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


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WORST_CASE(Omega(n^1), ?)
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 7792 ms]
(2) BOUNDS(n^1, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= A + 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H
start(A, B, C, D, E, F, G, H) -> Com_1(lbl42(A, B - 1, C, D, E, F, G, H)) :|: A >= 0 && C >= 0 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H
start(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D - 1, E, F, G, H)) :|: A >= 0 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H
start(A, B, C, D, E, F, G, H) -> Com_1(lbl72(A, 1 + B, C, D - 1, B, F, G, H)) :|: H >= C && A >= 0 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H
lbl72(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D, E, F, G, H)) :|: A >= D + 1 && D + 1 >= 0 && H + 1 >= B && E + 1 >= B && E + 1 <= B && G >= H && G <= H
lbl72(A, B, C, D, E, F, G, H) -> Com_1(lbl72(A, 1 + B, C, D, B, F, G, H)) :|: H >= B && A >= D + 1 && D + 1 >= 0 && H + 1 >= B && E + 1 >= B && E + 1 <= B && G >= H && G <= H
lbl42(A, B, C, D, E, F, G, H) -> Com_1(lbl42(A, B - 1, C, D, E, F, G, H)) :|: B >= 0 && B + 1 >= 0 && D >= 0 && A >= D && G >= H && G <= H
lbl42(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D - 1, E, F, G, H)) :|: B + 1 >= 0 && D >= 0 && A >= D && G >= H && G <= H
lbl42(A, B, C, D, E, F, G, H) -> Com_1(lbl72(A, 1 + B, C, D - 1, B, F, G, H)) :|: H >= B && B + 1 >= 0 && D >= 0 && A >= D && G >= H && G <= H
cut(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= 0 && D + 1 >= 0 && D + 1 <= 0 && G >= H && G <= H
cut(A, B, C, D, E, F, G, H) -> Com_1(lbl42(A, B - 1, C, D, E, F, G, H)) :|: D >= 0 && B >= 0 && D + 1 >= 0 && A >= D + 1 && G >= H && G <= H
cut(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D - 1, E, F, G, H)) :|: D >= 0 && D + 1 >= 0 && A >= D + 1 && G >= H && G <= H
cut(A, B, C, D, E, F, G, H) -> Com_1(lbl72(A, 1 + B, C, D - 1, B, F, G, H)) :|: H >= B && D >= 0 && D + 1 >= 0 && A >= D + 1 && G >= H && G <= H
start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, A, F, F, H, H)) :|: TRUE

The start-symbols are:[start0_8]


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

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: start0

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

      1: start -> lbl42 : B'=-1+B, [ A>=0 && C>=0 && B==C && D==A && E==F && G==H ], cost: 1

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

      3: start -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=C && A>=0 && B==C && D==A && E==F && G==H ], cost: 1

      4: lbl72 -> cut : [ A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1

      5: lbl72 -> lbl72 : B'=1+B, E'=B, [ H>=B && A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1

      6: lbl42 -> lbl42 : B'=-1+B, [ B>=0 && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

      7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

      8: lbl42 -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

      9: cut -> stop : [ A>=0 && 1+D==0 && G==H ], cost: 1

     10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && 1+D>=0 && A>=1+D && G==H ], cost: 1

     11: cut -> cut : D'=-1+D, [ D>=0 && 1+D>=0 && A>=1+D && G==H ], cost: 1

     12: cut -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && D>=0 && 1+D>=0 && A>=1+D && G==H ], cost: 1

     13: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1



Removed unreachable and leaf rules:

   Start location: start0

      1: start -> lbl42 : B'=-1+B, [ A>=0 && C>=0 && B==C && D==A && E==F && G==H ], cost: 1

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

      3: start -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=C && A>=0 && B==C && D==A && E==F && G==H ], cost: 1

      4: lbl72 -> cut : [ A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1

      5: lbl72 -> lbl72 : B'=1+B, E'=B, [ H>=B && A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1

      6: lbl42 -> lbl42 : B'=-1+B, [ B>=0 && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

      7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

      8: lbl42 -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

     10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && 1+D>=0 && A>=1+D && G==H ], cost: 1

     11: cut -> cut : D'=-1+D, [ D>=0 && 1+D>=0 && A>=1+D && G==H ], cost: 1

     12: cut -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && D>=0 && 1+D>=0 && A>=1+D && G==H ], cost: 1

     13: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1



Simplified all rules, resulting in:

   Start location: start0

      1: start -> lbl42 : B'=-1+B, [ A>=0 && C>=0 && B==C && D==A && E==F && G==H ], cost: 1

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

      3: start -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=C && A>=0 && B==C && D==A && E==F && G==H ], cost: 1

