NO

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

Simplified all rules, resulting in:
   Start location: l4
      0: l0 -> l1 : x^0'=-y^0+x^0, z^0'=z^post_1, [], cost: 1
      1: l0 -> l2 : y^0'=1+y^0, z^0'=-1+z^0, [ 2<=z^0 ], cost: 1
      3: l1 -> l0 : [ 2<=x^0 ], cost: 1
      2: l2 -> l0 : [], cost: 1
      4: l3 -> l1 : [], cost: 1
      5: l4 -> l3 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      0: l0 -> l1 : x^0'=-y^0+x^0, z^0'=z^post_1, [], cost: 1
      7: l0 -> l0 : y^0'=1+y^0, z^0'=-1+z^0, [ 2<=z^0 ], cost: 2
      3: l1 -> l0 : [ 2<=x^0 ], cost: 1
      6: l4 -> l1 : [], cost: 2

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

   Accelerated rule 7 with backward acceleration, yielding the new rule 8.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 7.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
      0: l0 -> l1 : x^0'=-y^0+x^0, z^0'=z^post_1, [], cost: 1
      8: l0 -> l0 : y^0'=-1+y^0+z^0, z^0'=1, [ -1+z^0>=0 ], cost: -2+2*z^0
      3: l1 -> l0 : [ 2<=x^0 ], cost: 1
      6: l4 -> l1 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      0: l0 -> l1 : x^0'=-y^0+x^0, z^0'=z^post_1, [], cost: 1
      3: l1 -> l0 : [ 2<=x^0 ], cost: 1
      9: l1 -> l0 : y^0'=-1+y^0+z^0, z^0'=1, [ 2<=x^0 && -1+z^0>=0 ], cost: -1+2*z^0
      6: l4 -> l1 : [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l4
     10: l1 -> l1 : x^0'=-y^0+x^0, z^0'=z^post_1, [ 2<=x^0 ], cost: 2
     11: l1 -> l1 : x^0'=1-y^0-z^0+x^0, y^0'=-1+y^0+z^0, z^0'=z^post_1, [ 2<=x^0 && -1+z^0>=0 ], cost: 2*z^0
      6: l4 -> l1 : [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     10: l1 -> l1 : x^0'=-y^0+x^0, z^0'=z^post_1, [ 2<=x^0 ], cost: 2
     11: l1 -> l1 : x^0'=1-y^0-z^0+x^0, y^0'=-1+y^0+z^0, z^0'=z^post_1, [ 2<=x^0 && -1+z^0>=0 ], cost: 2*z^0

