/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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


MAYBE
proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 7993 ms]
(2) BOUNDS(1, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B, C, D, E, F, G, H, I, J) -> Com_1(f15(1, 4, K, 0, L, 0, 0, 0, 0, 0)) :|: K >= 0 && L >= 0
f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C, D + 1, E, 0, 0, 0, 0, 0)) :|: 0 >= D && 0 >= C && B >= 1 && I >= 0 && I <= 0
f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B - 1, C, 0, E, K, 0, 0, 0, 0)) :|: D >= 1 && 0 >= C && K >= 0 && B >= 1 && 1 >= K && I >= 0 && I <= 0
f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A + 1, A + 4, K, 0, E, L, 0, 0, 0, 0)) :|: 0 >= C && L >= 0 && 1 >= L && 0 >= B && K >= 0 && I >= 0 && I <= 0
f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C - 1, D, E, K, 0, 0, 0, 0)) :|: C >= 1 && 1 >= K && K >= 0 && I >= 0 && I <= 0
f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f77(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= H && J >= 1 + E
f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f77(A, B, C, D, E, F, G, H, I, J)) :|: H >= 1
f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f48(A, B, C, D + 1, E, F, 0, H, I, J)) :|: E >= J && 0 >= H && 0 >= D && 0 >= C && B >= 1
f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f48(A, B - 1, C, 0, E, F, K, H, I, J)) :|: E >= J && 0 >= H && D >= 1 && 0 >= C && K >= 0 && B >= 1 && 1 >= K
f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f48(A + 1, A + 4, K, 0, E, F, L, H, I, J)) :|: E >= J && 0 >= H && 0 >= C && L >= 0 && 1 >= L && 0 >= B && K >= 0
f36(A, B, C, D, E, F, G, H, I, J) -> Com_1(f48(A, B, C - 1, D, E, F, K, H, I, J)) :|: E >= J && 0 >= H && C >= 1 && 1 >= K && K >= 0
f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C, D, E, F, G, H, I, J + 1)) :|: 0 >= G
f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C, D, E, F, G, H, I, J + 1)) :|: F >= 1 && G >= 1
f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C, D + 1, E, F, G, 0, I, J + 1)) :|: G >= 1 && 0 >= F && E + 1 >= A && 0 >= D && 0 >= C && B >= 1
f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B - 1, C, 0, E, F, G, K, I, J + 1)) :|: G >= 1 && 0 >= F && E + 1 >= A && D >= 1 && 0 >= C && K >= 0 && B >= 1 && 1 >= K
f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A + 1, A + 4, K, 0, E, F, G, L, I, J + 1)) :|: G >= 1 && 0 >= F && E >= A && 0 >= C && L >= 0 && 1 >= L && 0 >= B && K >= 0
f48(A, B, C, D, E, F, G, H, I, J) -> Com_1(f36(A, B, C - 1, D, E, F, G, K, I, J + 1)) :|: G >= 1 && 0 >= F && E + 1 >= A && C >= 1 && 1 >= K && K >= 0
f77(A, B, C, D, E, F, G, H, I, J) -> Com_1(f15(A, B, C, D, E, F, G, H, I, J)) :|: H >= 1
f77(A, B, C, D, E, F, G, H, I, J) -> Com_1(f15(A, B, C, D, E, F, G, H, 1, J)) :|: 0 >= H
f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f81(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= I + 1
f15(A, B, C, D, E, F, G, H, I, J) -> Com_1(f81(A, B, C, D, E, F, G, H, I, J)) :|: I >= 1

The start-symbols are:[f0_10]


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

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f0 -> f15 : A'=1, B'=4, C'=free, D'=0, E'=free_1, F'=0, G'=0, H'=0, Q'=0, J'=0, [ free>=0 && free_1>=0 ], cost: 1

      1: f15 -> f36 : D'=1+D, F'=0, G'=0, H'=0, Q'=0, J'=0, [ 0>=D && 0>=C && B>=1 && Q==0 ], cost: 1

      2: f15 -> f36 : B'=-1+B, D'=0, F'=free_2, G'=0, H'=0, Q'=0, J'=0, [ D>=1 && 0>=C && free_2>=0 && B>=1 && 1>=free_2 && Q==0 ], cost: 1

      3: f15 -> f36 : A'=1+A, B'=4+A, C'=free_3, D'=0, F'=free_4, G'=0, H'=0, Q'=0, J'=0, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && free_3>=0 && Q==0 ], cost: 1

      4: f15 -> f36 : C'=-1+C, F'=free_5, G'=0, H'=0, Q'=0, J'=0, [ C>=1 && 1>=free_5 && free_5>=0 && Q==0 ], cost: 1

     19: f15 -> f81 : [ 0>=1+Q ], cost: 1

     20: f15 -> f81 : [ Q>=1 ], cost: 1

      5: f36 -> f77 : [ 0>=H && J>=1+E ], cost: 1

      6: f36 -> f77 : [ H>=1 ], cost: 1

      7: f36 -> f48 : D'=1+D, G'=0, [ E>=J && 0>=H && 0>=D && 0>=C && B>=1 ], cost: 1

      8: f36 -> f48 : B'=-1+B, D'=0, G'=free_6, [ E>=J && 0>=H && D>=1 && 0>=C && free_6>=0 && B>=1 && 1>=free_6 ], cost: 1

      9: f36 -> f48 : A'=1+A, B'=4+A, C'=free_7, D'=0, G'=free_8, [ E>=J && 0>=H && 0>=C && free_8>=0 && 1>=free_8 && 0>=B && free_7>=0 ], cost: 1

     10: f36 -> f48 : C'=-1+C, G'=free_9, [ E>=J && 0>=H && C>=1 && 1>=free_9 && free_9>=0 ], cost: 1

     11: f48 -> f36 : J'=1+J, [ 0>=G ], cost: 1

     12: f48 -> f36 : J'=1+J, [ F>=1 && G>=1 ], cost: 1

     13: f48 -> f36 : D'=1+D, H'=0, J'=1+J, [ G>=1 && 0>=F && 1+E>=A && 0>=D && 0>=C && B>=1 ], cost: 1

     14: f48 -> f36 : B'=-1+B, D'=0, H'=free_10, J'=1+J, [ G>=1 && 0>=F && 1+E>=A && D>=1 && 0>=C && free_10>=0 && B>=1 && 1>=free_10 ], cost: 1

     15: f48 -> f36 : A'=1+A, B'=4+A, C'=free_11, D'=0, H'=free_12, J'=1+J, [ G>=1 && 0>=F && E>=A && 0>=C && free_12>=0 && 1>=free_12 && 0>=B && free_11>=0 ], cost: 1

     16: f48 -> f36 : C'=-1+C, H'=free_13, J'=1+J, [ G>=1 && 0>=F && 1+E>=A && C>=1 && 1>=free_13 && free_13>=0 ], cost: 1

