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


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


WORST_CASE(Omega(n^1), ?)
proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 4032 ms]
(2) BOUNDS(n^1, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f2(0, 0, 0, D + C, E + B - 1, F + A - 1, G + 1, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: A >= 1 && B >= 1
f999(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(1, 1, H - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, C1)) :|: H >= 1 && C >= 0 && C <= 0 && B >= 0 && B <= 0 && A >= 0 && A <= 0 && D >= 0 && D <= 0 && E >= 0 && E <= 0 && F >= 0 && F <= 0 && G >= 0 && G <= 0 && I >= 0 && I <= 0 && J >= 0 && J <= 0 && K >= 0 && K <= 0 && L >= 0 && L <= 0 && M >= 0 && M <= 0 && N >= 0 && N <= 0 && O >= 0 && O <= 0 && P >= 0 && P <= 0 && Q >= 0 && Q <= 0 && R >= 0 && R <= 0 && S >= 0 && S <= 0 && T >= 0 && T <= 0 && U >= 0 && U <= 0 && V >= 0 && V <= 0 && W >= 0 && W <= 0 && X >= 0 && X <= 0 && Y >= 0 && Y <= 0 && Z >= 0 && Z <= 0 && A1 >= 0 && A1 <= 0 && B1 >= 0 && B1 <= 0
f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(A + 1, B + 1, H + C - 1, D, E, F, G, 0, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: H + C >= 1
f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(A + 1, B + 1, C + H + D - 1, 0, E, F, G, 0, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: H + D >= 1
f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f2(A, B, C, I + D - 1, K + E, M + F, N + G, H, 0, J + 1, 0, L + 1, 0, 0, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: D >= 1
f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(A + L + 1, B + J + 1, C + I + D - 1, 0, 0, 0, 0, H, 0, 0, K + E, 0, M + F, N + G, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: D >= 1
f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(A + 1, B + 1, C + H + I + D - 2, 0, 0, 0, 0, 0, 0, J + 1, K + E, L + 1, M + F, N + G, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: H + I + D >= 2 && D >= 1
f1(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f1(R + A + S + 1, P + B + Q + 1, O + C - 1, D, E, F, G, H, I, J, K, L, M, N, 0, 0, 0, 0, 0, T, U, V, W, X, Y, Z, A1, B1, C1)) :|: C >= 1
f2(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1) -> Com_1(f2(A, B, C, T + D + U + 1, V + E + W - 1, X + F + Z + B1, Y + G + A1, H, I, J, K, L, M, N, O, P, Q, R, S, 0, 0, 0, 0, 0, 0, 0, 0, 0, D1)) :|: G >= 1 && F >= C1 && C1 >= 1 && E >= C1

The start-symbols are:[f999_29]


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

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f999

      0: f1 -> f2 : A'=0, B'=0, C'=0, D'=D+C, E'=-1+E+B, F'=-1+F+A, G'=1+G, [ A>=1 && B>=1 ], cost: 1

      2: f1 -> f1 : A'=1+A, B'=1+B, C'=-1+H+C, H'=0, [ H+C>=1 ], cost: 1

      7: f1 -> f1 : A'=1+R+S+A, B'=1+B+P+Q_1, C'=-1+O+C, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ C>=1 ], cost: 1

      1: f999 -> f1 : A'=1, A1'=0, B'=1, B1'=0, C'=-1+H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ H>=1 && C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 ], cost: 1

      3: f2 -> f1 : A'=1+A, B'=1+B, C'=-1+H+D+C, D'=0, H'=0, [ H+D>=1 ], cost: 1

      4: f2 -> f2 : D'=-1+Q+D, E'=E+K, F'=F+M, G'=G+N, Q'=0, J'=1+J, K'=0, L'=1+L, M'=0, N'=0, [ D>=1 ], cost: 1

      5: f2 -> f1 : A'=1+L+A, B'=1+B+J, C'=-1+Q+D+C, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=E+K, L'=0, M'=F+M, N'=G+N, [ D>=1 ], cost: 1

      6: f2 -> f1 : A'=1+A, B'=1+B, C'=-2+H+Q+D+C, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=E+K, L'=1+L, M'=F+M, N'=G+N, [ H+Q+D>=2 && D>=1 ], cost: 1

      8: f2 -> f2 : A1'=0, B1'=0, C1'=free, D'=1+U+D+T, E'=-1+E+V+W, F'=X+F+B1+Z, G'=Y+G+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ G>=1 && F>=C1 && C1>=1 && E>=C1 ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 0.

