/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(INF, INF).

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 47.8 s]
(2) BOUNDS(INF, INF)


----------------------------------------

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B, C, D, E, F, G, H, I) -> Com_1(f9(0, 1, 1, 0, 0, J, G, H, I)) :|: J >= 1
f9(A, B, C, D, E, F, G, H, I) -> Com_1(f20(A, B, C - 1, D, D, 0, A - 2, 1, A - 2)) :|: A >= 3 && C >= 1 && D >= E && D <= E && F >= 0 && F <= 0
f9(A, B, C, D, E, F, G, H, I) -> Com_1(f20(A, B, C - 1, D, D, 0, A, 0, A)) :|: 2 >= A && C >= 1 && D >= E && D <= E && F >= 0 && F <= 0
f9(A, B, C, D, E, F, G, H, I) -> Com_1(f20(0, B + 1, B + 1, D, D, J, G, H, I)) :|: J >= 1 && A >= 3 && 0 >= C && D >= E && D <= E && F >= 0 && F <= 0
f9(A, B, C, D, E, F, G, H, I) -> Com_1(f20(A + 1, B + 1, B + 1, D, D, J, G, H, I)) :|: J >= 1 && 2 >= A && 0 >= C && D >= E && D <= E && F >= 0 && F <= 0
f9(A, B, C, D, E, F, G, H, I) -> Com_1(f20(A, B, C, D, D, F - 1, G, J, K)) :|: 0 >= F + 1 && D >= E && D <= E
f9(A, B, C, D, E, F, G, H, I) -> Com_1(f20(A, B, C, D, D, F - 1, G, J, K)) :|: F >= 1 && D >= E && D <= E
f20(A, B, C, D, E, F, G, H, I) -> Com_1(f32(A, B, C, 0, E, F, G, H, 0)) :|: I >= 0 && I <= 0
f20(A, B, C, D, E, F, G, H, I) -> Com_1(f32(A, B, C, 1, E, F, G, H, I)) :|: 0 >= I + 1
f20(A, B, C, D, E, F, G, H, I) -> Com_1(f32(A, B, C, 1, E, F, G, H, I)) :|: I >= 1
f32(A, B, C, D, E, F, G, H, I) -> Com_1(f9(A, B, C, D, 0, F, G, 0, I)) :|: H >= 0 && H <= 0
f32(A, B, C, D, E, F, G, H, I) -> Com_1(f9(A, B, C, D, 1, F, G, H, I)) :|: 0 >= H + 1
f32(A, B, C, D, E, F, G, H, I) -> Com_1(f9(A, B, C, D, 1, F, G, H, I)) :|: H >= 1
f9(A, B, C, D, E, F, G, H, I) -> Com_1(f38(A, B, C, D, E, F, G, H, I)) :|: E >= D + 1
f9(A, B, C, D, E, F, G, H, I) -> Com_1(f38(A, B, C, D, E, F, G, H, I)) :|: D >= 1 + E

The start-symbols are:[f0_9]


----------------------------------------

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f0 -> f9 : A'=0, B'=1, C'=1, D'=0, E'=0, F'=free, [ free>=1 ], cost: 1

      1: f9 -> f20 : C'=-1+C, E'=D, F'=0, G'=-2+A, H'=1, Q'=-2+A, [ A>=3 && C>=1 && D==E && F==0 ], cost: 1

      2: f9 -> f20 : C'=-1+C, E'=D, F'=0, G'=A, H'=0, Q'=A, [ 2>=A && C>=1 && D==E && F==0 ], cost: 1

      3: f9 -> f20 : A'=0, B'=1+B, C'=1+B, E'=D, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 ], cost: 1

      4: f9 -> f20 : A'=1+A, B'=1+B, C'=1+B, E'=D, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 ], cost: 1

      5: f9 -> f20 : E'=D, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E ], cost: 1

      6: f9 -> f20 : E'=D, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E ], cost: 1

     13: f9 -> f38 : [ E>=1+D ], cost: 1

     14: f9 -> f38 : [ D>=1+E ], cost: 1

      7: f20 -> f32 : D'=0, Q'=0, [ Q==0 ], cost: 1

      8: f20 -> f32 : D'=1, [ 0>=1+Q ], cost: 1

      9: f20 -> f32 : D'=1, [ Q>=1 ], cost: 1

     10: f32 -> f9 : E'=0, H'=0, [ H==0 ], cost: 1

     11: f32 -> f9 : E'=1, [ 0>=1+H ], cost: 1

     12: f32 -> f9 : E'=1, [ H>=1 ], cost: 1



Checking for constant complexity:

   The following rule is satisfiable with cost >= 1, yielding constant complexity:

      0: f0 -> f9 : A'=0, B'=1, C'=1, D'=0, E'=0, F'=free, [ free>=1 ], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f0 -> f9 : A'=0, B'=1, C'=1, D'=0, E'=0, F'=free, [ free>=1 ], cost: 1