     17: f77 -> f15 : [ H>=1 ], cost: 1

     18: f77 -> f15 : Q'=1, [ 0>=H ], cost: 1



Checking for constant complexity:

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

      0: f0 -> f15 : A'=1, B'=4, C'=free, D'=0, E'=free_1, F'=0, G'=0, H'=0, Q'=0, J'=0, [ free>=0 && free_1>=0 ], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f0 -> f15 : A'=1, B'=4, C'=free, D'=0, E'=free_1, F'=0, G'=0, H'=0, Q'=0, J'=0, [ free>=0 && free_1>=0 ], cost: 1

      1: f15 -> f36 : D'=1+D, F'=0, G'=0, H'=0, Q'=0, J'=0, [ 0>=D && 0>=C && B>=1 && Q==0 ], cost: 1

      2: f15 -> f36 : B'=-1+B, D'=0, F'=free_2, G'=0, H'=0, Q'=0, J'=0, [ D>=1 && 0>=C && free_2>=0 && B>=1 && 1>=free_2 && Q==0 ], cost: 1

      3: f15 -> f36 : A'=1+A, B'=4+A, C'=free_3, D'=0, F'=free_4, G'=0, H'=0, Q'=0, J'=0, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && free_3>=0 && Q==0 ], cost: 1

      4: f15 -> f36 : C'=-1+C, F'=free_5, G'=0, H'=0, Q'=0, J'=0, [ C>=1 && 1>=free_5 && free_5>=0 && Q==0 ], cost: 1

      5: f36 -> f77 : [ 0>=H && J>=1+E ], cost: 1

      6: f36 -> f77 : [ H>=1 ], cost: 1

      7: f36 -> f48 : D'=1+D, G'=0, [ E>=J && 0>=H && 0>=D && 0>=C && B>=1 ], cost: 1

      8: f36 -> f48 : B'=-1+B, D'=0, G'=free_6, [ E>=J && 0>=H && D>=1 && 0>=C && free_6>=0 && B>=1 && 1>=free_6 ], cost: 1

      9: f36 -> f48 : A'=1+A, B'=4+A, C'=free_7, D'=0, G'=free_8, [ E>=J && 0>=H && 0>=C && free_8>=0 && 1>=free_8 && 0>=B && free_7>=0 ], cost: 1

     10: f36 -> f48 : C'=-1+C, G'=free_9, [ E>=J && 0>=H && C>=1 && 1>=free_9 && free_9>=0 ], cost: 1

     11: f48 -> f36 : J'=1+J, [ 0>=G ], cost: 1

     12: f48 -> f36 : J'=1+J, [ F>=1 && G>=1 ], cost: 1

     13: f48 -> f36 : D'=1+D, H'=0, J'=1+J, [ G>=1 && 0>=F && 1+E>=A && 0>=D && 0>=C && B>=1 ], cost: 1

     14: f48 -> f36 : B'=-1+B, D'=0, H'=free_10, J'=1+J, [ G>=1 && 0>=F && 1+E>=A && D>=1 && 0>=C && free_10>=0 && B>=1 && 1>=free_10 ], cost: 1

     15: f48 -> f36 : A'=1+A, B'=4+A, C'=free_11, D'=0, H'=free_12, J'=1+J, [ G>=1 && 0>=F && E>=A && 0>=C && free_12>=0 && 1>=free_12 && 0>=B && free_11>=0 ], cost: 1

     16: f48 -> f36 : C'=-1+C, H'=free_13, J'=1+J, [ G>=1 && 0>=F && 1+E>=A && C>=1 && 1>=free_13 && free_13>=0 ], cost: 1

     17: f77 -> f15 : [ H>=1 ], cost: 1

     18: f77 -> f15 : Q'=1, [ 0>=H ], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on tree-shaped paths):

   Start location: f0

      0: f0 -> f15 : A'=1, B'=4, C'=free, D'=0, E'=free_1, F'=0, G'=0, H'=0, Q'=0, J'=0, [ free>=0 && free_1>=0 ], cost: 1

      1: f15 -> f36 : D'=1+D, F'=0, G'=0, H'=0, Q'=0, J'=0, [ 0>=D && 0>=C && B>=1 && Q==0 ], cost: 1

      2: f15 -> f36 : B'=-1+B, D'=0, F'=free_2, G'=0, H'=0, Q'=0, J'=0, [ D>=1 && 0>=C && free_2>=0 && B>=1 && 1>=free_2 && Q==0 ], cost: 1

      3: f15 -> f36 : A'=1+A, B'=4+A, C'=free_3, D'=0, F'=free_4, G'=0, H'=0, Q'=0, J'=0, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && free_3>=0 && Q==0 ], cost: 1

      4: f15 -> f36 : C'=-1+C, F'=free_5, G'=0, H'=0, Q'=0, J'=0, [ C>=1 && 1>=free_5 && free_5>=0 && Q==0 ], cost: 1

     21: f36 -> f36 : D'=1+D, G'=0, J'=1+J, [ E>=J && 0>=H && 0>=D && 0>=C && B>=1 ], cost: 2

     22: f36 -> f36 : B'=-1+B, D'=0, G'=free_6, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && free_6>=0 && B>=1 && 0>=free_6 ], cost: 2

     23: f36 -> f36 : B'=-1+B, D'=0, G'=free_6, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && B>=1 && 1>=free_6 && F>=1 && free_6>=1 ], cost: 2

     24: f36 -> f36 : B'=-1+B, D'=1, G'=free_6, H'=0, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && 1>=free_6 && free_6>=1 && 0>=F && 1+E>=A && -1+B>=1 ], cost: 2

     25: f36 -> f36 : A'=1+A, B'=4+A, C'=free_11, D'=0, G'=free_6, H'=free_12, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && B>=1 && 1>=free_6 && free_6>=1 && 0>=F && E>=A && free_12>=0 && 1>=free_12 && 0>=-1+B && free_11>=0 ], cost: 2

     26: f36 -> f36 : A'=1+A, B'=4+A, C'=free_7, D'=0, G'=free_8, J'=1+J, [ E>=J && 0>=H && 0>=C && free_8>=0 && 0>=B && free_7>=0 && 0>=free_8 ], cost: 2

     27: f36 -> f36 : A'=1+A, B'=4+A, C'=free_7, D'=0, G'=free_8, J'=1+J, [ E>=J && 0>=H && 0>=C && 1>=free_8 && 0>=B && free_7>=0 && F>=1 && free_8>=1 ], cost: 2

     28: f36 -> f36 : A'=1+A, B'=4+A, C'=free_7, D'=1, G'=free_8, H'=0, J'=1+J, [ E>=J && 0>=H && 0>=C && 1>=free_8 && 0>=B && free_7>=0 && free_8>=1 && 0>=F && 1+E>=1+A && 0>=free_7 && 4+A>=1 ], cost: 2