   Accelerating the following rules:

      2: f1 -> f1 : A'=1+A, B'=1+B, C'=-1+H+C, H'=0, [ H+C>=1 ], cost: 1

      7: f1 -> f1 : A'=1+R+S+A, B'=1+B+P+Q_1, C'=-1+O+C, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ C>=1 ], cost: 1



   Accelerated rule 2 with metering function H+C, yielding the new rule 9.

   Accelerated rule 7 with backward acceleration, yielding the new rule 10.

   Removing the simple loops: 2 7.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      4: f2 -> f2 : D'=-1+Q+D, E'=E+K, F'=F+M, G'=G+N, Q'=0, J'=1+J, K'=0, L'=1+L, M'=0, N'=0, [ D>=1 ], cost: 1

      8: f2 -> f2 : A1'=0, B1'=0, C1'=free, D'=1+U+D+T, E'=-1+E+V+W, F'=X+F+B1+Z, G'=Y+G+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ G>=1 && F>=C1 && C1>=1 && E>=C1 ], cost: 1



   Accelerated rule 4 with backward acceleration, yielding the new rule 11.

      During metering: Instantiating temporary variables by {free==X+F+B1+Z}

   Found no metering function for rule 8.

   Removing the simple loops: 4.



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

   Start location: f999

      0: f1 -> f2 : A'=0, B'=0, C'=0, D'=D+C, E'=-1+E+B, F'=-1+F+A, G'=1+G, [ A>=1 && B>=1 ], cost: 1

      9: f1 -> f1 : A'=H+A+C, B'=H+B+C, C'=-H, H'=0, [ H+C>=1 ], cost: H+C

     10: f1 -> f1 : A'=A+C, B'=B+C, C'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ C>=1 ], cost: C

      1: f999 -> f1 : A'=1, A1'=0, B'=1, B1'=0, C'=-1+H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ H>=1 && C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 ], cost: 1

      3: f2 -> f1 : A'=1+A, B'=1+B, C'=-1+H+D+C, D'=0, H'=0, [ H+D>=1 ], cost: 1

      5: f2 -> f1 : A'=1+L+A, B'=1+B+J, C'=-1+Q+D+C, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=E+K, L'=0, M'=F+M, N'=G+N, [ D>=1 ], cost: 1

      6: f2 -> f1 : A'=1+A, B'=1+B, C'=-2+H+Q+D+C, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=E+K, L'=1+L, M'=F+M, N'=G+N, [ H+Q+D>=2 && D>=1 ], cost: 1

      8: f2 -> f2 : A1'=0, B1'=0, C1'=free, D'=1+U+D+T, E'=-1+E+V+W, F'=X+F+B1+Z, G'=Y+G+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ G>=1 && F>=C1 && C1>=1 && E>=C1 ], cost: 1

     11: f2 -> f2 : D'=0, E'=E, F'=F, G'=G, Q'=0, J'=D+J, K'=0, L'=L+D, M'=0, N'=0, [ D>=1 ], cost: D



Chained accelerated rules (with incoming rules):

   Start location: f999

      0: f1 -> f2 : A'=0, B'=0, C'=0, D'=D+C, E'=-1+E+B, F'=-1+F+A, G'=1+G, [ A>=1 && B>=1 ], cost: 1

     20: f1 -> f2 : A'=0, A1'=0, B'=0, B1'=0, C'=0, C1'=free, D'=1+U+D+T+C, E'=-2+E+B+V+W, F'=-1+X+F+B1+A+Z, G'=1+Y+G+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 ], cost: 2

     21: f1 -> f2 : A'=0, B'=0, C'=0, D'=0, E'=-1+E+B, F'=-1+F+A, G'=1+G, Q'=0, J'=D+J+C, K'=0, L'=L+D+C, M'=0, N'=0, [ A>=1 && B>=1 && D+C>=1 ], cost: 1+D+C