      4: lbl72 -> cut : [ A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1

      5: lbl72 -> lbl72 : B'=1+B, E'=B, [ H>=B && A>=1+D && 1+D>=0 && 1+E==B && G==H ], cost: 1

      6: lbl42 -> lbl42 : B'=-1+B, [ B>=0 && D>=0 && A>=D && G==H ], cost: 1

      7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

      8: lbl42 -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

     10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && A>=1+D && G==H ], cost: 1

     11: cut -> cut : D'=-1+D, [ D>=0 && A>=1+D && G==H ], cost: 1

     12: cut -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && D>=0 && A>=1+D && G==H ], cost: 1

     13: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      5: lbl72 -> lbl72 : B'=1+B, E'=B, [ H>=B && A>=1+D && 1+D>=0 && 1+E==B && G==H ], cost: 1



   Accelerated rule 5 with metering function 1+H-B, yielding the new rule 14.

   Removing the simple loops: 5.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      6: lbl42 -> lbl42 : B'=-1+B, [ B>=0 && D>=0 && A>=D && G==H ], cost: 1



   Accelerated rule 6 with metering function 1+B, yielding the new rule 15.

   Removing the simple loops: 6.



Accelerating simple loops of location 3.

   Accelerating the following rules:

     11: cut -> cut : D'=-1+D, [ D>=0 && A>=1+D && G==H ], cost: 1



   Accelerated rule 11 with metering function 1+D, yielding the new rule 16.

   Removing the simple loops: 11.



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

   Start location: start0

      1: start -> lbl42 : B'=-1+B, [ A>=0 && C>=0 && B==C && D==A && E==F && G==H ], cost: 1

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

      3: start -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=C && A>=0 && B==C && D==A && E==F && G==H ], cost: 1

      4: lbl72 -> cut : [ A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1

     14: lbl72 -> lbl72 : B'=1+H, E'=H, [ H>=B && A>=1+D && 1+D>=0 && 1+E==B && G==H ], cost: 1+H-B

      7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

      8: lbl42 -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

     15: lbl42 -> lbl42 : B'=-1, [ B>=0 && D>=0 && A>=D && G==H ], cost: 1+B

     10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && A>=1+D && G==H ], cost: 1

     12: cut -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && D>=0 && A>=1+D && G==H ], cost: 1

     16: cut -> cut : D'=-1, [ D>=0 && A>=1+D && G==H ], cost: 1+D

     13: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: start0

      1: start -> lbl42 : B'=-1+B, [ A>=0 && C>=0 && B==C && D==A && E==F && G==H ], cost: 1

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

      3: start -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=C && A>=0 && B==C && D==A && E==F && G==H ], cost: 1

     17: start -> lbl72 : B'=1+H, D'=-1+D, E'=H, [ H>=C && A>=0 && B==C && D==A && E==F && G==H && H>=1+B && D>=0 ], cost: 1+H-B

     20: start -> lbl42 : B'=-1, [ A>=0 && C>=0 && B==C && D==A && E==F && G==H && -1+B>=0 && D>=0 ], cost: 1+B

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

      4: lbl72 -> cut : [ A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1

     23: lbl72 -> cut : D'=-1, [ A>=1+D && 1+H>=B && 1+E==B && G==H && D>=0 ], cost: 2+D

      7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

      8: lbl42 -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

     18: lbl42 -> lbl72 : B'=1+H, D'=-1+D, E'=H, [ 1+B>=0 && D>=0 && A>=D && G==H && H>=1+B ], cost: 1+H-B

     24: lbl42 -> cut : D'=-1, [ 1+B>=0 && A>=D && G==H && -1+D>=0 ], cost: 1+D

     10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && A>=1+D && G==H ], cost: 1

     12: cut -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && D>=0 && A>=1+D && G==H ], cost: 1

     19: cut -> lbl72 : B'=1+H, D'=-1+D, E'=H, [ D>=0 && A>=1+D && G==H && H>=1+B ], cost: 1+H-B

     21: cut -> lbl42 : B'=-1, [ D>=0 && A>=1+D && G==H && -1+B>=0 ], cost: 1+B

     13: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: start0

      4: lbl72 -> cut : [ A>=1+D && 1+D>=0 && 1+H>=B && 1+E==B && G==H ], cost: 1

     23: lbl72 -> cut : D'=-1, [ A>=1+D && 1+H>=B && 1+E==B && G==H && D>=0 ], cost: 2+D

      7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

      8: lbl42 -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

     18: lbl42 -> lbl72 : B'=1+H, D'=-1+D, E'=H, [ 1+B>=0 && D>=0 && A>=D && G==H && H>=1+B ], cost: 1+H-B

