WORST_CASE(Omega(1),?)

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

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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: l3 -> l2 : id^0'=id^post_6, m^0'=m^post_6, x^0'=x^post_6, [ id^0==id^post_6 && m^0==m^post_6 && x^0==x^post_6 ], cost: 1

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

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l3
      0: l0 -> l1 : x^0'=1+x^0, [ x^0<=m^0 && 0<=1+x^0 ], cost: 1
      1: l0 -> l1 : x^0'=0, [ 1+m^0<=x^0 && 1<=x^0 && 0<=1+m^0 ], cost: 1
      2: l1 -> l0 : [ 1+id^0<=x^0 ], cost: 1
      3: l1 -> l0 : [ 1+x^0<=id^0 ], cost: 1
      6: l3 -> l1 : x^0'=1+id^0, [ id^0<=m^0 && 1<=id^0 ], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l3
      7: l1 -> l1 : x^0'=1+x^0, [ 1+id^0<=x^0 && x^0<=m^0 && 0<=1+x^0 ], cost: 2
      8: l1 -> l1 : x^0'=0, [ 1+id^0<=x^0 && 1+m^0<=x^0 && 1<=x^0 && 0<=1+m^0 ], cost: 2
      9: l1 -> l1 : x^0'=1+x^0, [ 1+x^0<=id^0 && x^0<=m^0 && 0<=1+x^0 ], cost: 2
     10: l1 -> l1 : x^0'=0, [ 1+x^0<=id^0 && 1+m^0<=x^0 && 1<=x^0 && 0<=1+m^0 ], cost: 2
      6: l3 -> l1 : x^0'=1+id^0, [ id^0<=m^0 && 1<=id^0 ], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      7: l1 -> l1 : x^0'=1+x^0, [ 1+id^0<=x^0 && x^0<=m^0 && 0<=1+x^0 ], cost: 2
      8: l1 -> l1 : x^0'=0, [ 1+id^0<=x^0 && 1+m^0<=x^0 && 1<=x^0 && 0<=1+m^0 ], cost: 2
      9: l1 -> l1 : x^0'=1+x^0, [ 1+x^0<=id^0 && x^0<=m^0 && 0<=1+x^0 ], cost: 2
     10: l1 -> l1 : x^0'=0, [ 1+x^0<=id^0 && 1+m^0<=x^0 && 1<=x^0 && 0<=1+m^0 ], cost: 2

   Accelerated rule 7 with backward acceleration, yielding the new rule 11.
   Failed to prove monotonicity of the guard of rule 8.
   Accelerated rule 9 with backward acceleration, yielding the new rule 12.
   Accelerated rule 9 with backward acceleration, yielding the new rule 13.
   Failed to prove monotonicity of the guard of rule 10.
[accelerate] Nesting with 5 inner and 4 outer candidates
   Nested simple loops 8 (outer loop) and 11 (inner loop) with Rule(1 | 1+id^0<=x^0, 1+m^0<=x^0, 0<=1+m^0, 1+id^0<=0, k_4>=1, 1<=1+m^0, | 4*k_4+2*k_4*m^0 || 1 | 2=1+m^0, ), resulting in the new rules: 14, 15.
   Nested simple loops 7 (outer loop) and 8 (inner loop) with Rule(1 | 1+id^0<=x^0, 1<=x^0, 1+id^0<=0, 0<=m^0, k_5>=1, 1+m^0<=1, | 4*k_5 || 1 | 2=1, ), resulting in the new rules: 16, 17.
   Nested simple loops 10 (outer loop) and 13 (inner loop) with Rule(1 | 0<=1+x^0, 1+m^0-x^0>=0, 2+m^0<=id^0, 1<=1+m^0, | NONTERM || 4 | ), resulting in the new rules: 18, 19.
   Nested simple loops 9 (outer loop) and 10 (inner loop) with Rule(1 | 1+x^0<=id^0, 1<=x^0, 1<=id^0, 0<=m^0, k_6>=1, 1+m^0<=1, | 4*k_6 || 1 | 2=1, ), resulting in the new rules: 20, 21.
   Removing the simple loops: 7 8 9 10.