      1: f9 -> f20 : C'=-1+C, E'=D, F'=0, G'=-2+A, H'=1, Q'=-2+A, [ A>=3 && C>=1 && D==E && F==0 ], cost: 1

      2: f9 -> f20 : C'=-1+C, E'=D, F'=0, G'=A, H'=0, Q'=A, [ 2>=A && C>=1 && D==E && F==0 ], cost: 1

      3: f9 -> f20 : A'=0, B'=1+B, C'=1+B, E'=D, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 ], cost: 1

      4: f9 -> f20 : A'=1+A, B'=1+B, C'=1+B, E'=D, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 ], cost: 1

      5: f9 -> f20 : E'=D, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E ], cost: 1

      6: f9 -> f20 : E'=D, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E ], cost: 1

      7: f20 -> f32 : D'=0, Q'=0, [ Q==0 ], cost: 1

      8: f20 -> f32 : D'=1, [ 0>=1+Q ], cost: 1

      9: f20 -> f32 : D'=1, [ Q>=1 ], cost: 1

     10: f32 -> f9 : E'=0, H'=0, [ H==0 ], cost: 1

     11: f32 -> f9 : E'=1, [ 0>=1+H ], cost: 1

     12: f32 -> f9 : E'=1, [ H>=1 ], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on tree-shaped paths):

   Start location: f0

      0: f0 -> f9 : A'=0, B'=1, C'=1, D'=0, E'=0, F'=free, [ free>=1 ], cost: 1

     15: f9 -> f32 : C'=-1+C, D'=1, E'=D, F'=0, G'=-2+A, H'=1, Q'=-2+A, [ A>=3 && C>=1 && D==E && F==0 ], cost: 2

     16: f9 -> f32 : C'=-1+C, D'=0, E'=D, F'=0, G'=A, H'=0, Q'=0, [ C>=1 && D==E && F==0 && A==0 ], cost: 2

     17: f9 -> f32 : C'=-1+C, D'=1, E'=D, F'=0, G'=A, H'=0, Q'=A, [ C>=1 && D==E && F==0 && 0>=1+A ], cost: 2

     18: f9 -> f32 : C'=-1+C, D'=1, E'=D, F'=0, G'=A, H'=0, Q'=A, [ 2>=A && C>=1 && D==E && F==0 && A>=1 ], cost: 2

     19: f9 -> f32 : A'=0, B'=1+B, C'=1+B, D'=0, E'=D, F'=free_1, Q'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 ], cost: 2

     20: f9 -> f32 : A'=0, B'=1+B, C'=1+B, D'=1, E'=D, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && 0>=1+Q ], cost: 2

     21: f9 -> f32 : A'=0, B'=1+B, C'=1+B, D'=1, E'=D, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q>=1 ], cost: 2

     22: f9 -> f32 : A'=1+A, B'=1+B, C'=1+B, D'=0, E'=D, F'=free_2, Q'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 ], cost: 2

     23: f9 -> f32 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=D, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && 0>=1+Q ], cost: 2

     24: f9 -> f32 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=D, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q>=1 ], cost: 2

     25: f9 -> f32 : D'=0, E'=D, F'=-1+F, H'=free_3, Q'=0, [ 0>=1+F && D==E && free_4==0 ], cost: 2

     26: f9 -> f32 : D'=1, E'=D, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E && 0>=1+free_4 ], cost: 2

     27: f9 -> f32 : D'=1, E'=D, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E && free_4>=1 ], cost: 2

     28: f9 -> f32 : D'=0, E'=D, F'=-1+F, H'=free_5, Q'=0, [ F>=1 && D==E && free_6==0 ], cost: 2

     29: f9 -> f32 : D'=1, E'=D, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E && 0>=1+free_6 ], cost: 2

     30: f9 -> f32 : D'=1, E'=D, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E && free_6>=1 ], cost: 2

     10: f32 -> f9 : E'=0, H'=0, [ H==0 ], cost: 1

     11: f32 -> f9 : E'=1, [ 0>=1+H ], cost: 1

     12: f32 -> f9 : E'=1, [ H>=1 ], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: f0

      0: f0 -> f9 : A'=0, B'=1, C'=1, D'=0, E'=0, F'=free, [ free>=1 ], cost: 1

     31: f9 -> f9 : C'=-1+C, D'=1, E'=1, F'=0, G'=-2+A, H'=1, Q'=-2+A, [ A>=3 && C>=1 && D==E && F==0 ], cost: 3

     32: f9 -> f9 : C'=-1+C, D'=0, E'=0, F'=0, G'=A, H'=0, Q'=0, [ C>=1 && D==E && F==0 && A==0 ], cost: 3

     33: f9 -> f9 : C'=-1+C, D'=1, E'=0, F'=0, G'=A, H'=0, Q'=A, [ C>=1 && D==E && F==0 && 0>=1+A ], cost: 3