      1: f999 -> f1 : A'=1, A1'=0, B'=1, B1'=0, C'=-1+H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ H>=1 && C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 ], cost: 1

     12: f999 -> f1 : A'=H, A1'=0, B'=H, B1'=0, C'=0, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 && -1+H>=1 ], cost: H

     16: f999 -> f1 : A'=H, A1'=0, B'=H, B1'=0, C'=0, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 && -1+H>=1 ], cost: H

      3: f2 -> f1 : A'=1+A, B'=1+B, C'=-1+H+D+C, D'=0, H'=0, [ H+D>=1 ], cost: 1

      5: f2 -> f1 : A'=1+L+A, B'=1+B+J, C'=-1+Q+D+C, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=E+K, L'=0, M'=F+M, N'=G+N, [ D>=1 ], cost: 1

      6: f2 -> f1 : A'=1+A, B'=1+B, C'=-2+H+Q+D+C, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=E+K, L'=1+L, M'=F+M, N'=G+N, [ H+Q+D>=2 && D>=1 ], cost: 1

     13: f2 -> f1 : A'=H+D+A+C, B'=H+B+D+C, C'=0, D'=0, H'=0, [ H+D>=1 && -1+H+D+C>=1 ], cost: H+D+C

     14: f2 -> f1 : A'=H+L+Q+D+A+C, B'=H+B+Q+D+J+C, C'=-H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=E+K, L'=0, M'=F+M, N'=G+N, [ D>=1 && -1+H+Q+D+C>=1 ], cost: H+Q+D+C

     15: f2 -> f1 : A'=-1+H+Q+D+A+C, B'=-1+H+B+Q+D+C, C'=0, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=E+K, L'=1+L, M'=F+M, N'=G+N, [ H+Q+D>=2 && D>=1 && -2+H+Q+D+C>=1 ], cost: -1+H+Q+D+C

     17: f2 -> f1 : A'=H+D+A+C, B'=H+B+D+C, C'=0, D'=0, H'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ H+D>=1 && -1+H+D+C>=1 ], cost: H+D+C

     18: f2 -> f1 : A'=L+Q+D+A+C, B'=B+Q+D+J+C, C'=0, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=E+K, L'=0, M'=F+M, N'=G+N, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ D>=1 && -1+Q+D+C>=1 ], cost: Q+D+C

     19: f2 -> f1 : A'=-1+H+Q+D+A+C, B'=-1+H+B+Q+D+C, C'=0, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=E+K, L'=1+L, M'=F+M, N'=G+N, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ H+Q+D>=2 && D>=1 && -2+H+Q+D+C>=1 ], cost: -1+H+Q+D+C



Eliminated locations (on tree-shaped paths):

   Start location: f999

     22: f1 -> f1 : A'=1, B'=1, C'=-1+H+D+C, D'=0, E'=-1+E+B, F'=-1+F+A, G'=1+G, H'=0, [ A>=1 && B>=1 && H+D+C>=1 ], cost: 2

     23: f1 -> f1 : A'=1+L, B'=1+J, C'=-1+Q+D+C, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=-1+E+B+K, L'=0, M'=-1+F+M+A, N'=1+G+N, [ A>=1 && B>=1 && D+C>=1 ], cost: 2

     24: f1 -> f1 : A'=1, B'=1, C'=-2+H+Q+D+C, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-1+E+B+K, L'=1+L, M'=-1+F+M+A, N'=1+G+N, [ A>=1 && B>=1 && H+Q+D+C>=2 && D+C>=1 ], cost: 2

     25: f1 -> f1 : A'=H+D+C, B'=H+D+C, C'=0, D'=0, E'=-1+E+B, F'=-1+F+A, G'=1+G, H'=0, [ A>=1 && B>=1 && -1+H+D+C>=1 ], cost: 1+H+D+C

     26: f1 -> f1 : A'=H+L+Q+D+C, B'=H+Q+D+J+C, C'=-H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=-1+E+B+K, L'=0, M'=-1+F+M+A, N'=1+G+N, [ A>=1 && B>=1 && D+C>=1 && -1+H+Q+D+C>=1 ], cost: 1+H+Q+D+C