     24: lbl42 -> cut : D'=-1, [ 1+B>=0 && A>=D && G==H && -1+D>=0 ], cost: 1+D

     10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && A>=1+D && G==H ], cost: 1

     12: cut -> lbl72 : B'=1+B, D'=-1+D, E'=B, [ H>=B && D>=0 && A>=1+D && G==H ], cost: 1

     19: cut -> lbl72 : B'=1+H, D'=-1+D, E'=H, [ D>=0 && A>=1+D && G==H && H>=1+B ], cost: 1+H-B

     21: cut -> lbl42 : B'=-1, [ D>=0 && A>=1+D && G==H && -1+B>=0 ], cost: 1+B

     25: start0 -> lbl42 : B'=-1+C, D'=A, E'=F, G'=H, [ A>=0 && C>=0 ], cost: 2

     26: start0 -> cut : B'=C, D'=-1+A, E'=F, G'=H, [ A>=0 ], cost: 2

     27: start0 -> lbl72 : B'=1+C, D'=-1+A, E'=C, G'=H, [ H>=C && A>=0 ], cost: 2

     28: start0 -> lbl72 : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && H>=1+C ], cost: 2-C+H

     29: start0 -> lbl42 : B'=-1, D'=A, E'=F, G'=H, [ A>=0 && -1+C>=0 ], cost: 2+C

     30: start0 -> cut : B'=C, D'=-1, E'=F, G'=H, [ -1+A>=0 ], cost: 2+A



Eliminated location lbl72 (as a last resort):

   Start location: start0

      7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

     24: lbl42 -> cut : D'=-1, [ 1+B>=0 && A>=D && G==H && -1+D>=0 ], cost: 1+D

     31: lbl42 -> cut : B'=1+B, D'=-1+D, E'=B, [ H>=B && 1+B>=0 && D>=0 && A>=D && G==H ], cost: 2

     32: lbl42 -> cut : B'=1+B, D'=-1, E'=B, [ H>=B && 1+B>=0 && A>=D && G==H && -1+D>=0 ], cost: 2+D

     35: lbl42 -> cut : B'=1+H, D'=-1+D, E'=H, [ 1+B>=0 && D>=0 && A>=D && G==H && H>=1+B ], cost: 2+H-B

     36: lbl42 -> cut : B'=1+H, D'=-1, E'=H, [ 1+B>=0 && A>=D && G==H && H>=1+B && -1+D>=0 ], cost: 2+D+H-B

     10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && A>=1+D && G==H ], cost: 1

     21: cut -> lbl42 : B'=-1, [ D>=0 && A>=1+D && G==H && -1+B>=0 ], cost: 1+B

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

     34: cut -> cut : B'=1+B, D'=-1, E'=B, [ H>=B && A>=1+D && G==H && -1+D>=0 ], cost: 2+D

     37: cut -> cut : B'=1+H, D'=-1+D, E'=H, [ D>=0 && A>=1+D && G==H && H>=1+B ], cost: 2+H-B

     38: cut -> cut : B'=1+H, D'=-1, E'=H, [ A>=1+D && G==H && H>=1+B && -1+D>=0 ], cost: 2+D+H-B

     25: start0 -> lbl42 : B'=-1+C, D'=A, E'=F, G'=H, [ A>=0 && C>=0 ], cost: 2

     26: start0 -> cut : B'=C, D'=-1+A, E'=F, G'=H, [ A>=0 ], cost: 2

     29: start0 -> lbl42 : B'=-1, D'=A, E'=F, G'=H, [ A>=0 && -1+C>=0 ], cost: 2+C

     30: start0 -> cut : B'=C, D'=-1, E'=F, G'=H, [ -1+A>=0 ], cost: 2+A

     39: start0 -> cut : B'=1+C, D'=-1+A, E'=C, G'=H, [ H>=C && A>=0 ], cost: 3

     40: start0 -> cut : B'=1+C, D'=-1, E'=C, G'=H, [ H>=C && -1+A>=0 ], cost: 3+A

     41: start0 -> cut : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && H>=1+C ], cost: 3-C+H

     42: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ H>=1+C && -1+A>=0 ], cost: 3-C+A+H



Applied pruning (of leafs and parallel rules):

   Start location: start0

      7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

     24: lbl42 -> cut : D'=-1, [ 1+B>=0 && A>=D && G==H && -1+D>=0 ], cost: 1+D

     32: lbl42 -> cut : B'=1+B, D'=-1, E'=B, [ H>=B && 1+B>=0 && A>=D && G==H && -1+D>=0 ], cost: 2+D