     34: f9 -> f9 : C'=-1+C, D'=1, E'=0, F'=0, G'=A, H'=0, Q'=A, [ 2>=A && C>=1 && D==E && F==0 && A>=1 ], cost: 3

     35: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=0, E'=0, F'=free_1, H'=0, Q'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && H==0 ], cost: 3

     36: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=0, E'=1, F'=free_1, Q'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && 0>=1+H ], cost: 3

     37: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=0, E'=1, F'=free_1, Q'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && H>=1 ], cost: 3

     38: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=0, F'=free_1, H'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && 0>=1+Q && H==0 ], cost: 3

     39: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && 0>=1+Q && 0>=1+H ], cost: 3

     40: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && 0>=1+Q && H>=1 ], cost: 3

     41: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=0, F'=free_1, H'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q>=1 && H==0 ], cost: 3

     42: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q>=1 && 0>=1+H ], cost: 3

     43: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q>=1 && H>=1 ], cost: 3

     44: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=0, E'=0, F'=free_2, H'=0, Q'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && H==0 ], cost: 3

     45: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=0, E'=1, F'=free_2, Q'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && 0>=1+H ], cost: 3

     46: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=0, E'=1, F'=free_2, Q'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && H>=1 ], cost: 3

     47: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=0, F'=free_2, H'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && 0>=1+Q && H==0 ], cost: 3

     48: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && 0>=1+Q && 0>=1+H ], cost: 3

     49: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && 0>=1+Q && H>=1 ], cost: 3

     50: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=0, F'=free_2, H'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q>=1 && H==0 ], cost: 3

     51: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q>=1 && 0>=1+H ], cost: 3

     52: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q>=1 && H>=1 ], cost: 3

     53: f9 -> f9 : D'=0, E'=0, F'=-1+F, H'=0, Q'=0, [ 0>=1+F && D==E && free_4==0 && free_3==0 ], cost: 3

     54: f9 -> f9 : D'=0, E'=1, F'=-1+F, H'=free_3, Q'=0, [ 0>=1+F && D==E && free_4==0 && 0>=1+free_3 ], cost: 3

     55: f9 -> f9 : D'=0, E'=1, F'=-1+F, H'=free_3, Q'=0, [ 0>=1+F && D==E && free_4==0 && free_3>=1 ], cost: 3

     56: f9 -> f9 : D'=1, E'=0, F'=-1+F, H'=0, Q'=free_4, [ 0>=1+F && D==E && 0>=1+free_4 && free_3==0 ], cost: 3

     57: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E && 0>=1+free_4 && 0>=1+free_3 ], cost: 3

     58: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E && 0>=1+free_4 && free_3>=1 ], cost: 3

     59: f9 -> f9 : D'=1, E'=0, F'=-1+F, H'=0, Q'=free_4, [ 0>=1+F && D==E && free_4>=1 && free_3==0 ], cost: 3

     60: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E && free_4>=1 && 0>=1+free_3 ], cost: 3

     61: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E && free_4>=1 && free_3>=1 ], cost: 3

     62: f9 -> f9 : D'=0, E'=0, F'=-1+F, H'=0, Q'=0, [ F>=1 && D==E && free_6==0 && free_5==0 ], cost: 3

     63: f9 -> f9 : D'=0, E'=1, F'=-1+F, H'=free_5, Q'=0, [ F>=1 && D==E && free_6==0 && 0>=1+free_5 ], cost: 3

     64: f9 -> f9 : D'=0, E'=1, F'=-1+F, H'=free_5, Q'=0, [ F>=1 && D==E && free_6==0 && free_5>=1 ], cost: 3

     65: f9 -> f9 : D'=1, E'=0, F'=-1+F, H'=0, Q'=free_6, [ F>=1 && D==E && 0>=1+free_6 && free_5==0 ], cost: 3

     66: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E && 0>=1+free_6 && 0>=1+free_5 ], cost: 3

     67: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E && 0>=1+free_6 && free_5>=1 ], cost: 3

     68: f9 -> f9 : D'=1, E'=0, F'=-1+F, H'=0, Q'=free_6, [ F>=1 && D==E && free_6>=1 && free_5==0 ], cost: 3

     69: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E && free_6>=1 && 0>=1+free_5 ], cost: 3

     70: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E && free_6>=1 && free_5>=1 ], cost: 3



Accelerating simple loops of location 1.

   Simplified some of the simple loops (and removed duplicate rules).