     29: f36 -> f36 : A'=2+A, B'=5+A, C'=free_11, D'=0, G'=free_8, H'=free_12, J'=1+J, [ E>=J && 0>=H && 0>=C && 1>=free_8 && 0>=B && free_7>=0 && free_8>=1 && 0>=F && E>=1+A && 0>=free_7 && free_12>=0 && 1>=free_12 && 0>=4+A && free_11>=0 ], cost: 2

     30: f36 -> f36 : A'=1+A, B'=4+A, C'=-1+free_7, D'=0, G'=free_8, H'=free_13, J'=1+J, [ E>=J && 0>=H && 0>=C && 1>=free_8 && 0>=B && free_8>=1 && 0>=F && 1+E>=1+A && free_7>=1 && 1>=free_13 && free_13>=0 ], cost: 2

     31: f36 -> f36 : C'=-1+C, G'=free_9, J'=1+J, [ E>=J && 0>=H && C>=1 && free_9>=0 && 0>=free_9 ], cost: 2

     32: f36 -> f36 : C'=-1+C, G'=free_9, J'=1+J, [ E>=J && 0>=H && C>=1 && 1>=free_9 && F>=1 && free_9>=1 ], cost: 2

     33: f36 -> f36 : C'=-1+C, D'=1+D, G'=free_9, H'=0, J'=1+J, [ E>=J && 0>=H && C>=1 && 1>=free_9 && free_9>=1 && 0>=F && 1+E>=A && 0>=D && 0>=-1+C && B>=1 ], cost: 2

     34: f36 -> f36 : B'=-1+B, C'=-1+C, D'=0, G'=free_9, H'=free_10, J'=1+J, [ E>=J && 0>=H && C>=1 && 1>=free_9 && free_9>=1 && 0>=F && 1+E>=A && D>=1 && 0>=-1+C && free_10>=0 && B>=1 && 1>=free_10 ], cost: 2

     35: f36 -> f36 : A'=1+A, B'=4+A, C'=free_11, D'=0, G'=free_9, H'=free_12, J'=1+J, [ E>=J && 0>=H && C>=1 && 1>=free_9 && free_9>=1 && 0>=F && E>=A && 0>=-1+C && free_12>=0 && 1>=free_12 && 0>=B && free_11>=0 ], cost: 2

     36: f36 -> f36 : C'=-2+C, G'=free_9, H'=free_13, J'=1+J, [ E>=J && 0>=H && 1>=free_9 && free_9>=1 && 0>=F && 1+E>=A && -1+C>=1 && 1>=free_13 && free_13>=0 ], cost: 2

     37: f36 -> f15 : Q'=1, [ 0>=H && J>=1+E ], cost: 2

     38: f36 -> f15 : [ H>=1 ], cost: 2



Accelerating simple loops of location 2.

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

   Accelerating the following rules:

     21: f36 -> f36 : D'=1+D, G'=0, J'=1+J, [ E>=J && 0>=H && 0>=D && 0>=C && B>=1 ], cost: 2

     22: f36 -> f36 : B'=-1+B, D'=0, G'=0, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && B>=1 ], cost: 2

     23: f36 -> f36 : B'=-1+B, D'=0, G'=1, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && B>=1 && F>=1 ], cost: 2

     24: f36 -> f36 : B'=-1+B, D'=1, G'=1, H'=0, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && 0>=F && 1+E>=A && -1+B>=1 ], cost: 2

     25: f36 -> f36 : A'=1+A, B'=4+A, C'=free_11, D'=0, G'=1, H'=free_12, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && 1-B==0 && 0>=F && E>=A && free_12>=0 && 1>=free_12 && free_11>=0 ], cost: 2

     26: f36 -> f36 : A'=1+A, B'=4+A, C'=free_7, D'=0, G'=0, J'=1+J, [ E>=J && 0>=H && 0>=C && 0>=B && free_7>=0 ], cost: 2

     27: f36 -> f36 : A'=1+A, B'=4+A, C'=free_7, D'=0, G'=1, J'=1+J, [ E>=J && 0>=H && 0>=C && 0>=B && free_7>=0 && F>=1 ], cost: 2

     28: f36 -> f36 : A'=1+A, B'=4+A, C'=0, D'=1, G'=1, H'=0, J'=1+J, [ E>=J && 0>=H && 0>=C && 0>=B && 0>=F && 1+E>=1+A && 4+A>=1 ], cost: 2

     29: f36 -> f36 : A'=2+A, B'=5+A, C'=free_11, D'=0, G'=1, H'=free_12, J'=1+J, [ E>=J && 0>=H && 0>=C && 0>=B && 0>=F && E>=1+A && free_12>=0 && 1>=free_12 && 0>=4+A && free_11>=0 ], cost: 2

     30: f36 -> f36 : A'=1+A, B'=4+A, C'=-1+free_7, D'=0, G'=1, H'=free_13, J'=1+J, [ E>=J && 0>=H && 0>=C && 0>=B && 0>=F && 1+E>=1+A && free_7>=1 && 1>=free_13 && free_13>=0 ], cost: 2

     31: f36 -> f36 : C'=-1+C, G'=0, J'=1+J, [ E>=J && 0>=H && C>=1 ], cost: 2

     32: f36 -> f36 : C'=-1+C, G'=1, J'=1+J, [ E>=J && 0>=H && C>=1 && F>=1 ], cost: 2

     33: f36 -> f36 : C'=-1+C, D'=1+D, G'=1, H'=0, J'=1+J, [ E>=J && 0>=H && 1-C==0 && 0>=F && 1+E>=A && 0>=D && B>=1 ], cost: 2

     34: f36 -> f36 : B'=-1+B, C'=-1+C, D'=0, G'=1, H'=free_10, J'=1+J, [ E>=J && 0>=H && 1-C==0 && 0>=F && 1+E>=A && D>=1 && free_10>=0 && B>=1 && 1>=free_10 ], cost: 2

     35: f36 -> f36 : A'=1+A, B'=4+A, C'=free_11, D'=0, G'=1, H'=free_12, J'=1+J, [ E>=J && 0>=H && 1-C==0 && 0>=F && E>=A && free_12>=0 && 1>=free_12 && 0>=B && free_11>=0 ], cost: 2

     36: f36 -> f36 : C'=-2+C, G'=1, H'=free_13, J'=1+J, [ E>=J && 0>=H && 0>=F && 1+E>=A && -1+C>=1 && 1>=free_13 && free_13>=0 ], cost: 2



   Found no metering function for rule 21.

   Found no metering function for rule 22.

   Found no metering function for rule 23.

   Found no metering function for rule 24.

   Found no metering function for rule 25.

   Found no metering function for rule 26.

   Found no metering function for rule 27.

   Found no metering function for rule 28.

   Found no metering function for rule 29.

   Found no metering function for rule 30.