     27: f1 -> f1 : A'=-1+H+Q+D+C, B'=-1+H+Q+D+C, C'=0, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-1+E+B+K, L'=1+L, M'=-1+F+M+A, N'=1+G+N, [ A>=1 && B>=1 && D+C>=1 && -2+H+Q+D+C>=1 ], cost: H+Q+D+C

     28: f1 -> f1 : A'=H+D+C, B'=H+D+C, C'=0, D'=0, E'=-1+E+B, F'=-1+F+A, G'=1+G, H'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ A>=1 && B>=1 && -1+H+D+C>=1 ], cost: 1+H+D+C

     29: f1 -> f1 : A'=L+Q+D+C, B'=Q+D+J+C, C'=0, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=-1+E+B+K, L'=0, M'=-1+F+M+A, N'=1+G+N, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ A>=1 && B>=1 && D+C>=1 && -1+Q+D+C>=1 ], cost: 1+Q+D+C

     30: f1 -> f1 : A'=-1+H+Q+D+C, B'=-1+H+Q+D+C, C'=0, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-1+E+B+K, L'=1+L, M'=-1+F+M+A, N'=1+G+N, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ A>=1 && B>=1 && D+C>=1 && -2+H+Q+D+C>=1 ], cost: H+Q+D+C

     31: f1 -> f1 : A'=1, A1'=0, B'=1, B1'=0, C'=H+U+D+T+C, C1'=free, D'=0, E'=-2+E+B+V+W, F'=-1+X+F+B1+A+Z, G'=1+Y+G+A1, H'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+H+U+D+T+C>=1 ], cost: 3

     32: f1 -> f1 : A'=1+L, A1'=0, B'=1+J, B1'=0, C'=U+Q+D+T+C, C1'=free, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=-2+E+B+V+W+K, L'=0, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 ], cost: 3

     33: f1 -> f1 : A'=1, A1'=0, B'=1, B1'=0, C'=-1+H+U+Q+D+T+C, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-2+E+B+V+W+K, L'=1+L, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+H+U+Q+D+T+C>=2 && 1+U+D+T+C>=1 ], cost: 3

     34: f1 -> f1 : A'=1+H+U+D+T+C, A1'=0, B'=1+H+U+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=-2+E+B+V+W, F'=-1+X+F+B1+A+Z, G'=1+Y+G+A1, H'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && H+U+D+T+C>=1 ], cost: 3+H+U+D+T+C

     35: f1 -> f1 : A'=1+H+U+L+Q+D+T+C, A1'=0, B'=1+H+U+Q+D+J+T+C, B1'=0, C'=-H, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=-2+E+B+V+W+K, L'=0, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && H+U+Q+D+T+C>=1 ], cost: 3+H+U+Q+D+T+C

     36: f1 -> f1 : A'=H+U+Q+D+T+C, A1'=0, B'=H+U+Q+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-2+E+B+V+W+K, L'=1+L, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && -1+H+U+Q+D+T+C>=1 ], cost: 2+H+U+Q+D+T+C

     37: f1 -> f1 : A'=1+H+U+D+T+C, A1'=0, B'=1+H+U+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=-2+E+B+V+W, F'=-1+X+F+B1+A+Z, G'=1+Y+G+A1, H'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && H+U+D+T+C>=1 ], cost: 3+H+U+D+T+C

     38: f1 -> f1 : A'=1+U+L+Q+D+T+C, A1'=0, B'=1+U+Q+D+J+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=-2+E+B+V+W+K, L'=0, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && U+Q+D+T+C>=1 ], cost: 3+U+Q+D+T+C

     39: f1 -> f1 : A'=H+U+Q+D+T+C, A1'=0, B'=H+U+Q+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-2+E+B+V+W+K, L'=1+L, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && -1+H+U+Q+D+T+C>=1 ], cost: 2+H+U+Q+D+T+C

     40: f1 -> f1 : A'=1, B'=1, C'=-1+H, D'=0, E'=-1+E+B, F'=-1+F+A, G'=1+G, H'=0, Q'=0, J'=D+J+C, K'=0, L'=L+D+C, M'=0, N'=0, [ A>=1 && B>=1 && D+C>=1 && H>=1 ], cost: 2+D+C