     35: lbl42 -> cut : B'=1+H, D'=-1+D, E'=H, [ 1+B>=0 && D>=0 && A>=D && G==H && H>=1+B ], cost: 2+H-B

     36: lbl42 -> cut : B'=1+H, D'=-1, E'=H, [ 1+B>=0 && A>=D && G==H && H>=1+B && -1+D>=0 ], cost: 2+D+H-B

     10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && A>=1+D && G==H ], cost: 1

     21: cut -> lbl42 : B'=-1, [ D>=0 && A>=1+D && G==H && -1+B>=0 ], cost: 1+B

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

     34: cut -> cut : B'=1+B, D'=-1, E'=B, [ H>=B && A>=1+D && G==H && -1+D>=0 ], cost: 2+D

     37: cut -> cut : B'=1+H, D'=-1+D, E'=H, [ D>=0 && A>=1+D && G==H && H>=1+B ], cost: 2+H-B

     38: cut -> cut : B'=1+H, D'=-1, E'=H, [ A>=1+D && G==H && H>=1+B && -1+D>=0 ], cost: 2+D+H-B

     25: start0 -> lbl42 : B'=-1+C, D'=A, E'=F, G'=H, [ A>=0 && C>=0 ], cost: 2

     26: start0 -> cut : B'=C, D'=-1+A, E'=F, G'=H, [ A>=0 ], cost: 2

     29: start0 -> lbl42 : B'=-1, D'=A, E'=F, G'=H, [ A>=0 && -1+C>=0 ], cost: 2+C

     30: start0 -> cut : B'=C, D'=-1, E'=F, G'=H, [ -1+A>=0 ], cost: 2+A

     40: start0 -> cut : B'=1+C, D'=-1, E'=C, G'=H, [ H>=C && -1+A>=0 ], cost: 3+A

     41: start0 -> cut : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && H>=1+C ], cost: 3-C+H

     42: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ H>=1+C && -1+A>=0 ], cost: 3-C+A+H



Accelerating simple loops of location 3.

   Accelerating the following rules:

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

     34: cut -> cut : B'=1+B, D'=-1, E'=B, [ H>=B && A>=1+D && G==H && -1+D>=0 ], cost: 2+D

     37: cut -> cut : B'=1+H, D'=-1+D, E'=H, [ D>=0 && A>=1+D && G==H && H>=1+B ], cost: 2+H-B

     38: cut -> cut : B'=1+H, D'=-1, E'=H, [ A>=1+D && G==H && H>=1+B && -1+D>=0 ], cost: 2+D+H-B



   Accelerated rule 33 with backward acceleration, yielding the new rule 43.

   Accelerated rule 33 with backward acceleration, yielding the new rule 44.

   Found no metering function for rule 34.

   Found no metering function for rule 37.

   Found no metering function for rule 38.

   Removing the simple loops: 33.



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

   Start location: start0

      7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

     24: lbl42 -> cut : D'=-1, [ 1+B>=0 && A>=D && G==H && -1+D>=0 ], cost: 1+D

     32: lbl42 -> cut : B'=1+B, D'=-1, E'=B, [ H>=B && 1+B>=0 && A>=D && G==H && -1+D>=0 ], cost: 2+D

     35: lbl42 -> cut : B'=1+H, D'=-1+D, E'=H, [ 1+B>=0 && D>=0 && A>=D && G==H && H>=1+B ], cost: 2+H-B

     36: lbl42 -> cut : B'=1+H, D'=-1, E'=H, [ 1+B>=0 && A>=D && G==H && H>=1+B && -1+D>=0 ], cost: 2+D+H-B

     10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && A>=1+D && G==H ], cost: 1

     21: cut -> lbl42 : B'=-1, [ D>=0 && A>=1+D && G==H && -1+B>=0 ], cost: 1+B

     34: cut -> cut : B'=1+B, D'=-1, E'=B, [ H>=B && A>=1+D && G==H && -1+D>=0 ], cost: 2+D

     37: cut -> cut : B'=1+H, D'=-1+D, E'=H, [ D>=0 && A>=1+D && G==H && H>=1+B ], cost: 2+H-B

     38: cut -> cut : B'=1+H, D'=-1, E'=H, [ A>=1+D && G==H && H>=1+B && -1+D>=0 ], cost: 2+D+H-B

     43: cut -> cut : B'=1+H, D'=-1+D-H+B, E'=H, [ H>=B && D>=0 && A>=1+D && G==H && D-H+B>=0 && A>=1+D-H+B ], cost: 2+2*H-2*B

     44: cut -> cut : B'=1+D+B, D'=-1, E'=D+B, [ H>=B && D>=0 && A>=1+D && G==H && H>=D+B && A>=1 ], cost: 2+2*D