   Found no metering function for rule 31.

   Found no metering function for rule 32.

   Accelerated rule 33 with metering function -1+C, yielding the new rule 39.

   Accelerated rule 34 with metering function -1+C, yielding the new rule 40.

      During metering: Instantiating temporary variables by {free_11==0,free_12==1}

   Accelerated rule 35 with metering function -1+C, yielding the new rule 41.

   Found no metering function for rule 36.

   Removing the simple loops: 33 34 35.



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

   Start location: f0

      0: f0 -> f15 : A'=1, B'=4, C'=free, D'=0, E'=free_1, F'=0, G'=0, H'=0, Q'=0, J'=0, [ free>=0 && free_1>=0 ], cost: 1

      1: f15 -> f36 : D'=1+D, F'=0, G'=0, H'=0, Q'=0, J'=0, [ 0>=D && 0>=C && B>=1 && Q==0 ], cost: 1

      2: f15 -> f36 : B'=-1+B, D'=0, F'=free_2, G'=0, H'=0, Q'=0, J'=0, [ D>=1 && 0>=C && free_2>=0 && B>=1 && 1>=free_2 && Q==0 ], cost: 1

      3: f15 -> f36 : A'=1+A, B'=4+A, C'=free_3, D'=0, F'=free_4, G'=0, H'=0, Q'=0, J'=0, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && free_3>=0 && Q==0 ], cost: 1

      4: f15 -> f36 : C'=-1+C, F'=free_5, G'=0, H'=0, Q'=0, J'=0, [ C>=1 && 1>=free_5 && free_5>=0 && Q==0 ], cost: 1

     21: f36 -> f36 : D'=1+D, G'=0, J'=1+J, [ E>=J && 0>=H && 0>=D && 0>=C && B>=1 ], cost: 2

     22: f36 -> f36 : B'=-1+B, D'=0, G'=0, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && B>=1 ], cost: 2

     23: f36 -> f36 : B'=-1+B, D'=0, G'=1, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && B>=1 && F>=1 ], cost: 2

     24: f36 -> f36 : B'=-1+B, D'=1, G'=1, H'=0, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && 0>=F && 1+E>=A && -1+B>=1 ], cost: 2

     25: f36 -> f36 : A'=1+A, B'=4+A, C'=free_11, D'=0, G'=1, H'=free_12, J'=1+J, [ E>=J && 0>=H && D>=1 && 0>=C && 1-B==0 && 0>=F && E>=A && free_12>=0 && 1>=free_12 && free_11>=0 ], cost: 2

     26: f36 -> f36 : A'=1+A, B'=4+A, C'=free_7, D'=0, G'=0, J'=1+J, [ E>=J && 0>=H && 0>=C && 0>=B && free_7>=0 ], cost: 2

     27: f36 -> f36 : A'=1+A, B'=4+A, C'=free_7, D'=0, G'=1, J'=1+J, [ E>=J && 0>=H && 0>=C && 0>=B && free_7>=0 && F>=1 ], cost: 2

     28: f36 -> f36 : A'=1+A, B'=4+A, C'=0, D'=1, G'=1, H'=0, J'=1+J, [ E>=J && 0>=H && 0>=C && 0>=B && 0>=F && 1+E>=1+A && 4+A>=1 ], cost: 2

     29: f36 -> f36 : A'=2+A, B'=5+A, C'=free_11, D'=0, G'=1, H'=free_12, J'=1+J, [ E>=J && 0>=H && 0>=C && 0>=B && 0>=F && E>=1+A && free_12>=0 && 1>=free_12 && 0>=4+A && free_11>=0 ], cost: 2

     30: f36 -> f36 : A'=1+A, B'=4+A, C'=-1+free_7, D'=0, G'=1, H'=free_13, J'=1+J, [ E>=J && 0>=H && 0>=C && 0>=B && 0>=F && 1+E>=1+A && free_7>=1 && 1>=free_13 && free_13>=0 ], cost: 2

     31: f36 -> f36 : C'=-1+C, G'=0, J'=1+J, [ E>=J && 0>=H && C>=1 ], cost: 2

     32: f36 -> f36 : C'=-1+C, G'=1, J'=1+J, [ E>=J && 0>=H && C>=1 && F>=1 ], cost: 2

     36: f36 -> f36 : C'=-2+C, G'=1, H'=free_13, J'=1+J, [ E>=J && 0>=H && 0>=F && 1+E>=A && -1+C>=1 && 1>=free_13 && free_13>=0 ], cost: 2

     37: f36 -> f15 : Q'=1, [ 0>=H && J>=1+E ], cost: 2

     38: f36 -> f15 : [ H>=1 ], cost: 2

     39: f36 -> f36 : C'=1, D'=-1+C+D, G'=1, H'=0, J'=-1+C+J, [ E>=J && 0>=H && 1-C==0 && 0>=F && 1+E>=A && 0>=D && B>=1 && -1+C>=1 ], cost: -2+2*C

     40: f36 -> f36 : B'=1-C+B, C'=1, D'=0, G'=1, H'=free_10, J'=-1+C+J, [ E>=J && 0>=H && 1-C==0 && 0>=F && 1+E>=A && D>=1 && free_10>=0 && B>=1 && 1>=free_10 && -1+C>=1 ], cost: -2+2*C

     41: f36 -> f36 : A'=-1+C+A, B'=2+C+A, C'=0, D'=0, G'=1, H'=1, J'=-1+C+J, [ E>=J && 0>=H && 1-C==0 && 0>=F && E>=A && 0>=B && -1+C>=1 ], cost: -2+2*C



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f0 -> f15 : A'=1, B'=4, C'=free, D'=0, E'=free_1, F'=0, G'=0, H'=0, Q'=0, J'=0, [ free>=0 && free_1>=0 ], cost: 1

      1: f15 -> f36 : D'=1+D, F'=0, G'=0, H'=0, Q'=0, J'=0, [ 0>=D && 0>=C && B>=1 && Q==0 ], cost: 1

      2: f15 -> f36 : B'=-1+B, D'=0, F'=free_2, G'=0, H'=0, Q'=0, J'=0, [ D>=1 && 0>=C && free_2>=0 && B>=1 && 1>=free_2 && Q==0 ], cost: 1

      3: f15 -> f36 : A'=1+A, B'=4+A, C'=free_3, D'=0, F'=free_4, G'=0, H'=0, Q'=0, J'=0, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && free_3>=0 && Q==0 ], cost: 1

      4: f15 -> f36 : C'=-1+C, F'=free_5, G'=0, H'=0, Q'=0, J'=0, [ C>=1 && 1>=free_5 && free_5>=0 && Q==0 ], cost: 1

     42: f15 -> f36 : D'=2+D, F'=0, G'=0, H'=0, Q'=0, J'=1, [ 0>=C && B>=1 && Q==0 && E>=0 && 0>=1+D ], cost: 3