   Accelerating the following rules:

     31: f9 -> f9 : C'=-1+C, D'=1, E'=1, F'=0, G'=-2+A, H'=1, Q'=-2+A, [ A>=3 && C>=1 && D==E && F==0 ], cost: 3

     32: f9 -> f9 : C'=-1+C, D'=0, E'=0, F'=0, G'=A, H'=0, Q'=0, [ C>=1 && D==E && F==0 && A==0 ], cost: 3

     33: f9 -> f9 : C'=-1+C, D'=1, E'=0, F'=0, G'=A, H'=0, Q'=A, [ C>=1 && D==E && F==0 && 0>=1+A ], cost: 3

     34: f9 -> f9 : C'=-1+C, D'=1, E'=0, F'=0, G'=A, H'=0, Q'=A, [ 2>=A && C>=1 && D==E && F==0 && A>=1 ], cost: 3

     35: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=0, E'=0, F'=free_1, H'=0, Q'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && H==0 ], cost: 3

     36: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=0, E'=1, F'=free_1, Q'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && 0>=1+H ], cost: 3

     37: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=0, E'=1, F'=free_1, Q'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && H>=1 ], cost: 3

     38: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=0, F'=free_1, H'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && 0>=1+Q && H==0 ], cost: 3

     39: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && 0>=1+Q && 0>=1+H ], cost: 3

     40: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && 0>=1+Q && H>=1 ], cost: 3

     41: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=0, F'=free_1, H'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q>=1 && H==0 ], cost: 3

     42: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q>=1 && 0>=1+H ], cost: 3

     43: f9 -> f9 : A'=0, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q>=1 && H>=1 ], cost: 3

     44: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=0, E'=0, F'=free_2, H'=0, Q'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && H==0 ], cost: 3

     45: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=0, E'=1, F'=free_2, Q'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && 0>=1+H ], cost: 3

     46: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=0, E'=1, F'=free_2, Q'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && H>=1 ], cost: 3

     47: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=0, F'=free_2, H'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && 0>=1+Q && H==0 ], cost: 3

     48: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && 0>=1+Q && 0>=1+H ], cost: 3

     49: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && 0>=1+Q && H>=1 ], cost: 3

     50: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=0, F'=free_2, H'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q>=1 && H==0 ], cost: 3

     51: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q>=1 && 0>=1+H ], cost: 3

     52: f9 -> f9 : A'=1+A, B'=1+B, C'=1+B, D'=1, E'=1, F'=free_2, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q>=1 && H>=1 ], cost: 3

     53: f9 -> f9 : D'=0, E'=0, F'=-1+F, H'=0, Q'=0, [ 0>=1+F && D==E ], cost: 3

     54: f9 -> f9 : D'=0, E'=1, F'=-1+F, H'=free_3, Q'=0, [ 0>=1+F && D==E && 0>=1+free_3 ], cost: 3

     55: f9 -> f9 : D'=0, E'=1, F'=-1+F, H'=free_3, Q'=0, [ 0>=1+F && D==E && free_3>=1 ], cost: 3

     56: f9 -> f9 : D'=1, E'=0, F'=-1+F, H'=0, Q'=free_4, [ 0>=1+F && D==E && 0>=1+free_4 ], cost: 3

     57: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E && 0>=1+free_4 && 0>=1+free_3 ], cost: 3

     58: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E && 0>=1+free_4 && free_3>=1 ], cost: 3

     59: f9 -> f9 : D'=1, E'=0, F'=-1+F, H'=0, Q'=free_4, [ 0>=1+F && D==E && free_4>=1 ], cost: 3

     60: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E && free_4>=1 && 0>=1+free_3 ], cost: 3

     61: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_3, Q'=free_4, [ 0>=1+F && D==E && free_4>=1 && free_3>=1 ], cost: 3

     62: f9 -> f9 : D'=0, E'=0, F'=-1+F, H'=0, Q'=0, [ F>=1 && D==E ], cost: 3

     63: f9 -> f9 : D'=0, E'=1, F'=-1+F, H'=free_5, Q'=0, [ F>=1 && D==E && 0>=1+free_5 ], cost: 3

     64: f9 -> f9 : D'=0, E'=1, F'=-1+F, H'=free_5, Q'=0, [ F>=1 && D==E && free_5>=1 ], cost: 3

     65: f9 -> f9 : D'=1, E'=0, F'=-1+F, H'=0, Q'=free_6, [ F>=1 && D==E && 0>=1+free_6 ], cost: 3

     66: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E && 0>=1+free_6 && 0>=1+free_5 ], cost: 3

     67: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E && 0>=1+free_6 && free_5>=1 ], cost: 3

     68: f9 -> f9 : D'=1, E'=0, F'=-1+F, H'=0, Q'=free_6, [ F>=1 && D==E && free_6>=1 ], cost: 3

     69: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E && free_6>=1 && 0>=1+free_5 ], cost: 3

     70: f9 -> f9 : D'=1, E'=1, F'=-1+F, H'=free_5, Q'=free_6, [ F>=1 && D==E && free_6>=1 && free_5>=1 ], cost: 3



   Accelerated rule 31 with metering function C, yielding the new rule 71.

   Accelerated rule 32 with metering function C, yielding the new rule 72.

   Accelerated rule 33 with metering function -D+E, yielding the new rule 73.

   Accelerated rule 34 with metering function -D+E, yielding the new rule 74.