     25: start0 -> lbl42 : B'=-1+C, D'=A, E'=F, G'=H, [ A>=0 && C>=0 ], cost: 2

     26: start0 -> cut : B'=C, D'=-1+A, E'=F, G'=H, [ A>=0 ], cost: 2

     29: start0 -> lbl42 : B'=-1, D'=A, E'=F, G'=H, [ A>=0 && -1+C>=0 ], cost: 2+C

     30: start0 -> cut : B'=C, D'=-1, E'=F, G'=H, [ -1+A>=0 ], cost: 2+A

     40: start0 -> cut : B'=1+C, D'=-1, E'=C, G'=H, [ H>=C && -1+A>=0 ], cost: 3+A

     41: start0 -> cut : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && H>=1+C ], cost: 3-C+H

     42: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ H>=1+C && -1+A>=0 ], cost: 3-C+A+H



Chained accelerated rules (with incoming rules):

   Start location: start0

      7: lbl42 -> cut : D'=-1+D, [ 1+B>=0 && D>=0 && A>=D && G==H ], cost: 1

     24: lbl42 -> cut : D'=-1, [ 1+B>=0 && A>=D && G==H && -1+D>=0 ], cost: 1+D

     32: lbl42 -> cut : B'=1+B, D'=-1, E'=B, [ H>=B && 1+B>=0 && A>=D && G==H && -1+D>=0 ], cost: 2+D

     35: lbl42 -> cut : B'=1+H, D'=-1+D, E'=H, [ 1+B>=0 && D>=0 && A>=D && G==H && H>=1+B ], cost: 2+H-B

     36: lbl42 -> cut : B'=1+H, D'=-1, E'=H, [ 1+B>=0 && A>=D && G==H && H>=1+B && -1+D>=0 ], cost: 2+D+H-B

     45: lbl42 -> cut : B'=1+B, D'=-1, E'=B, [ 1+B>=0 && A>=D && G==H && H>=B && -2+D>=0 ], cost: 2+D

     47: lbl42 -> cut : B'=1+H, D'=-2+D, E'=H, [ 1+B>=0 && A>=D && G==H && -1+D>=0 && H>=1+B ], cost: 3+H-B

     49: lbl42 -> cut : B'=1+H, D'=-1, E'=H, [ 1+B>=0 && A>=D && G==H && H>=1+B && -2+D>=0 ], cost: 2+D+H-B

     51: lbl42 -> cut : B'=1+H, D'=-2+D-H+B, E'=H, [ 1+B>=0 && A>=D && G==H && H>=B && -1+D>=0 && -1+D-H+B>=0 && A>=D-H+B ], cost: 3+2*H-2*B

     53: lbl42 -> cut : B'=D+B, D'=-1, E'=-1+D+B, [ 1+B>=0 && A>=D && G==H && H>=B && -1+D>=0 && H>=-1+D+B && A>=1 ], cost: 1+2*D

     10: cut -> lbl42 : B'=-1+B, [ D>=0 && B>=0 && A>=1+D && G==H ], cost: 1

     21: cut -> lbl42 : B'=-1, [ D>=0 && A>=1+D && G==H && -1+B>=0 ], cost: 1+B

     25: start0 -> lbl42 : B'=-1+C, D'=A, E'=F, G'=H, [ A>=0 && C>=0 ], cost: 2

     26: start0 -> cut : B'=C, D'=-1+A, E'=F, G'=H, [ A>=0 ], cost: 2

     29: start0 -> lbl42 : B'=-1, D'=A, E'=F, G'=H, [ A>=0 && -1+C>=0 ], cost: 2+C

     30: start0 -> cut : B'=C, D'=-1, E'=F, G'=H, [ -1+A>=0 ], cost: 2+A

     40: start0 -> cut : B'=1+C, D'=-1, E'=C, G'=H, [ H>=C && -1+A>=0 ], cost: 3+A

     41: start0 -> cut : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && H>=1+C ], cost: 3-C+H

     42: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ H>=1+C && -1+A>=0 ], cost: 3-C+A+H

     46: start0 -> cut : B'=1+C, D'=-1, E'=C, G'=H, [ H>=C && -2+A>=0 ], cost: 3+A

     48: start0 -> cut : B'=1+H, D'=-2+A, E'=H, G'=H, [ -1+A>=0 && H>=1+C ], cost: 4-C+H

     50: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ H>=1+C && -2+A>=0 ], cost: 3-C+A+H

     52: start0 -> cut : B'=1+H, D'=-2+C+A-H, E'=H, G'=H, [ H>=C && -1+A>=0 && -1+C+A-H>=0 ], cost: 4-2*C+2*H