     43: f15 -> f36 : B'=-1+B, D'=1, F'=free_2, G'=0, H'=0, Q'=0, J'=1, [ D>=1 && 0>=C && free_2>=0 && 1>=free_2 && Q==0 && E>=0 && -1+B>=1 ], cost: 3

     44: f15 -> f36 : A'=1+A, B'=4+A, C'=0, D'=1, F'=free_4, G'=0, H'=0, Q'=0, J'=1, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && Q==0 && E>=0 && 4+A>=1 ], cost: 3

     45: f15 -> f36 : C'=-1+C, D'=1+D, F'=free_5, G'=0, H'=0, Q'=0, J'=1, [ 1-C==0 && 1>=free_5 && free_5>=0 && Q==0 && E>=0 && 0>=D && B>=1 ], cost: 3

     46: f15 -> f36 : B'=-1+B, D'=0, F'=0, G'=0, H'=0, Q'=0, J'=1, [ D==0 && 0>=C && B>=1 && Q==0 && E>=0 ], cost: 3

     47: f15 -> f36 : B'=-1+B, C'=-1+C, D'=0, F'=free_5, G'=0, H'=0, Q'=0, J'=1, [ 1-C==0 && 1>=free_5 && free_5>=0 && Q==0 && E>=0 && D>=1 && B>=1 ], cost: 3

     48: f15 -> f36 : B'=-1+B, C'=-1+C, D'=0, F'=1, G'=1, H'=0, Q'=0, J'=1, [ 1-C==0 && Q==0 && E>=0 && D>=1 && B>=1 ], cost: 3

     49: f15 -> f36 : B'=-1+B, D'=1, F'=0, G'=1, H'=0, Q'=0, J'=1, [ D==0 && 0>=C && Q==0 && E>=0 && 1+E>=A && -1+B>=1 ], cost: 3

     50: f15 -> f36 : B'=-1+B, C'=-1+C, D'=1, F'=0, G'=1, H'=0, Q'=0, J'=1, [ 1-C==0 && Q==0 && E>=0 && D>=1 && 1+E>=A && -1+B>=1 ], cost: 3

     51: f15 -> f36 : A'=1+A, B'=4+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=0, J'=1, [ D==0 && 0>=C && Q==0 && E>=0 && 1-B==0 && E>=A && free_12>=0 && 1>=free_12 && free_11>=0 ], cost: 3

     52: f15 -> f36 : A'=1+A, B'=4+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=0, J'=1, [ 1-C==0 && Q==0 && E>=0 && D>=1 && 1-B==0 && E>=A && free_12>=0 && 1>=free_12 && free_11>=0 ], cost: 3

     53: f15 -> f36 : A'=1+A, B'=4+A, C'=free_7, D'=0, F'=free_2, G'=0, H'=0, Q'=0, J'=1, [ D>=1 && 0>=C && free_2>=0 && 1-B==0 && 1>=free_2 && Q==0 && E>=0 && free_7>=0 ], cost: 3

     54: f15 -> f36 : A'=2+A, B'=5+A, C'=free_7, D'=0, F'=free_4, G'=0, H'=0, Q'=0, J'=1, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && Q==0 && E>=0 && 0>=4+A && free_7>=0 ], cost: 3

     55: f15 -> f36 : A'=1+A, B'=4+A, C'=free_7, D'=0, F'=free_5, G'=0, H'=0, Q'=0, J'=1, [ 1-C==0 && 1>=free_5 && free_5>=0 && Q==0 && E>=0 && 0>=B && free_7>=0 ], cost: 3

     56: f15 -> f36 : A'=1+A, B'=4+A, C'=free_7, D'=0, F'=1, G'=1, H'=0, Q'=0, J'=1, [ D>=1 && 0>=C && 1-B==0 && Q==0 && E>=0 && free_7>=0 ], cost: 3

     57: f15 -> f36 : A'=2+A, B'=5+A, C'=free_7, D'=0, F'=1, G'=1, H'=0, Q'=0, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && 0>=4+A && free_7>=0 ], cost: 3

     58: f15 -> f36 : A'=1+A, B'=4+A, C'=free_7, D'=0, F'=1, G'=1, H'=0, Q'=0, J'=1, [ 1-C==0 && Q==0 && E>=0 && 0>=B && free_7>=0 ], cost: 3

     59: f15 -> f36 : A'=1+A, B'=4+A, C'=0, D'=1, F'=0, G'=1, H'=0, Q'=0, J'=1, [ D>=1 && 0>=C && 1-B==0 && Q==0 && E>=0 && 1+E>=1+A && 4+A>=1 ], cost: 3

     60: f15 -> f36 : A'=2+A, B'=5+A, C'=0, D'=1, F'=0, G'=1, H'=0, Q'=0, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && 4+A==0 && 1+E>=2+A ], cost: 3

     61: f15 -> f36 : A'=1+A, B'=4+A, C'=0, D'=1, F'=0, G'=1, H'=0, Q'=0, J'=1, [ 1-C==0 && Q==0 && E>=0 && 0>=B && 1+E>=1+A && 4+A>=1 ], cost: 3

     62: f15 -> f36 : A'=2+A, B'=5+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=0, J'=1, [ D>=1 && 0>=C && 1-B==0 && Q==0 && E>=0 && E>=1+A && free_12>=0 && 1>=free_12 && 0>=4+A && free_11>=0 ], cost: 3

     63: f15 -> f36 : A'=3+A, B'=6+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=0, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && E>=2+A && free_12>=0 && 1>=free_12 && 0>=5+A && free_11>=0 ], cost: 3

     64: f15 -> f36 : A'=2+A, B'=5+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=0, J'=1, [ 1-C==0 && Q==0 && E>=0 && 0>=B && E>=1+A && free_12>=0 && 1>=free_12 && 0>=4+A && free_11>=0 ], cost: 3

     65: f15 -> f36 : A'=1+A, B'=4+A, C'=-1+free_7, D'=0, F'=0, G'=1, H'=free_13, Q'=0, J'=1, [ D>=1 && 0>=C && 1-B==0 && Q==0 && E>=0 && 1+E>=1+A && free_7>=1 && 1>=free_13 && free_13>=0 ], cost: 3

     66: f15 -> f36 : A'=2+A, B'=5+A, C'=-1+free_7, D'=0, F'=0, G'=1, H'=free_13, Q'=0, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && 0>=4+A && 1+E>=2+A && free_7>=1 && 1>=free_13 && free_13>=0 ], cost: 3

     67: f15 -> f36 : A'=1+A, B'=4+A, C'=-1+free_7, D'=0, F'=0, G'=1, H'=free_13, Q'=0, J'=1, [ 1-C==0 && Q==0 && E>=0 && 0>=B && 1+E>=1+A && free_7>=1 && 1>=free_13 && free_13>=0 ], cost: 3