      During metering: Instantiating temporary variables by {free_1==1}

   Accelerated rule 35 with metering function -F, yielding the new rule 75.

   Accelerated rule 36 with metering function D-E, yielding the new rule 76.

   Accelerated rule 37 with metering function D-E, yielding the new rule 77.

   Accelerated rule 38 with metering function -D+E, yielding the new rule 78.

      During metering: Instantiating temporary variables by {free_1==1}

   Accelerated rule 39 with metering function -F, yielding the new rule 79.

      During metering: Instantiating temporary variables by {free_1==1}

   Accelerated rule 40 with metering function -F, yielding the new rule 80.

   Accelerated rule 41 with metering function -D+E, yielding the new rule 81.

      During metering: Instantiating temporary variables by {free_1==1}

   Accelerated rule 42 with metering function -F, yielding the new rule 82.

      During metering: Instantiating temporary variables by {free_1==1}

   Accelerated rule 43 with metering function -F, yielding the new rule 83.

      During metering: Instantiating temporary variables by {free_2==1}

   Accelerated rule 44 with metering function -F, yielding the new rule 84.

   Accelerated rule 45 with metering function D-E, yielding the new rule 85.

   Accelerated rule 46 with metering function D-E, yielding the new rule 86.

   Accelerated rule 47 with metering function -D+E, yielding the new rule 87.

      During metering: Instantiating temporary variables by {free_2==1}

   Accelerated rule 48 with metering function -F, yielding the new rule 88.

      During metering: Instantiating temporary variables by {free_2==1}

   Accelerated rule 49 with metering function -F, yielding the new rule 89.

   Accelerated rule 50 with metering function -D+E, yielding the new rule 90.

      During metering: Instantiating temporary variables by {free_2==1}

   Accelerated rule 51 with metering function -F, yielding the new rule 91.

      During metering: Instantiating temporary variables by {free_2==1}

   Accelerated rule 52 with metering function -F, yielding the new rule 92.

   Accelerated rule 53 with NONTERM, yielding the new rule 93.

   Accelerated rule 54 with metering function 1+D-E, yielding the new rule 94.

   Accelerated rule 55 with metering function 1+D-E, yielding the new rule 95.

   Accelerated rule 56 with metering function 1-D+E, yielding the new rule 96.

   Accelerated rule 57 with NONTERM, yielding the new rule 97.

   Accelerated rule 58 with NONTERM, yielding the new rule 98.

   Accelerated rule 59 with metering function 1-D+E, yielding the new rule 99.

   Accelerated rule 60 with NONTERM, yielding the new rule 100.

   Accelerated rule 61 with NONTERM, yielding the new rule 101.

   Accelerated rule 62 with metering function F, yielding the new rule 102.

   Accelerated rule 63 with metering function D-E, yielding the new rule 103.

   Accelerated rule 64 with metering function D-E, yielding the new rule 104.

   Accelerated rule 65 with metering function -D+E, yielding the new rule 105.

   Accelerated rule 66 with metering function F, yielding the new rule 106.

   Accelerated rule 67 with metering function F, yielding the new rule 107.

   Accelerated rule 68 with metering function -D+E, yielding the new rule 108.

   Accelerated rule 69 with metering function F, yielding the new rule 109.

   Accelerated rule 70 with metering function F, yielding the new rule 110.

      During metering: Instantiating temporary variables by {free_1==1}

   Nested simple loops 43 (outer loop) and 71 (inner loop) with metering function -F, resulting in the new rules: 111.

   Nested simple loops 44 (outer loop) and 72 (inner loop) with metering function -A, resulting in the new rules: 112.

      During metering: Instantiating temporary variables by {free_5==-1,free_6==-1}

   Nested simple loops 35 (outer loop) and 106 (inner loop) with metering function meter (where 2*meter==H+Q), resulting in the new rules: 113.

      During metering: Instantiating temporary variables by {free_5==-1,free_6==-1}

   Nested simple loops 44 (outer loop) and 106 (inner loop) with metering function meter_1 (where 2*meter_1==H+Q), resulting in the new rules: 114.

      During metering: Instantiating temporary variables by {free_5==1,free_6==-1}

   Nested simple loops 35 (outer loop) and 107 (inner loop) with metering function meter_2 (where 2*meter_2==-H+Q), resulting in the new rules: 115.

      During metering: Instantiating temporary variables by {free_5==1,free_6==-1}

   Nested simple loops 44 (outer loop) and 107 (inner loop) with metering function meter_3 (where 2*meter_3==-H+Q), resulting in the new rules: 116.

      During metering: Instantiating temporary variables by {free_5==-1,free_6==1}

   Nested simple loops 35 (outer loop) and 109 (inner loop) with metering function meter_4 (where 2*meter_4==H-Q), resulting in the new rules: 117.

      During metering: Instantiating temporary variables by {free_5==-1,free_6==1}

   Nested simple loops 44 (outer loop) and 109 (inner loop) with metering function meter_5 (where 2*meter_5==H-Q), resulting in the new rules: 118.