Accelerated all simple loops using metering functions (where possible):
   Start location: l3
     11: l1 -> l1 : x^0'=1+m^0, [ 1+id^0<=x^0 && 0<=1+x^0 && 1+m^0-x^0>=0 ], cost: 2+2*m^0-2*x^0
     12: l1 -> l1 : x^0'=id^0, [ 0<=1+x^0 && -x^0+id^0>=0 && -1+id^0<=m^0 ], cost: -2*x^0+2*id^0
     13: l1 -> l1 : x^0'=1+m^0, [ 0<=1+x^0 && 1+m^0-x^0>=0 && 1+m^0<=id^0 ], cost: 2+2*m^0-2*x^0
     14: l1 -> l1 : x^0'=1+m^0, [ 1+id^0<=x^0 && 1+m^0<=x^0 && 1+id^0<=0 && k_4>=1 && 1<=1+m^0 ], cost: 4*k_4+2*k_4*m^0
     15: l1 -> l1 : x^0'=1+m^0, [ 1+id^0<=x^0 && 0<=1+x^0 && 1+m^0-x^0>=0 && 1+id^0<=1+m^0 && 1+id^0<=0 && k_4>=1 && 1<=1+m^0 ], cost: 2+4*k_4+2*m^0-2*x^0+2*k_4*m^0
     16: l1 -> l1 : x^0'=1, [ 1+id^0<=x^0 && 1<=x^0 && 1+id^0<=0 && 0<=m^0 && k_5>=1 && 1+m^0<=1 ], cost: 4*k_5
     17: l1 -> l1 : x^0'=1, [ 1+id^0<=x^0 && x^0<=m^0 && 1<=1+x^0 && 1+id^0<=0 && 0<=m^0 && k_5>=1 && 1+m^0<=1 ], cost: 2+4*k_5
     18: l1 -> [4] : [ 0<=1+x^0 && 1+m^0-x^0>=0 && 2+m^0<=id^0 && 1<=1+m^0 ], cost: NONTERM
     19: l1 -> [4] : [ 1+x^0<=id^0 && 1+m^0<=x^0 && 1<=x^0 && 2+m^0<=id^0 && 1<=1+m^0 ], cost: NONTERM
     20: l1 -> l1 : x^0'=1, [ 1+x^0<=id^0 && 1<=x^0 && 1<=id^0 && 0<=m^0 && k_6>=1 && 1+m^0<=1 ], cost: 4*k_6
     21: l1 -> l1 : x^0'=1, [ x^0<=m^0 && 2+x^0<=id^0 && 1<=1+x^0 && 1<=id^0 && 0<=m^0 && k_6>=1 && 1+m^0<=1 ], cost: 2+4*k_6
      6: l3 -> l1 : x^0'=1+id^0, [ id^0<=m^0 && 1<=id^0 ], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l3
      6: l3 -> l1 : x^0'=1+id^0, [ id^0<=m^0 && 1<=id^0 ], cost: 2
     22: l3 -> l1 : x^0'=1+m^0, [ id^0<=m^0 && 1<=id^0 ], cost: 2+2*m^0-2*id^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l3
     22: l3 -> l1 : x^0'=1+m^0, [ id^0<=m^0 && 1<=id^0 ], cost: 2+2*m^0-2*id^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l3
     22: l3 -> l1 : x^0'=1+m^0, [ id^0<=m^0 && 1<=id^0 ], cost: 2+2*m^0-2*id^0

Computing asymptotic complexity for rule 22
   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:  [ id^0==id^post_6 && m^0==m^post_6 && x^0==x^post_6 ]

WORST_CASE(Omega(1),?)