     68: f15 -> f36 : A'=1+A, B'=4+A, C'=-1+free_3, D'=0, F'=free_4, G'=0, H'=0, Q'=0, J'=1, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && Q==0 && E>=0 && free_3>=1 ], cost: 3

     69: f15 -> f36 : C'=-2+C, F'=free_5, G'=0, H'=0, Q'=0, J'=1, [ 1>=free_5 && free_5>=0 && Q==0 && E>=0 && -1+C>=1 ], cost: 3

     70: f15 -> f36 : A'=1+A, B'=4+A, C'=-1+free_3, D'=0, F'=1, G'=1, H'=0, Q'=0, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && free_3>=1 ], cost: 3

     71: f15 -> f36 : C'=-2+C, F'=1, G'=1, H'=0, Q'=0, J'=1, [ Q==0 && E>=0 && -1+C>=1 ], cost: 3

     72: f15 -> f36 : A'=1+A, B'=4+A, C'=-2+free_3, D'=0, F'=0, G'=1, H'=free_13, Q'=0, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && 1+E>=1+A && -1+free_3>=1 && 1>=free_13 && free_13>=0 ], cost: 3

     73: f15 -> f36 : C'=-3+C, F'=0, G'=1, H'=free_13, Q'=0, J'=1, [ Q==0 && E>=0 && 1+E>=A && -2+C>=1 && 1>=free_13 && free_13>=0 ], cost: 3

     37: f36 -> f15 : Q'=1, [ 0>=H && J>=1+E ], cost: 2

     38: f36 -> f15 : [ H>=1 ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: f0

      0: f0 -> f15 : A'=1, B'=4, C'=free, D'=0, E'=free_1, F'=0, G'=0, H'=0, Q'=0, J'=0, [ free>=0 && free_1>=0 ], cost: 1

     74: f15 -> f15 : D'=1+D, F'=0, G'=0, H'=0, Q'=1, J'=0, [ 0>=D && 0>=C && B>=1 && Q==0 && 0>=1+E ], cost: 3

     75: f15 -> f15 : B'=-1+B, D'=0, F'=free_2, G'=0, H'=0, Q'=1, J'=0, [ D>=1 && 0>=C && free_2>=0 && B>=1 && 1>=free_2 && Q==0 && 0>=1+E ], cost: 3

     76: f15 -> f15 : A'=1+A, B'=4+A, C'=free_3, D'=0, F'=free_4, G'=0, H'=0, Q'=1, J'=0, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && free_3>=0 && Q==0 && 0>=1+E ], cost: 3

     77: f15 -> f15 : C'=-1+C, F'=free_5, G'=0, H'=0, Q'=1, J'=0, [ C>=1 && 1>=free_5 && free_5>=0 && Q==0 && 0>=1+E ], cost: 3

     78: f15 -> f15 : D'=2+D, F'=0, G'=0, H'=0, Q'=1, J'=1, [ 0>=C && B>=1 && Q==0 && E>=0 && 0>=1+D && 1>=1+E ], cost: 5

     79: f15 -> f15 : B'=-1+B, D'=1, F'=free_2, G'=0, H'=0, Q'=1, J'=1, [ D>=1 && 0>=C && free_2>=0 && 1>=free_2 && Q==0 && E>=0 && -1+B>=1 && 1>=1+E ], cost: 5

     80: f15 -> f15 : A'=1+A, B'=4+A, C'=0, D'=1, F'=free_4, G'=0, H'=0, Q'=1, J'=1, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && Q==0 && E>=0 && 4+A>=1 && 1>=1+E ], cost: 5

     81: f15 -> f15 : C'=-1+C, D'=1+D, F'=free_5, G'=0, H'=0, Q'=1, J'=1, [ 1-C==0 && 1>=free_5 && free_5>=0 && Q==0 && E>=0 && 0>=D && B>=1 && 1>=1+E ], cost: 5

     82: f15 -> f15 : B'=-1+B, D'=0, F'=0, G'=0, H'=0, Q'=1, J'=1, [ D==0 && 0>=C && B>=1 && Q==0 && E>=0 && 1>=1+E ], cost: 5

     83: f15 -> f15 : B'=-1+B, C'=-1+C, D'=0, F'=free_5, G'=0, H'=0, Q'=1, J'=1, [ 1-C==0 && 1>=free_5 && free_5>=0 && Q==0 && E>=0 && D>=1 && B>=1 && 1>=1+E ], cost: 5

     84: f15 -> f15 : B'=-1+B, C'=-1+C, D'=0, F'=1, G'=1, H'=0, Q'=1, J'=1, [ 1-C==0 && Q==0 && E>=0 && D>=1 && B>=1 && 1>=1+E ], cost: 5

     85: f15 -> f15 : B'=-1+B, D'=1, F'=0, G'=1, H'=0, Q'=1, J'=1, [ D==0 && 0>=C && Q==0 && E>=0 && 1+E>=A && -1+B>=1 && 1>=1+E ], cost: 5

     86: f15 -> f15 : B'=-1+B, C'=-1+C, D'=1, F'=0, G'=1, H'=0, Q'=1, J'=1, [ 1-C==0 && Q==0 && E>=0 && D>=1 && 1+E>=A && -1+B>=1 && 1>=1+E ], cost: 5

     87: f15 -> f15 : A'=1+A, B'=4+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=1, J'=1, [ D==0 && 0>=C && Q==0 && E>=0 && 1-B==0 && E>=A && free_12>=0 && free_11>=0 && 0>=free_12 && 1>=1+E ], cost: 5

     88: f15 -> f15 : A'=1+A, B'=4+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=0, J'=1, [ D==0 && 0>=C && Q==0 && E>=0 && 1-B==0 && E>=A && 1>=free_12 && free_11>=0 && free_12>=1 ], cost: 5

     89: f15 -> f15 : A'=1+A, B'=4+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=1, J'=1, [ 1-C==0 && Q==0 && E>=0 && D>=1 && 1-B==0 && E>=A && free_12>=0 && free_11>=0 && 0>=free_12 && 1>=1+E ], cost: 5

     90: f15 -> f15 : A'=1+A, B'=4+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=0, J'=1, [ 1-C==0 && Q==0 && E>=0 && D>=1 && 1-B==0 && E>=A && 1>=free_12 && free_11>=0 && free_12>=1 ], cost: 5

     91: f15 -> f15 : A'=1+A, B'=4+A, C'=free_7, D'=0, F'=free_2, G'=0, H'=0, Q'=1, J'=1, [ D>=1 && 0>=C && free_2>=0 && 1-B==0 && 1>=free_2 && Q==0 && E>=0 && free_7>=0 && 1>=1+E ], cost: 5