     54: start0 -> cut : B'=C+A, D'=-1, E'=-1+C+A, G'=H, [ H>=C && -1+A>=0 && H>=-1+C+A ], cost: 2+2*A



Eliminated location lbl42 (as a last resort):

   Start location: start0

     55: cut -> cut : B'=-1+B, D'=-1+D, [ D>=0 && B>=0 && A>=1+D && G==H ], cost: 2

     56: cut -> cut : B'=-1+B, D'=-1, [ B>=0 && A>=1+D && G==H && -1+D>=0 ], cost: 2+D

     57: cut -> cut : B'=B, D'=-1, E'=-1+B, [ B>=0 && A>=1+D && G==H && H>=-1+B && -1+D>=0 ], cost: 3+D

     58: cut -> cut : B'=1+H, D'=-1+D, E'=H, [ D>=0 && B>=0 && A>=1+D && G==H && H>=B ], cost: 4+H-B

     59: cut -> cut : B'=1+H, D'=-1, E'=H, [ B>=0 && A>=1+D && G==H && H>=B && -1+D>=0 ], cost: 4+D+H-B

     60: cut -> cut : B'=B, D'=-1, E'=-1+B, [ B>=0 && A>=1+D && G==H && H>=-1+B && -2+D>=0 ], cost: 3+D

     61: cut -> cut : B'=1+H, D'=-2+D, E'=H, [ B>=0 && A>=1+D && G==H && -1+D>=0 && H>=B ], cost: 5+H-B

     62: cut -> cut : B'=1+H, D'=-1, E'=H, [ B>=0 && A>=1+D && G==H && H>=B && -2+D>=0 ], cost: 4+D+H-B

     63: cut -> cut : B'=1+H, D'=-3+D-H+B, E'=H, [ B>=0 && A>=1+D && G==H && H>=-1+B && -1+D>=0 && -2+D-H+B>=0 && A>=-1+D-H+B ], cost: 6+2*H-2*B

     64: cut -> cut : B'=-1+D+B, D'=-1, E'=-2+D+B, [ B>=0 && A>=1+D && G==H && H>=-1+B && -1+D>=0 && H>=-2+D+B && A>=1 ], cost: 2+2*D

     65: cut -> cut : B'=-1, D'=-1+D, [ D>=0 && A>=1+D && G==H && -1+B>=0 ], cost: 2+B

     66: cut -> cut : B'=-1, D'=-1, [ A>=1+D && G==H && -1+B>=0 && -1+D>=0 ], cost: 2+D+B

     67: cut -> cut : B'=0, D'=-1, E'=-1, [ A>=1+D && G==H && -1+B>=0 && H>=-1 && -1+D>=0 ], cost: 3+D+B

     68: cut -> cut : B'=1+H, D'=-1+D, E'=H, [ D>=0 && A>=1+D && G==H && -1+B>=0 && H>=0 ], cost: 4+H+B

     69: cut -> cut : B'=1+H, D'=-1, E'=H, [ A>=1+D && G==H && -1+B>=0 && H>=0 && -1+D>=0 ], cost: 4+D+H+B

     70: cut -> cut : B'=0, D'=-1, E'=-1, [ A>=1+D && G==H && -1+B>=0 && H>=-1 && -2+D>=0 ], cost: 3+D+B

     71: cut -> cut : B'=1+H, D'=-2+D, E'=H, [ A>=1+D && G==H && -1+B>=0 && -1+D>=0 && H>=0 ], cost: 5+H+B

     72: cut -> cut : B'=1+H, D'=-1, E'=H, [ A>=1+D && G==H && -1+B>=0 && H>=0 && -2+D>=0 ], cost: 4+D+H+B

     73: cut -> cut : B'=1+H, D'=-3+D-H, E'=H, [ A>=1+D && G==H && -1+B>=0 && H>=-1 && -1+D>=0 && -2+D-H>=0 && A>=-1+D-H ], cost: 6+2*H+B

     74: cut -> cut : B'=-1+D, D'=-1, E'=-2+D, [ A>=1+D && G==H && -1+B>=0 && H>=-1 && -1+D>=0 && H>=-2+D && A>=1 ], cost: 2+2*D+B

     26: start0 -> cut : B'=C, D'=-1+A, E'=F, G'=H, [ A>=0 ], cost: 2

     30: start0 -> cut : B'=C, D'=-1, E'=F, G'=H, [ -1+A>=0 ], cost: 2+A

     40: start0 -> cut : B'=1+C, D'=-1, E'=C, G'=H, [ H>=C && -1+A>=0 ], cost: 3+A

     41: start0 -> cut : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && H>=1+C ], cost: 3-C+H