     41: f1 -> f1 : A'=H, B'=H, C'=0, D'=0, E'=-1+E+B, F'=-1+F+A, G'=1+G, H'=0, Q'=0, J'=D+J+C, K'=0, L'=L+D+C, M'=0, N'=0, [ A>=1 && B>=1 && D+C>=1 && -1+H>=1 ], cost: 1+H+D+C

     42: f1 -> f1 : A'=H, B'=H, C'=0, D'=0, E'=-1+E+B, F'=-1+F+A, G'=1+G, H'=0, Q'=0, J'=D+J+C, K'=0, L'=L+D+C, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, [ A>=1 && B>=1 && D+C>=1 && -1+H>=1 ], cost: 1+H+D+C

     43: f1 -> [5] : [ A>=1 && B>=1 && D+C>=1 ], cost: 1+D+C

      1: f999 -> f1 : A'=1, A1'=0, B'=1, B1'=0, C'=-1+H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ H>=1 && C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 ], cost: 1

     12: f999 -> f1 : A'=H, A1'=0, B'=H, B1'=0, C'=0, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 && -1+H>=1 ], cost: H

     16: f999 -> f1 : A'=H, A1'=0, B'=H, B1'=0, C'=0, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 && -1+H>=1 ], cost: H



Applied pruning (of leafs and parallel rules):

   Start location: f999

     35: f1 -> f1 : A'=1+H+U+L+Q+D+T+C, A1'=0, B'=1+H+U+Q+D+J+T+C, B1'=0, C'=-H, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=-2+E+B+V+W+K, L'=0, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && H+U+Q+D+T+C>=1 ], cost: 3+H+U+Q+D+T+C

     36: f1 -> f1 : A'=H+U+Q+D+T+C, A1'=0, B'=H+U+Q+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-2+E+B+V+W+K, L'=1+L, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && -1+H+U+Q+D+T+C>=1 ], cost: 2+H+U+Q+D+T+C

     37: f1 -> f1 : A'=1+H+U+D+T+C, A1'=0, B'=1+H+U+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=-2+E+B+V+W, F'=-1+X+F+B1+A+Z, G'=1+Y+G+A1, H'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && H+U+D+T+C>=1 ], cost: 3+H+U+D+T+C

     38: f1 -> f1 : A'=1+U+L+Q+D+T+C, A1'=0, B'=1+U+Q+D+J+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=-2+E+B+V+W+K, L'=0, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && U+Q+D+T+C>=1 ], cost: 3+U+Q+D+T+C

     39: f1 -> f1 : A'=H+U+Q+D+T+C, A1'=0, B'=H+U+Q+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-2+E+B+V+W+K, L'=1+L, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && -1+H+U+Q+D+T+C>=1 ], cost: 2+H+U+Q+D+T+C

     43: f1 -> [5] : [ A>=1 && B>=1 && D+C>=1 ], cost: 1+D+C

      1: f999 -> f1 : A'=1, A1'=0, B'=1, B1'=0, C'=-1+H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ H>=1 && C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 ], cost: 1

     16: f999 -> f1 : A'=H, A1'=0, B'=H, B1'=0, C'=0, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 && -1+H>=1 ], cost: H



Accelerating simple loops of location 0.

   Accelerating the following rules:

     35: f1 -> f1 : A'=1+H+U+L+Q+D+T+C, A1'=0, B'=1+H+U+Q+D+J+T+C, B1'=0, C'=-H, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=-2+E+B+V+W+K, L'=0, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && H+U+Q+D+T+C>=1 ], cost: 3+H+U+Q+D+T+C

     36: f1 -> f1 : A'=H+U+Q+D+T+C, A1'=0, B'=H+U+Q+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-2+E+B+V+W+K, L'=1+L, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && -1+H+U+Q+D+T+C>=1 ], cost: 2+H+U+Q+D+T+C

     37: f1 -> f1 : A'=1+H+U+D+T+C, A1'=0, B'=1+H+U+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=-2+E+B+V+W, F'=-1+X+F+B1+A+Z, G'=1+Y+G+A1, H'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && H+U+D+T+C>=1 ], cost: 3+H+U+D+T+C

     38: f1 -> f1 : A'=1+U+L+Q+D+T+C, A1'=0, B'=1+U+Q+D+J+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=-2+E+B+V+W+K, L'=0, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && U+Q+D+T+C>=1 ], cost: 3+U+Q+D+T+C

     39: f1 -> f1 : A'=H+U+Q+D+T+C, A1'=0, B'=H+U+Q+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-2+E+B+V+W+K, L'=1+L, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && -1+H+U+Q+D+T+C>=1 ], cost: 2+H+U+Q+D+T+C



   Found no metering function for rule 35.