[test] deduced pseudo-invariant 1+y^0<=0, also trying -1-y^0<=-1
   Accelerated rule 10 with non-termination, yielding the new rule 12.
   Accelerated rule 10 with non-termination, yielding the new rule 13.
   Accelerated rule 10 with backward acceleration, yielding the new rule 14.
   Accelerated rule 10 with non-termination, yielding the new rule 15.
   Accelerated rule 10 with backward acceleration, yielding the new rule 16.
[test] deduced pseudo-invariant 1-z^post_1<=0, also trying -1+z^post_1<=-1
[test] deduced pseudo-invariant 1-y^0-z^0<=0, also trying -1+y^0+z^0<=-1
   Accelerated rule 11 with non-termination, yielding the new rule 17.
   Accelerated rule 11 with non-termination, yielding the new rule 18.
   Accelerated rule 11 with backward acceleration, yielding the new rule 19.
   Accelerated rule 11 with backward acceleration, yielding the new rule 20.
[accelerate] Nesting with 3 inner and 2 outer candidates
   Also removing duplicate rules: 12 13.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
     10: l1 -> l1 : x^0'=-y^0+x^0, z^0'=z^post_1, [ 2<=x^0 ], cost: 2
     11: l1 -> l1 : x^0'=1-y^0-z^0+x^0, y^0'=-1+y^0+z^0, z^0'=z^post_1, [ 2<=x^0 && -1+z^0>=0 ], cost: 2*z^0
     14: l1 -> [6] : [ 2<=x^0 && 1+y^0<=0 ], cost: NONTERM
     15: l1 -> [6] : [ y^0==0 && x^0==2 ], cost: NONTERM
     16: l1 -> l1 : x^0'=-y^0*k_2+x^0, z^0'=z^post_1, [ -1-y^0<=-1 && k_2>=1 && 2<=-y^0*(-1+k_2)+x^0 ], cost: 2*k_2
     17: l1 -> [6] : [ z^post_1==1 && y^0==0 && z^0==1 && x^0==2 ], cost: NONTERM
     18: l1 -> [6] : [ 1-y^0-z^0<=0 && z^post_1==1 && y^0==0 && z^0==1 && x^0==2 ], cost: NONTERM
     19: l1 -> l1 : x^0'=1/2*k_4^2+1/2*k_4-1/2*k_4^2*z^post_1-k_4*y^0+x^0-1/2*k_4*z^post_1, y^0'=-k_4+y^0+k_4*z^post_1, z^0'=z^post_1, [ -1+z^0>=0 && 1-z^post_1<=0 && 1-y^0-z^0<=0 && k_4>=1 && 2<=-1/2+1/2*k_4-1/2*z^post_1*(-1+k_4)^2-1/2*z^post_1*(-1+k_4)+1/2*(-1+k_4)^2-y^0*(-1+k_4)+x^0 ], cost: 2*k_4*z^post_1
     20: l1 -> l1 : x^0'=1/2*k_5^2-y^0*k_5+1/2*k_5-1/2*z^post_1*k_5-1/2*z^post_1*k_5^2+x^0, y^0'=y^0-k_5+z^post_1*k_5, z^0'=z^post_1, [ 2<=x^0 && -1+z^0>=0 && 1-z^post_1<=0 && k_5>=1 && z^post_1+y^0+z^post_1*(-1+k_5)-k_5<=-1 ], cost: 2*z^post_1*k_5
      6: l4 -> l1 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      6: l4 -> l1 : [], cost: 2
     21: l4 -> l1 : x^0'=-y^0+x^0, z^0'=z^post_1, [ 2<=x^0 ], cost: 4
     22: l4 -> l1 : x^0'=1-y^0-z^0+x^0, y^0'=-1+y^0+z^0, z^0'=z^post_1, [ 2<=x^0 && -1+z^0>=0 ], cost: 2+2*z^0
     23: l4 -> [6] : [ 2<=x^0 && 1+y^0<=0 ], cost: NONTERM
     24: l4 -> [6] : [ y^0==0 && x^0==2 ], cost: NONTERM
     25: l4 -> l1 : x^0'=-y^0*k_2+x^0, z^0'=z^post_1, [ -1-y^0<=-1 && k_2>=1 && 2<=-y^0*(-1+k_2)+x^0 ], cost: 2+2*k_2
     26: l4 -> [6] : [ y^0==0 && z^0==1 && x^0==2 ], cost: NONTERM
     27: l4 -> [6] : [ 1-y^0-z^0<=0 && y^0==0 && z^0==1 && x^0==2 ], cost: NONTERM
     28: l4 -> l1 : x^0'=1/2*k_4^2+1/2*k_4-1/2*k_4^2*z^post_1-k_4*y^0+x^0-1/2*k_4*z^post_1, y^0'=-k_4+y^0+k_4*z^post_1, z^0'=z^post_1, [ -1+z^0>=0 && 1-z^post_1<=0 && 1-y^0-z^0<=0 && k_4>=1 && 2<=-1/2+1/2*k_4-1/2*z^post_1*(-1+k_4)^2-1/2*z^post_1*(-1+k_4)+1/2*(-1+k_4)^2-y^0*(-1+k_4)+x^0 ], cost: 2+2*k_4*z^post_1
     29: l4 -> l1 : x^0'=1/2*k_5^2-y^0*k_5+1/2*k_5-1/2*z^post_1*k_5-1/2*z^post_1*k_5^2+x^0, y^0'=y^0-k_5+z^post_1*k_5, z^0'=z^post_1, [ 2<=x^0 && -1+z^0>=0 && 1-z^post_1<=0 && k_5>=1 && z^post_1+y^0+z^post_1*(-1+k_5)-k_5<=-1 ], cost: 2+2*z^post_1*k_5