     92: f15 -> f15 : A'=2+A, B'=5+A, C'=free_7, D'=0, F'=free_4, G'=0, H'=0, Q'=1, J'=1, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && Q==0 && E>=0 && 0>=4+A && free_7>=0 && 1>=1+E ], cost: 5

     93: f15 -> f15 : A'=1+A, B'=4+A, C'=free_7, D'=0, F'=free_5, G'=0, H'=0, Q'=1, J'=1, [ 1-C==0 && 1>=free_5 && free_5>=0 && Q==0 && E>=0 && 0>=B && free_7>=0 && 1>=1+E ], cost: 5

     94: f15 -> f15 : A'=1+A, B'=4+A, C'=free_7, D'=0, F'=1, G'=1, H'=0, Q'=1, J'=1, [ D>=1 && 0>=C && 1-B==0 && Q==0 && E>=0 && free_7>=0 && 1>=1+E ], cost: 5

     95: f15 -> f15 : A'=2+A, B'=5+A, C'=free_7, D'=0, F'=1, G'=1, H'=0, Q'=1, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && 0>=4+A && free_7>=0 && 1>=1+E ], cost: 5

     96: f15 -> f15 : A'=1+A, B'=4+A, C'=free_7, D'=0, F'=1, G'=1, H'=0, Q'=1, J'=1, [ 1-C==0 && Q==0 && E>=0 && 0>=B && free_7>=0 && 1>=1+E ], cost: 5

     97: f15 -> f15 : A'=1+A, B'=4+A, C'=0, D'=1, F'=0, G'=1, H'=0, Q'=1, J'=1, [ D>=1 && 0>=C && 1-B==0 && Q==0 && E>=0 && 1+E>=1+A && 4+A>=1 && 1>=1+E ], cost: 5

     98: f15 -> f15 : A'=2+A, B'=5+A, C'=0, D'=1, F'=0, G'=1, H'=0, Q'=1, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && 4+A==0 && 1+E>=2+A && 1>=1+E ], cost: 5

     99: f15 -> f15 : A'=1+A, B'=4+A, C'=0, D'=1, F'=0, G'=1, H'=0, Q'=1, J'=1, [ 1-C==0 && Q==0 && E>=0 && 0>=B && 1+E>=1+A && 4+A>=1 && 1>=1+E ], cost: 5

    100: f15 -> f15 : A'=2+A, B'=5+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=1, J'=1, [ D>=1 && 0>=C && 1-B==0 && Q==0 && E>=0 && E>=1+A && free_12>=0 && 0>=4+A && free_11>=0 && 0>=free_12 && 1>=1+E ], cost: 5

    101: f15 -> f15 : A'=2+A, B'=5+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=0, J'=1, [ D>=1 && 0>=C && 1-B==0 && Q==0 && E>=0 && E>=1+A && 1>=free_12 && 0>=4+A && free_11>=0 && free_12>=1 ], cost: 5

    102: f15 -> f15 : A'=3+A, B'=6+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=1, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && E>=2+A && free_12>=0 && 0>=5+A && free_11>=0 && 0>=free_12 && 1>=1+E ], cost: 5

    103: f15 -> f15 : A'=3+A, B'=6+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=0, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && E>=2+A && 1>=free_12 && 0>=5+A && free_11>=0 && free_12>=1 ], cost: 5

    104: f15 -> f15 : A'=2+A, B'=5+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=1, J'=1, [ 1-C==0 && Q==0 && E>=0 && 0>=B && E>=1+A && free_12>=0 && 0>=4+A && free_11>=0 && 0>=free_12 && 1>=1+E ], cost: 5

    105: f15 -> f15 : A'=2+A, B'=5+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=0, J'=1, [ 1-C==0 && Q==0 && E>=0 && 0>=B && E>=1+A && 1>=free_12 && 0>=4+A && free_11>=0 && free_12>=1 ], cost: 5

    106: f15 -> f15 : A'=1+A, B'=4+A, C'=-1+free_7, D'=0, F'=0, G'=1, H'=free_13, Q'=1, J'=1, [ D>=1 && 0>=C && 1-B==0 && Q==0 && E>=0 && 1+E>=1+A && free_7>=1 && free_13>=0 && 0>=free_13 && 1>=1+E ], cost: 5

    107: f15 -> f15 : A'=1+A, B'=4+A, C'=-1+free_7, D'=0, F'=0, G'=1, H'=free_13, Q'=0, J'=1, [ D>=1 && 0>=C && 1-B==0 && Q==0 && E>=0 && 1+E>=1+A && free_7>=1 && 1>=free_13 && free_13>=1 ], cost: 5

    108: f15 -> f15 : A'=2+A, B'=5+A, C'=-1+free_7, D'=0, F'=0, G'=1, H'=free_13, Q'=1, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && 0>=4+A && 1+E>=2+A && free_7>=1 && free_13>=0 && 0>=free_13 && 1>=1+E ], cost: 5

    109: f15 -> f15 : A'=2+A, B'=5+A, C'=-1+free_7, D'=0, F'=0, G'=1, H'=free_13, Q'=0, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && 0>=4+A && 1+E>=2+A && free_7>=1 && 1>=free_13 && free_13>=1 ], cost: 5

    110: f15 -> f15 : A'=1+A, B'=4+A, C'=-1+free_7, D'=0, F'=0, G'=1, H'=free_13, Q'=1, J'=1, [ 1-C==0 && Q==0 && E>=0 && 0>=B && 1+E>=1+A && free_7>=1 && free_13>=0 && 0>=free_13 && 1>=1+E ], cost: 5

    111: f15 -> f15 : A'=1+A, B'=4+A, C'=-1+free_7, D'=0, F'=0, G'=1, H'=free_13, Q'=0, J'=1, [ 1-C==0 && Q==0 && E>=0 && 0>=B && 1+E>=1+A && free_7>=1 && 1>=free_13 && free_13>=1 ], cost: 5

    112: f15 -> f15 : A'=1+A, B'=4+A, C'=-1+free_3, D'=0, F'=free_4, G'=0, H'=0, Q'=1, J'=1, [ 0>=C && free_4>=0 && 1>=free_4 && 0>=B && Q==0 && E>=0 && free_3>=1 && 1>=1+E ], cost: 5

    113: f15 -> f15 : C'=-2+C, F'=free_5, G'=0, H'=0, Q'=1, J'=1, [ 1>=free_5 && free_5>=0 && Q==0 && E>=0 && -1+C>=1 && 1>=1+E ], cost: 5

    114: f15 -> f15 : A'=1+A, B'=4+A, C'=-1+free_3, D'=0, F'=1, G'=1, H'=0, Q'=1, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && free_3>=1 && 1>=1+E ], cost: 5

    115: f15 -> f15 : C'=-2+C, F'=1, G'=1, H'=0, Q'=1, J'=1, [ Q==0 && E>=0 && -1+C>=1 && 1>=1+E ], cost: 5