   Found no metering function for rule 36.

   Found no metering function for rule 37.

   Found no metering function for rule 38.

   Found no metering function for rule 39.

   Removing the simple loops:.



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

   Start location: f999

     35: f1 -> f1 : A'=1+H+U+L+Q+D+T+C, A1'=0, B'=1+H+U+Q+D+J+T+C, B1'=0, C'=-H, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=-2+E+B+V+W+K, L'=0, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && H+U+Q+D+T+C>=1 ], cost: 3+H+U+Q+D+T+C

     36: f1 -> f1 : A'=H+U+Q+D+T+C, A1'=0, B'=H+U+Q+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-2+E+B+V+W+K, L'=1+L, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && -1+H+U+Q+D+T+C>=1 ], cost: 2+H+U+Q+D+T+C

     37: f1 -> f1 : A'=1+H+U+D+T+C, A1'=0, B'=1+H+U+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=-2+E+B+V+W, F'=-1+X+F+B1+A+Z, G'=1+Y+G+A1, H'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && H+U+D+T+C>=1 ], cost: 3+H+U+D+T+C

     38: f1 -> f1 : A'=1+U+L+Q+D+T+C, A1'=0, B'=1+U+Q+D+J+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, Q'=0, J'=0, K'=-2+E+B+V+W+K, L'=0, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && U+Q+D+T+C>=1 ], cost: 3+U+Q+D+T+C

     39: f1 -> f1 : A'=H+U+Q+D+T+C, A1'=0, B'=H+U+Q+D+T+C, B1'=0, C'=0, C1'=free, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=1+J, K'=-2+E+B+V+W+K, L'=1+L, M'=-1+X+F+B1+M+A+Z, N'=1+Y+G+N+A1, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ A>=1 && B>=1 && 1+G>=1 && -1+F+A>=C1 && C1>=1 && -1+E+B>=C1 && 1+U+D+T+C>=1 && -1+H+U+Q+D+T+C>=1 ], cost: 2+H+U+Q+D+T+C

     43: f1 -> [5] : [ A>=1 && B>=1 && D+C>=1 ], cost: 1+D+C

      1: f999 -> f1 : A'=1, A1'=0, B'=1, B1'=0, C'=-1+H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ H>=1 && C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 ], cost: 1

     16: f999 -> f1 : A'=H, A1'=0, B'=H, B1'=0, C'=0, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 && -1+H>=1 ], cost: H



Chained accelerated rules (with incoming rules):

   Start location: f999

     43: f1 -> [5] : [ A>=1 && B>=1 && D+C>=1 ], cost: 1+D+C

      1: f999 -> f1 : A'=1, A1'=0, B'=1, B1'=0, C'=-1+H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ H>=1 && C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 ], cost: 1

     16: f999 -> f1 : A'=H, A1'=0, B'=H, B1'=0, C'=0, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 && -1+H>=1 ], cost: H



Eliminated locations (on tree-shaped paths):

   Start location: f999

     44: f999 -> [5] : A'=1, A1'=0, B'=1, B1'=0, C'=-1+H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 && -1+H>=1 ], cost: 1+H

     45: f999 -> [7] : [ C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 && -1+H>=1 ], cost: H



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f999

     44: f999 -> [5] : A'=1, A1'=0, B'=1, B1'=0, C'=-1+H, D'=0, E'=0, F'=0, G'=0, H'=0, Q'=0, J'=0, K'=0, L'=0, M'=0, N'=0, O'=0, P'=0, Q_1'=0, R'=0, S'=0, T'=0, U'=0, V'=0, W'=0, X'=0, Y'=0, Z'=0, [ C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 && -1+H>=1 ], cost: 1+H