      During metering: Instantiating temporary variables by {free_5==1,free_6==1}

   Nested simple loops 35 (outer loop) and 110 (inner loop) with metering function meter_6 (where 2*meter_6==-H-Q), resulting in the new rules: 119.

      During metering: Instantiating temporary variables by {free_5==1,free_6==1}

   Nested simple loops 44 (outer loop) and 110 (inner loop) with metering function meter_7 (where 2*meter_7==-H-Q), resulting in the new rules: 120.

   Removing the simple loops: 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70.



Accelerated all simple loops using metering functions (where possible):

   Start location: f0

      0: f0 -> f9 : A'=0, B'=1, C'=1, D'=0, E'=0, F'=free, [ free>=1 ], cost: 1

     71: f9 -> f9 : C'=0, D'=1, E'=1, F'=0, G'=-2+A, H'=1, Q'=-2+A, [ A>=3 && C>=1 && D==E && F==0 ], cost: 3*C

     72: f9 -> f9 : C'=0, D'=0, E'=0, F'=0, G'=A, H'=0, Q'=0, [ C>=1 && D==E && F==0 && A==0 ], cost: 3*C

     73: f9 -> f9 : C'=C+D-E, D'=1, E'=0, F'=0, G'=A, H'=0, Q'=A, [ C>=1 && D==E && F==0 && 0>=1+A && -D+E>=1 ], cost: -3*D+3*E

     74: f9 -> f9 : C'=C+D-E, D'=1, E'=0, F'=0, G'=A, H'=0, Q'=A, [ 2>=A && C>=1 && D==E && F==0 && A>=1 && -D+E>=1 ], cost: -3*D+3*E

     75: f9 -> f9 : A'=0, B'=-F+B, C'=-F+B, D'=0, E'=0, F'=1, H'=0, Q'=0, [ A>=3 && 0>=C && D==E && F==0 && Q==0 && H==0 && -F>=1 ], cost: -3*F

     76: f9 -> f9 : A'=0, B'=D-E+B, C'=D-E+B, D'=0, E'=1, F'=free_1, Q'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && 0>=1+H && D-E>=1 ], cost: 3*D-3*E

     77: f9 -> f9 : A'=0, B'=D-E+B, C'=D-E+B, D'=0, E'=1, F'=free_1, Q'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && H>=1 && D-E>=1 ], cost: 3*D-3*E

     78: f9 -> f9 : A'=0, B'=-D+E+B, C'=-D+E+B, D'=1, E'=0, F'=free_1, H'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && 0>=1+Q && H==0 && -D+E>=1 ], cost: -3*D+3*E

     79: f9 -> f9 : A'=0, B'=-F+B, C'=-F+B, D'=1, E'=1, F'=1, [ A>=3 && 0>=C && D==E && F==0 && 0>=1+Q && 0>=1+H && -F>=1 ], cost: -3*F

     80: f9 -> f9 : A'=0, B'=-F+B, C'=-F+B, D'=1, E'=1, F'=1, [ A>=3 && 0>=C && D==E && F==0 && 0>=1+Q && H>=1 && -F>=1 ], cost: -3*F

     81: f9 -> f9 : A'=0, B'=-D+E+B, C'=-D+E+B, D'=1, E'=0, F'=free_1, H'=0, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q>=1 && H==0 && -D+E>=1 ], cost: -3*D+3*E

     82: f9 -> f9 : A'=0, B'=-F+B, C'=-F+B, D'=1, E'=1, F'=1, [ A>=3 && 0>=C && D==E && F==0 && Q>=1 && 0>=1+H && -F>=1 ], cost: -3*F

     83: f9 -> f9 : A'=0, B'=-F+B, C'=-F+B, D'=1, E'=1, F'=1, [ A>=3 && 0>=C && D==E && F==0 && Q>=1 && H>=1 && -F>=1 ], cost: -3*F

     84: f9 -> f9 : A'=-F+A, B'=-F+B, C'=-F+B, D'=0, E'=0, F'=1, H'=0, Q'=0, [ 2>=A && 0>=C && D==E && F==0 && Q==0 && H==0 && -F>=1 ], cost: -3*F

     85: f9 -> f9 : A'=D+A-E, B'=D-E+B, C'=D-E+B, D'=0, E'=1, F'=free_2, Q'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && 0>=1+H && D-E>=1 ], cost: 3*D-3*E

     86: f9 -> f9 : A'=D+A-E, B'=D-E+B, C'=D-E+B, D'=0, E'=1, F'=free_2, Q'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && H>=1 && D-E>=1 ], cost: 3*D-3*E

     87: f9 -> f9 : A'=-D+A+E, B'=-D+E+B, C'=-D+E+B, D'=1, E'=0, F'=free_2, H'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && 0>=1+Q && H==0 && -D+E>=1 ], cost: -3*D+3*E