    116: f15 -> f15 : A'=1+A, B'=4+A, C'=-2+free_3, D'=0, F'=0, G'=1, H'=free_13, Q'=1, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && 1+E>=1+A && -1+free_3>=1 && free_13>=0 && 0>=free_13 && 1>=1+E ], cost: 5

    117: f15 -> f15 : A'=1+A, B'=4+A, C'=-2+free_3, D'=0, F'=0, G'=1, H'=free_13, Q'=0, J'=1, [ 0>=C && 0>=B && Q==0 && E>=0 && 1+E>=1+A && -1+free_3>=1 && 1>=free_13 && free_13>=1 ], cost: 5

    118: f15 -> f15 : C'=-3+C, F'=0, G'=1, H'=free_13, Q'=1, J'=1, [ Q==0 && E>=0 && 1+E>=A && -2+C>=1 && free_13>=0 && 0>=free_13 && 1>=1+E ], cost: 5

    119: f15 -> f15 : C'=-3+C, F'=0, G'=1, H'=free_13, Q'=0, J'=1, [ Q==0 && E>=0 && 1+E>=A && -2+C>=1 && 1>=free_13 && free_13>=1 ], cost: 5



Applied pruning (of leafs and parallel rules):

   Start location: f0

      0: f0 -> f15 : A'=1, B'=4, C'=free, D'=0, E'=free_1, F'=0, G'=0, H'=0, Q'=0, J'=0, [ free>=0 && free_1>=0 ], cost: 1

     74: f15 -> f15 : D'=1+D, F'=0, G'=0, H'=0, Q'=1, J'=0, [ 0>=D && 0>=C && B>=1 && Q==0 && 0>=1+E ], cost: 3

     75: f15 -> f15 : B'=-1+B, D'=0, F'=free_2, G'=0, H'=0, Q'=1, J'=0, [ D>=1 && 0>=C && free_2>=0 && B>=1 && 1>=free_2 && Q==0 && 0>=1+E ], cost: 3

     77: f15 -> f15 : C'=-1+C, F'=free_5, G'=0, H'=0, Q'=1, J'=0, [ C>=1 && 1>=free_5 && free_5>=0 && Q==0 && 0>=1+E ], cost: 3

     81: f15 -> f15 : C'=-1+C, D'=1+D, F'=free_5, G'=0, H'=0, Q'=1, J'=1, [ 1-C==0 && 1>=free_5 && free_5>=0 && Q==0 && E>=0 && 0>=D && B>=1 && 1>=1+E ], cost: 5

     89: f15 -> f15 : A'=1+A, B'=4+A, C'=free_11, D'=0, F'=0, G'=1, H'=free_12, Q'=1, J'=1, [ 1-C==0 && Q==0 && E>=0 && D>=1 && 1-B==0 && E>=A && free_12>=0 && free_11>=0 && 0>=free_12 && 1>=1+E ], cost: 5



Accelerating simple loops of location 1.

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

   Accelerating the following rules:

     74: f15 -> f15 : D'=1+D, F'=0, G'=0, H'=0, Q'=1, J'=0, [ 0>=D && 0>=C && B>=1 && Q==0 && 0>=1+E ], cost: 3

     75: f15 -> f15 : B'=-1+B, D'=0, F'=free_2, G'=0, H'=0, Q'=1, J'=0, [ D>=1 && 0>=C && free_2>=0 && B>=1 && 1>=free_2 && Q==0 && 0>=1+E ], cost: 3

     77: f15 -> f15 : C'=-1+C, F'=free_5, G'=0, H'=0, Q'=1, J'=0, [ C>=1 && 1>=free_5 && free_5>=0 && Q==0 && 0>=1+E ], cost: 3

     81: f15 -> f15 : C'=-1+C, D'=1+D, F'=free_5, G'=0, H'=0, Q'=1, J'=1, [ 1-C==0 && 1>=free_5 && free_5>=0 && Q==0 && -E==0 && 0>=D && B>=1 ], cost: 5

     89: f15 -> f15 : A'=1+A, B'=4+A, C'=free_11, D'=0, F'=0, G'=1, H'=0, Q'=1, J'=1, [ 1-C==0 && Q==0 && -E==0 && D>=1 && 1-B==0 && E>=A && free_11>=0 ], cost: 5



   Accelerated rule 74 with metering function -Q, yielding the new rule 120.

   Accelerated rule 75 with metering function -Q, yielding the new rule 121.

   Accelerated rule 77 with metering function -Q, yielding the new rule 122.

   Accelerated rule 81 with metering function meter (where 2*meter==-1+C-Q), yielding the new rule 123.

   Accelerated rule 89 with metering function -E-Q, yielding the new rule 124.

   Removing the simple loops: 74 75 77 81 89.



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

   Start location: f0

      0: f0 -> f15 : A'=1, B'=4, C'=free, D'=0, E'=free_1, F'=0, G'=0, H'=0, Q'=0, J'=0, [ free>=0 && free_1>=0 ], cost: 1

    120: f15 -> f15 : D'=D-Q, F'=0, G'=0, H'=0, Q'=1, J'=0, [ 0>=D && 0>=C && B>=1 && Q==0 && 0>=1+E && -Q>=1 ], cost: -3*Q

    121: f15 -> f15 : B'=B+Q, D'=0, F'=free_2, G'=0, H'=0, Q'=1, J'=0, [ D>=1 && 0>=C && free_2>=0 && B>=1 && 1>=free_2 && Q==0 && 0>=1+E && -Q>=1 ], cost: -3*Q

    122: f15 -> f15 : C'=C+Q, F'=free_5, G'=0, H'=0, Q'=1, J'=0, [ C>=1 && 1>=free_5 && free_5>=0 && Q==0 && 0>=1+E && -Q>=1 ], cost: -3*Q

    123: f15 -> f15 : C'=-meter+C, D'=meter+D, F'=free_5, G'=0, H'=0, Q'=1, J'=1, [ 1-C==0 && 1>=free_5 && free_5>=0 && Q==0 && -E==0 && 0>=D && B>=1 && 2*meter==-1+C-Q && meter>=1 ], cost: 5*meter

    124: f15 -> f15 : A'=A-E-Q, B'=3+A-E-Q, C'=free_11, D'=0, F'=0, G'=1, H'=0, Q'=1, J'=1, [ 1-C==0 && Q==0 && -E==0 && D>=1 && 1-B==0 && E>=A && free_11>=0 && -E-Q>=1 ], cost: -5*E-5*Q



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f0 -> f15 : A'=1, B'=4, C'=free, D'=0, E'=free_1, F'=0, G'=0, H'=0, Q'=0, J'=0, [ free>=0 && free_1>=0 ], cost: 1



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

   Start location: f0

     <empty>



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     <empty>



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:  [ free>=0 && free_1>=0 ]



WORST_CASE(Omega(1),?)


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

(2)
BOUNDS(1, INF)