Computing asymptotic complexity for rule 44

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      1-W (+/+!), 1+Y (+/+!), 1-J (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1-E (+/+!), 1+G (+/+!), 1+L (+/+!), 1+B (+/+!), 1-A (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+F (+/+!), 1+K (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1-D (+/+!), 1+V (+/+!), 1-X (+/+!), 1+Q (+/+!), 1+N (+/+!), 1-P (+/+!), 1+C (+/+!), 1+U (+/+!), 1+H (+), 1-F (+/+!), 1-K (+/+!), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1+D (+/+!), 1-V (+/+!), 1+X (+/+!), 1-Q (+/+!), 1-N (+/+!), 1+P (+/+!), 1-C (+/+!), 1+W (+/+!), 1-Y (+/+!), 1+J (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1+E (+/+!), 1-G (+/+!), 1-L (+/+!), 1-B (+/+!), 1+A (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {C==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1-J (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1-E (+/+!), 1+G (+/+!), 1+L (+/+!), 1+B (+/+!), 1-A (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+F (+/+!), 1+K (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1-D (+/+!), 1+V (+/+!), 1-X (+/+!), 1+Q (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-F (+/+!), 1-K (+/+!), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1+D (+/+!), 1-V (+/+!), 1+X (+/+!), 1-Q (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1+J (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1+E (+/+!), 1-G (+/+!), 1-L (+/+!), 1-B (+/+!), 1+A (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {B==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1-J (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1-E (+/+!), 1+G (+/+!), 1+L (+/+!), 1-A (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+F (+/+!), 1+K (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1-D (+/+!), 1+V (+/+!), 1-X (+/+!), 1+Q (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-F (+/+!), 1-K (+/+!), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1+D (+/+!), 1-V (+/+!), 1+X (+/+!), 1-Q (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1+J (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1+E (+/+!), 1-G (+/+!), 1-L (+/+!), 1+A (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {A==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1-J (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1-E (+/+!), 1+G (+/+!), 1+L (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+F (+/+!), 1+K (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1-D (+/+!), 1+V (+/+!), 1-X (+/+!), 1+Q (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-F (+/+!), 1-K (+/+!), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1+D (+/+!), 1-V (+/+!), 1+X (+/+!), 1-Q (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1+J (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1+E (+/+!), 1-G (+/+!), 1-L (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {D==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1-J (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1-E (+/+!), 1+G (+/+!), 1+L (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+F (+/+!), 1+K (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+Q (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-F (+/+!), 1-K (+/+!), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1-Q (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1+J (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1+E (+/+!), 1-G (+/+!), 1-L (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {E==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1-J (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1+G (+/+!), 1+L (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+F (+/+!), 1+K (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+Q (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-F (+/+!), 1-K (+/+!), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1-Q (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1+J (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1-G (+/+!), 1-L (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {F==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1-J (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1+G (+/+!), 1+L (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+K (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+Q (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-K (+/+!), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1-Q (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1+J (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1-G (+/+!), 1-L (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {G==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1-J (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1+L (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+K (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+Q (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-K (+/+!), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1-Q (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1+J (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1-L (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {Q==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1-J (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1+L (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+K (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-K (+/+!), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1+J (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1-L (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {J==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1+L (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+K (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-K (+/+!), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1-L (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {K==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1+L (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1-L (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {L==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1-M (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1+M (+/+!), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {M==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+N (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1-N (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {N==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1-O (+/+!), 1+T (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1+O (+/+!), 1-T (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {O==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1+T (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1-P (+/+!), 1+U (+/+!), 1+H (+), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1+P (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1-T (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {P==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Q_1 (+/+!), 1+Z (+/+!), 1+T (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+U (+/+!), 1+H (+), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Q_1 (+/+!), 1-Z (+/+!), 1-T (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {Q_1==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Z (+/+!), 1+T (+/+!), 1-R (+/+!), 1-U (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+U (+/+!), 1+H (+), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Z (+/+!), 1-T (+/+!), 1+R (+/+!) [not solved]



      applying transformation rule (C) using substitution {R==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Z (+/+!), 1+T (+/+!), 1-U (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1+S (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+U (+/+!), 1+H (+), 1-A1 (+/+!), 1-S (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Z (+/+!), 1-T (+/+!) [not solved]