     42: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ H>=1+C && -1+A>=0 ], cost: 3-C+A+H

     46: start0 -> cut : B'=1+C, D'=-1, E'=C, G'=H, [ H>=C && -2+A>=0 ], cost: 3+A

     48: start0 -> cut : B'=1+H, D'=-2+A, E'=H, G'=H, [ -1+A>=0 && H>=1+C ], cost: 4-C+H

     50: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ H>=1+C && -2+A>=0 ], cost: 3-C+A+H

     52: start0 -> cut : B'=1+H, D'=-2+C+A-H, E'=H, G'=H, [ H>=C && -1+A>=0 && -1+C+A-H>=0 ], cost: 4-2*C+2*H

     54: start0 -> cut : B'=C+A, D'=-1, E'=-1+C+A, G'=H, [ H>=C && -1+A>=0 && H>=-1+C+A ], cost: 2+2*A

     75: start0 -> cut : B'=-1+C, D'=-1+A, E'=F, G'=H, [ A>=0 && C>=0 ], cost: 3

     76: start0 -> cut : B'=-1+C, D'=-1, E'=F, G'=H, [ C>=0 && -1+A>=0 ], cost: 3+A

     77: start0 -> cut : B'=C, D'=-1, E'=-1+C, G'=H, [ C>=0 && H>=-1+C && -1+A>=0 ], cost: 4+A

     78: start0 -> cut : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && C>=0 && H>=C ], cost: 5-C+H

     79: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ C>=0 && H>=C && -1+A>=0 ], cost: 5-C+A+H

     80: start0 -> cut : B'=C, D'=-1, E'=-1+C, G'=H, [ C>=0 && H>=-1+C && -2+A>=0 ], cost: 4+A

     81: start0 -> cut : B'=1+H, D'=-2+A, E'=H, G'=H, [ C>=0 && -1+A>=0 && H>=C ], cost: 6-C+H

     82: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ C>=0 && H>=C && -2+A>=0 ], cost: 5-C+A+H

     83: start0 -> cut : B'=1+H, D'=-3+C+A-H, E'=H, G'=H, [ C>=0 && H>=-1+C && -1+A>=0 && -2+C+A-H>=0 ], cost: 7-2*C+2*H

     84: start0 -> cut : B'=-1+C+A, D'=-1, E'=-2+C+A, G'=H, [ C>=0 && H>=-1+C && -1+A>=0 && H>=-2+C+A ], cost: 3+2*A

     85: start0 -> cut : B'=-1, D'=-1+A, E'=F, G'=H, [ A>=0 && -1+C>=0 ], cost: 3+C

     86: start0 -> cut : B'=-1, D'=-1, E'=F, G'=H, [ -1+C>=0 && -1+A>=0 ], cost: 3+C+A

     87: start0 -> cut : B'=0, D'=-1, E'=-1, G'=H, [ -1+C>=0 && H>=-1 && -1+A>=0 ], cost: 4+C+A

     88: start0 -> cut : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && -1+C>=0 && H>=0 ], cost: 5+C+H

     89: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ -1+C>=0 && H>=0 && -1+A>=0 ], cost: 5+C+A+H

     90: start0 -> cut : B'=0, D'=-1, E'=-1, G'=H, [ -1+C>=0 && H>=-1 && -2+A>=0 ], cost: 4+C+A

     91: start0 -> cut : B'=1+H, D'=-2+A, E'=H, G'=H, [ -1+C>=0 && -1+A>=0 && H>=0 ], cost: 6+C+H

     92: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ -1+C>=0 && H>=0 && -2+A>=0 ], cost: 5+C+A+H

     93: start0 -> cut : B'=1+H, D'=-3+A-H, E'=H, G'=H, [ -1+C>=0 && H>=-1 && -1+A>=0 && -2+A-H>=0 ], cost: 7+C+2*H

     94: start0 -> cut : B'=-1+A, D'=-1, E'=-2+A, G'=H, [ -1+C>=0 && H>=-1 && -1+A>=0 && H>=-2+A ], cost: 3+C+2*A



Applied pruning (of leafs and parallel rules):

   Start location: start0

     58: cut -> cut : B'=1+H, D'=-1+D, E'=H, [ D>=0 && B>=0 && A>=1+D && G==H && H>=B ], cost: 4+H-B

     61: cut -> cut : B'=1+H, D'=-2+D, E'=H, [ B>=0 && A>=1+D && G==H && -1+D>=0 && H>=B ], cost: 5+H-B