     88: f9 -> f9 : A'=-F+A, B'=-F+B, C'=-F+B, D'=1, E'=1, F'=1, [ 2>=A && 0>=C && D==E && F==0 && 0>=1+Q && 0>=1+H && -F>=1 ], cost: -3*F

     89: f9 -> f9 : A'=-F+A, B'=-F+B, C'=-F+B, D'=1, E'=1, F'=1, [ 2>=A && 0>=C && D==E && F==0 && 0>=1+Q && H>=1 && -F>=1 ], cost: -3*F

     90: f9 -> f9 : A'=-D+A+E, B'=-D+E+B, C'=-D+E+B, D'=1, E'=0, F'=free_2, H'=0, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q>=1 && H==0 && -D+E>=1 ], cost: -3*D+3*E

     91: f9 -> f9 : A'=-F+A, B'=-F+B, C'=-F+B, D'=1, E'=1, F'=1, [ 2>=A && 0>=C && D==E && F==0 && Q>=1 && 0>=1+H && -F>=1 ], cost: -3*F

     92: f9 -> f9 : A'=-F+A, B'=-F+B, C'=-F+B, D'=1, E'=1, F'=1, [ 2>=A && 0>=C && D==E && F==0 && Q>=1 && H>=1 && -F>=1 ], cost: -3*F

     93: f9 -> [5] : [ 0>=1+F && D==E ], cost: NONTERM

     94: f9 -> f9 : D'=0, E'=1, F'=-1+F-D+E, H'=free_3, Q'=0, [ 0>=1+F && D==E && 0>=1+free_3 ], cost: 3+3*D-3*E

     95: f9 -> f9 : D'=0, E'=1, F'=-1+F-D+E, H'=free_3, Q'=0, [ 0>=1+F && D==E && free_3>=1 ], cost: 3+3*D-3*E

     96: f9 -> f9 : D'=1, E'=0, F'=-1+F+D-E, H'=0, Q'=free_4, [ 0>=1+F && D==E && 0>=1+free_4 ], cost: 3-3*D+3*E

     97: f9 -> [5] : [ 0>=1+F && D==E && 0>=1+free_4 && 0>=1+free_3 ], cost: NONTERM

     98: f9 -> [5] : [ 0>=1+F && D==E && 0>=1+free_4 && free_3>=1 ], cost: NONTERM

     99: f9 -> f9 : D'=1, E'=0, F'=-1+F+D-E, H'=0, Q'=free_4, [ 0>=1+F && D==E && free_4>=1 ], cost: 3-3*D+3*E

    100: f9 -> [5] : [ 0>=1+F && D==E && free_4>=1 && 0>=1+free_3 ], cost: NONTERM

    101: f9 -> [5] : [ 0>=1+F && D==E && free_4>=1 && free_3>=1 ], cost: NONTERM

    102: f9 -> f9 : D'=0, E'=0, F'=0, H'=0, Q'=0, [ F>=1 && D==E ], cost: 3*F

    103: f9 -> f9 : D'=0, E'=1, F'=F-D+E, H'=free_5, Q'=0, [ F>=1 && D==E && 0>=1+free_5 && D-E>=1 ], cost: 3*D-3*E

    104: f9 -> f9 : D'=0, E'=1, F'=F-D+E, H'=free_5, Q'=0, [ F>=1 && D==E && free_5>=1 && D-E>=1 ], cost: 3*D-3*E

    105: f9 -> f9 : D'=1, E'=0, F'=F+D-E, H'=0, Q'=free_6, [ F>=1 && D==E && 0>=1+free_6 && -D+E>=1 ], cost: -3*D+3*E

    106: f9 -> f9 : D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ F>=1 && D==E && 0>=1+free_6 && 0>=1+free_5 ], cost: 3*F

    107: f9 -> f9 : D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ F>=1 && D==E && 0>=1+free_6 && free_5>=1 ], cost: 3*F

    108: f9 -> f9 : D'=1, E'=0, F'=F+D-E, H'=0, Q'=free_6, [ F>=1 && D==E && free_6>=1 && -D+E>=1 ], cost: -3*D+3*E

    109: f9 -> f9 : D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ F>=1 && D==E && free_6>=1 && 0>=1+free_5 ], cost: 3*F

    110: f9 -> f9 : D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ F>=1 && D==E && free_6>=1 && free_5>=1 ], cost: 3*F

    111: f9 -> f9 : A'=0, B'=-F+B, C'=-F+B, D'=1, E'=1, F'=1, G'=-2, H'=1, Q'=-2, [ A>=3 && C>=1 && D==E && F==0 && -F>=1 ], cost: -3/2*F+3/2*F^2-3*F*B

    112: f9 -> f9 : A'=0, B'=-A+B, C'=-A+B, D'=0, E'=0, F'=free_2, G'=-1, H'=0, Q'=0, [ C>=1 && D==E && F==0 && A==0 && free_2>=1 && -A>=1 ], cost: -3*A*B-3/2*A+3/2*A^2