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
     22: l4 -> l1 : x^0'=1-y^0-z^0+x^0, y^0'=-1+y^0+z^0, z^0'=z^post_1, [ 2<=x^0 && -1+z^0>=0 ], cost: 2+2*z^0
     23: l4 -> [6] : [ 2<=x^0 && 1+y^0<=0 ], cost: NONTERM
     24: l4 -> [6] : [ y^0==0 && x^0==2 ], cost: NONTERM
     25: l4 -> l1 : x^0'=-y^0*k_2+x^0, z^0'=z^post_1, [ -1-y^0<=-1 && k_2>=1 && 2<=-y^0*(-1+k_2)+x^0 ], cost: 2+2*k_2
     26: l4 -> [6] : [ y^0==0 && z^0==1 && x^0==2 ], cost: NONTERM
     27: l4 -> [6] : [ 1-y^0-z^0<=0 && y^0==0 && z^0==1 && x^0==2 ], cost: NONTERM
     28: l4 -> l1 : x^0'=1/2*k_4^2+1/2*k_4-1/2*k_4^2*z^post_1-k_4*y^0+x^0-1/2*k_4*z^post_1, y^0'=-k_4+y^0+k_4*z^post_1, z^0'=z^post_1, [ -1+z^0>=0 && 1-z^post_1<=0 && 1-y^0-z^0<=0 && k_4>=1 && 2<=-1/2+1/2*k_4-1/2*z^post_1*(-1+k_4)^2-1/2*z^post_1*(-1+k_4)+1/2*(-1+k_4)^2-y^0*(-1+k_4)+x^0 ], cost: 2+2*k_4*z^post_1
     29: l4 -> l1 : x^0'=1/2*k_5^2-y^0*k_5+1/2*k_5-1/2*z^post_1*k_5-1/2*z^post_1*k_5^2+x^0, y^0'=y^0-k_5+z^post_1*k_5, z^0'=z^post_1, [ 2<=x^0 && -1+z^0>=0 && 1-z^post_1<=0 && k_5>=1 && z^post_1+y^0+z^post_1*(-1+k_5)-k_5<=-1 ], cost: 2+2*z^post_1*k_5

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
     22: l4 -> l1 : x^0'=1-y^0-z^0+x^0, y^0'=-1+y^0+z^0, z^0'=z^post_1, [ 2<=x^0 && -1+z^0>=0 ], cost: 2+2*z^0
     23: l4 -> [6] : [ 2<=x^0 && 1+y^0<=0 ], cost: NONTERM
     24: l4 -> [6] : [ y^0==0 && x^0==2 ], cost: NONTERM
     25: l4 -> l1 : x^0'=-y^0*k_2+x^0, z^0'=z^post_1, [ -1-y^0<=-1 && k_2>=1 && 2<=-y^0*(-1+k_2)+x^0 ], cost: 2+2*k_2
     26: l4 -> [6] : [ y^0==0 && z^0==1 && x^0==2 ], cost: NONTERM
     27: l4 -> [6] : [ 1-y^0-z^0<=0 && y^0==0 && z^0==1 && x^0==2 ], cost: NONTERM
     28: l4 -> l1 : x^0'=1/2*k_4^2+1/2*k_4-1/2*k_4^2*z^post_1-k_4*y^0+x^0-1/2*k_4*z^post_1, y^0'=-k_4+y^0+k_4*z^post_1, z^0'=z^post_1, [ -1+z^0>=0 && 1-z^post_1<=0 && 1-y^0-z^0<=0 && k_4>=1 && 2<=-1/2+1/2*k_4-1/2*z^post_1*(-1+k_4)^2-1/2*z^post_1*(-1+k_4)+1/2*(-1+k_4)^2-y^0*(-1+k_4)+x^0 ], cost: 2+2*k_4*z^post_1
     29: l4 -> l1 : x^0'=1/2*k_5^2-y^0*k_5+1/2*k_5-1/2*z^post_1*k_5-1/2*z^post_1*k_5^2+x^0, y^0'=y^0-k_5+z^post_1*k_5, z^0'=z^post_1, [ 2<=x^0 && -1+z^0>=0 && 1-z^post_1<=0 && k_5>=1 && z^post_1+y^0+z^post_1*(-1+k_5)-k_5<=-1 ], cost: 2+2*z^post_1*k_5

Computing asymptotic complexity for rule 23
   Guard is satisfiable, yielding nontermination
   Resulting cost NONTERM has complexity: Nonterm

Found new complexity Nonterm.

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

NO