      applying transformation rule (C) using substitution {S==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Z (+/+!), 1+T (+/+!), 1-U (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+U (+/+!), 1+H (+), 1-A1 (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Z (+/+!), 1-T (+/+!) [not solved]



      applying transformation rule (C) using substitution {T==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Z (+/+!), 1-U (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+U (+/+!), 1+H (+), 1-A1 (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Z (+/+!) [not solved]



      applying transformation rule (C) using substitution {U==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Z (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1-B1 (+/+!), 1+V (+/+!), 1-X (+/+!), 1+H (+), 1-A1 (+/+!), 1+B1 (+/+!), 1-V (+/+!), 1+X (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Z (+/+!) [not solved]



      applying transformation rule (C) using substitution {V==0}

      resulting limit problem:

      1-W (+/+!), 1+Y (+/+!), 1 (+/+!), 1+Z (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1-B1 (+/+!), 1-X (+/+!), 1+H (+), 1-A1 (+/+!), 1+B1 (+/+!), 1+X (+/+!), 1+W (+/+!), 1-Y (+/+!), 1-Z (+/+!) [not solved]



      applying transformation rule (C) using substitution {W==0}

      resulting limit problem:

      1+Y (+/+!), 1 (+/+!), 1+Z (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1-B1 (+/+!), 1-X (+/+!), 1+H (+), 1-A1 (+/+!), 1+B1 (+/+!), 1+X (+/+!), 1-Y (+/+!), 1-Z (+/+!) [not solved]



      applying transformation rule (C) using substitution {X==0}

      resulting limit problem:

      1+Y (+/+!), 1 (+/+!), 1+Z (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1-B1 (+/+!), 1+H (+), 1-A1 (+/+!), 1+B1 (+/+!), 1-Y (+/+!), 1-Z (+/+!) [not solved]



      applying transformation rule (C) using substitution {Y==0}

      resulting limit problem:

      1 (+/+!), 1+Z (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1-B1 (+/+!), 1+H (+), 1-A1 (+/+!), 1+B1 (+/+!), 1-Z (+/+!) [not solved]



      applying transformation rule (C) using substitution {Z==0}

      resulting limit problem:

      1 (+/+!), -1+H (+/+!), 1+A1 (+/+!), 1-B1 (+/+!), 1+H (+), 1-A1 (+/+!), 1+B1 (+/+!) [not solved]



      applying transformation rule (C) using substitution {A1==0}

      resulting limit problem:

      1 (+/+!), -1+H (+/+!), 1-B1 (+/+!), 1+H (+), 1+B1 (+/+!) [not solved]



      applying transformation rule (C) using substitution {B1==0}

      resulting limit problem:

      1 (+/+!), -1+H (+/+!), 1+H (+) [not solved]



      applying transformation rule (B), deleting 1 (+/+!)

      resulting limit problem:

      -1+H (+/+!), 1+H (+) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



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

      resulting limit problem:

      [solved]



   Solution:

      X / 0

      H / n

      U / 0

      E / 0

      R / 0

      O / 0

      B / 0

      L / 0

      Y / 0

      Q / 0

      V / 0

      F / 0

      S / 0

      D / 0

      P / 0

      B1 / 0

      M / 0

      A / 0

      J / 0

      W / 0

      G / 0

      T / 0

      Q_1 / 0

      Z / 0

      C / 0

      N / 0

      A1 / 0

      K / 0

   Resulting cost 1+n has complexity: Poly(n^1)



Found new complexity Poly(n^1).



Obtained the following overall complexity (w.r.t. the length of the input n):

   Complexity:  Poly(n^1)

   Cpx degree:  1

   Solved cost: 1+n

   Rule cost:   1+H

   Rule guard:  [ C==0 && B==0 && A==0 && D==0 && E==0 && F==0 && G==0 && Q==0 && J==0 && K==0 && L==0 && M==0 && N==0 && O==0 && P==0 && Q_1==0 && R==0 && S==0 && T==0 && U==0 && V==0 && W==0 && X==0 && Y==0 && Z==0 && A1==0 && B1==0 && -1+H>=1 ]



WORST_CASE(Omega(n^1),?)


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

(2)
BOUNDS(n^1, INF)