=11+n^0, olde^0'=e^0, oldn^0'=n^0, [ copied^0<=0 && 1<=e^0 && n^0<=100 ], cost: 2
     13: l0 -> l0 : copied^0'=1, e^0'=-1+e^0, n^0'=-10+n^0, olde^0'=e^0, oldn^0'=n^0, [ copied^0<=0 && 1<=e^0 && 101<=n^0 ], cost: 2
     14: l0 -> l0 : e^0'=1+e^0, n^0'=11+n^0, [ 1<=e^0 && n^0<=100 ], cost: 2
     15: l0 -> l0 : e^0'=-1+e^0, n^0'=-10+n^0, [ 1<=e^0 && 101<=n^0 ], cost: 2
     11: l7 -> l0 : copied^0'=0, e^0'=1, n^0'=n^post_10, [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     12: l0 -> l0 : copied^0'=1, e^0'=1+e^0, n^0'=11+n^0, olde^0'=e^0, oldn^0'=n^0, [ copied^0<=0 && 1<=e^0 && n^0<=100 ], cost: 2
     13: l0 -> l0 : copied^0'=1, e^0'=-1+e^0, n^0'=-10+n^0, olde^0'=e^0, oldn^0'=n^0, [ copied^0<=0 && 1<=e^0 && 101<=n^0 ], cost: 2
     14: l0 -> l0 : e^0'=1+e^0, n^0'=11+n^0, [ 1<=e^0 && n^0<=100 ], cost: 2
     15: l0 -> l0 : e^0'=-1+e^0, n^0'=-10+n^0, [ 1<=e^0 && 101<=n^0 ], cost: 2

   Failed to prove monotonicity of the guard of rule 12.
   Failed to prove monotonicity of the guard of rule 13.
   Accelerated rule 14 with backward acceleration, yielding the new rule 16.
   Accelerated rule 15 with backward acceleration, yielding the new rule 17.
[accelerate] Nesting with 4 inner and 4 outer candidates
   Removing the simple loops: 14 15.

Accelerated all simple loops using metering functions (where possible):
   Start location: l7
     12: l0 -> l0 : copied^0'=1, e^0'=1+e^0, n^0'=11+n^0, olde^0'=e^0, oldn^0'=n^0, [ copied^0<=0 && 1<=e^0 && n^0<=100 ], cost: 2
     13: l0 -> l0 : copied^0'=1, e^0'=-1+e^0, n^0'=-10+n^0, olde^0'=e^0, oldn^0'=n^0, [ copied^0<=0 && 1<=e^0 && 101<=n^0 ], cost: 2
     16: l0 -> l0 : e^0'=e^0+k, n^0'=n^0+11*k, [ 1<=e^0 && k>=0 && -11+n^0+11*k<=100 ], cost: 2*k
     17: l0 -> l0 : e^0'=e^0-k_1, n^0'=-10*k_1+n^0, [ k_1>=0 && 1<=1+e^0-k_1 && 101<=10-10*k_1+n^0 ], cost: 2*k_1
     11: l7 -> l0 : copied^0'=0, e^0'=1, n^0'=n^post_10, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l7
     11: l7 -> l0 : copied^0'=0, e^0'=1, n^0'=n^post_10, [], cost: 2
     18: l7 -> l0 : copied^0'=1, e^0'=2, n^0'=11+n^post_10, olde^0'=1, oldn^0'=n^post_10, [ n^post_10<=100 ], cost: 4
     19: l7 -> l0 : copied^0'=1, e^0'=0, n^0'=-10+n^post_10, olde^0'=1, oldn^0'=n^post_10, [ 101<=n^post_10 ], cost: 4
     20: l7 -> l0 : copied^0'=0, e^0'=1+k, n^0'=n^post_10+11*k, [ k>=0 && -11+n^post_10+11*k<=100 ], cost: 2+2*k
     21: l7 -> l0 : copied^0'=0, e^0'=1-k_1, n^0'=n^post_10-10*k_1, [ k_1>=0 && 1<=2-k_1 && 101<=10+n^post_10-10*k_1 ], cost: 2+2*k_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l7
     20: l7 -> l0 : copied^0'=0, e^0'=1+k, n^0'=n^post_10+11*k, [ k>=0 && -11+n^post_10+11*k<=100 ], cost: 2+2*k
     21: l7 -> l0 : copied^0'=0, e^0'=1-k_1, n^0'=n^post_10-10*k_1, [ k_1>=0 && 1<=2-k_1 && 101<=10+n^post_10-10*k_1 ], cost: 2+2*k_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l7
     20: l7 -> l0 : copied^0'=0, e^0'=1+k, n^0'=n^post_10+11*k, [ k>=0 && -11+n^post_10+11*k<=100 ], cost: 2+2*k
     21: l7 -> l0 : copied^0'=0, e^0'=1-k_1, n^0'=n^post_10-10*k_1, [ k_1>=0 && 1<=2-k_1 && 101<=10+n^post_10-10*k_1 ], cost: 2+2*k_1

Computing asymptotic complexity for rule 20
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 21
   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:  [ copied^0==copied^post_11 && e^0==e^post_11 && n^0==n^post_11 && olde^0==olde^post_11 && oldn^0==oldn^post_11 ]

WORST_CASE(Omega(1),?)