    113: f9 -> f9 : A'=0, B'=meter+B, C'=meter+B, D'=1, E'=1, F'=0, H'=-1, Q'=-1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && H==0 && 2*meter==H+Q && meter>=1 ], cost: 3*free_1*meter+3*meter

    114: f9 -> f9 : A'=A+meter_1, B'=meter_1+B, C'=meter_1+B, D'=1, E'=1, F'=0, H'=-1, Q'=-1, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && H==0 && 2*meter_1==H+Q && meter_1>=1 ], cost: 3*free_2*meter_1+3*meter_1

    115: f9 -> f9 : A'=0, B'=meter_2+B, C'=meter_2+B, D'=1, E'=1, F'=0, H'=1, Q'=-1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && H==0 && 2*meter_2==-H+Q && meter_2>=1 ], cost: 3*meter_2+3*meter_2*free_1

    116: f9 -> f9 : A'=meter_3+A, B'=meter_3+B, C'=meter_3+B, D'=1, E'=1, F'=0, H'=1, Q'=-1, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && H==0 && 2*meter_3==-H+Q && meter_3>=1 ], cost: 3*meter_3+3*meter_3*free_2

    117: f9 -> f9 : A'=0, B'=meter_4+B, C'=meter_4+B, D'=1, E'=1, F'=0, H'=-1, Q'=1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && H==0 && 2*meter_4==H-Q && meter_4>=1 ], cost: 3*free_1*meter_4+3*meter_4

    118: f9 -> f9 : A'=meter_5+A, B'=meter_5+B, C'=meter_5+B, D'=1, E'=1, F'=0, H'=-1, Q'=1, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && H==0 && 2*meter_5==H-Q && meter_5>=1 ], cost: 3*meter_5+3*meter_5*free_2

    119: f9 -> f9 : A'=0, B'=B+meter_6, C'=B+meter_6, D'=1, E'=1, F'=0, H'=1, Q'=1, [ free_1>=1 && A>=3 && 0>=C && D==E && F==0 && Q==0 && H==0 && 2*meter_6==-H-Q && meter_6>=1 ], cost: 3*free_1*meter_6+3*meter_6

    120: f9 -> f9 : A'=A+meter_7, B'=B+meter_7, C'=B+meter_7, D'=1, E'=1, F'=0, H'=1, Q'=1, [ free_2>=1 && 2>=A && 0>=C && D==E && F==0 && Q==0 && H==0 && 2*meter_7==-H-Q && meter_7>=1 ], cost: 3*free_2*meter_7+3*meter_7



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f0 -> f9 : A'=0, B'=1, C'=1, D'=0, E'=0, F'=free, [ free>=1 ], cost: 1

    121: f0 -> f9 : A'=0, B'=1, C'=1, D'=0, E'=0, F'=0, H'=0, Q'=0, [ free>=1 ], cost: 1+3*free

    122: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && 0>=1+free_6 && 0>=1+free_5 ], cost: 1+3*free

    123: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && 0>=1+free_6 && free_5>=1 ], cost: 1+3*free

    124: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && free_6>=1 && 0>=1+free_5 ], cost: 1+3*free

    125: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && free_6>=1 && free_5>=1 ], cost: 1+3*free



Removed unreachable locations (and leaf rules with constant cost):

   Start location: f0

    121: f0 -> f9 : A'=0, B'=1, C'=1, D'=0, E'=0, F'=0, H'=0, Q'=0, [ free>=1 ], cost: 1+3*free

    122: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && 0>=1+free_6 && 0>=1+free_5 ], cost: 1+3*free

    123: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && 0>=1+free_6 && free_5>=1 ], cost: 1+3*free

    124: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && free_6>=1 && 0>=1+free_5 ], cost: 1+3*free

    125: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && free_6>=1 && free_5>=1 ], cost: 1+3*free



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

    121: f0 -> f9 : A'=0, B'=1, C'=1, D'=0, E'=0, F'=0, H'=0, Q'=0, [ free>=1 ], cost: 1+3*free

    122: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && 0>=1+free_6 && 0>=1+free_5 ], cost: 1+3*free

    123: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && 0>=1+free_6 && free_5>=1 ], cost: 1+3*free

    124: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && free_6>=1 && 0>=1+free_5 ], cost: 1+3*free

    125: f0 -> f9 : A'=0, B'=1, C'=1, D'=1, E'=1, F'=0, H'=free_5, Q'=free_6, [ free>=1 && free_6>=1 && free_5>=1 ], cost: 1+3*free



Computing asymptotic complexity for rule 121

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      1+3*free (+), free (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {free==n}

      resulting limit problem:

      [solved]



   Solution:

      free / n

   Resulting cost 1+3*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: 1+3*n

   Rule cost:   1+3*free

   Rule guard:  [ free>=1 ]



WORST_CASE(INF,?)


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(2)
BOUNDS(INF, INF)