     63: cut -> cut : B'=1+H, D'=-3+D-H+B, E'=H, [ B>=0 && A>=1+D && G==H && H>=-1+B && -1+D>=0 && -2+D-H+B>=0 && A>=-1+D-H+B ], cost: 6+2*H-2*B

     64: cut -> cut : B'=-1+D+B, D'=-1, E'=-2+D+B, [ B>=0 && A>=1+D && G==H && H>=-1+B && -1+D>=0 && H>=-2+D+B && A>=1 ], cost: 2+2*D

     72: cut -> cut : B'=1+H, D'=-1, E'=H, [ A>=1+D && G==H && -1+B>=0 && H>=0 && -2+D>=0 ], cost: 4+D+H+B

     41: start0 -> cut : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && H>=1+C ], cost: 3-C+H

     79: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ C>=0 && H>=C && -1+A>=0 ], cost: 5-C+A+H

     81: start0 -> cut : B'=1+H, D'=-2+A, E'=H, G'=H, [ C>=0 && -1+A>=0 && H>=C ], cost: 6-C+H

     83: start0 -> cut : B'=1+H, D'=-3+C+A-H, E'=H, G'=H, [ C>=0 && H>=-1+C && -1+A>=0 && -2+C+A-H>=0 ], cost: 7-2*C+2*H

     93: start0 -> cut : B'=1+H, D'=-3+A-H, E'=H, G'=H, [ -1+C>=0 && H>=-1 && -1+A>=0 && -2+A-H>=0 ], cost: 7+C+2*H



Accelerating simple loops of location 3.

   Accelerating the following rules:

     58: cut -> cut : B'=1+H, D'=-1+D, E'=H, [ D>=0 && B>=0 && A>=1+D && G==H && H>=B ], cost: 4+H-B

     61: cut -> cut : B'=1+H, D'=-2+D, E'=H, [ B>=0 && A>=1+D && G==H && -1+D>=0 && H>=B ], cost: 5+H-B

     63: cut -> cut : B'=1+H, D'=-3+D-H+B, E'=H, [ B>=0 && A>=1+D && G==H && H>=-1+B && -1+D>=0 && -2+D-H+B>=0 && A>=-1+D-H+B ], cost: 6+2*H-2*B

     64: cut -> cut : B'=-1+D+B, D'=-1, E'=-2+D+B, [ B>=0 && A>=1+D && G==H && H>=-1+B && -1+D>=0 && H>=-2+D+B && A>=1 ], cost: 2+2*D

     72: cut -> cut : B'=1+H, D'=-1, E'=H, [ A>=1+D && G==H && -1+B>=0 && H>=0 && -2+D>=0 ], cost: 4+D+H+B



   Found no metering function for rule 58.

   Found no metering function for rule 61.

   Accelerated rule 63 with metering function meter (where 2*meter==-1+D-H+B), yielding the new rule 95.

   Found no metering function for rule 64.

   Found no metering function for rule 72.

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

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

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

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

   Nested simple loops 72 (outer loop) and 95 (inner loop) with metering function meter_4 (where 3*meter_4==-3+D-H+B), resulting in the new rules: 96.

   Removing the simple loops: 63 72.



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

   Start location: start0

     58: cut -> cut : B'=1+H, D'=-1+D, E'=H, [ D>=0 && B>=0 && A>=1+D && G==H && H>=B ], cost: 4+H-B

     61: cut -> cut : B'=1+H, D'=-2+D, E'=H, [ B>=0 && A>=1+D && G==H && -1+D>=0 && H>=B ], cost: 5+H-B

     64: cut -> cut : B'=-1+D+B, D'=-1, E'=-2+D+B, [ B>=0 && A>=1+D && G==H && H>=-1+B && -1+D>=0 && H>=-2+D+B && A>=1 ], cost: 2+2*D

     95: cut -> cut : B'=1+H, D'=-2*meter+D, E'=H, [ B>=0 && A>=1+D && G==H && H>=-1+B && -1+D>=0 && -2+D-H+B>=0 && A>=-1+D-H+B && 2*meter==-1+D-H+B && meter>=1 ], cost: 4*meter

     96: cut -> cut : B'=1+H, D'=-1, E'=H, [ B>=0 && A>=1+D && G==H && H>=-1+B && A>=-1+D-H+B && 2==-1+D-H+B && H>=0 && -4+D>=0 && 3*meter_4==-3+D-H+B && meter_4>=1 ], cost: 2*meter_4*H+6*meter_4

     41: start0 -> cut : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && H>=1+C ], cost: 3-C+H

     79: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ C>=0 && H>=C && -1+A>=0 ], cost: 5-C+A+H

     81: start0 -> cut : B'=1+H, D'=-2+A, E'=H, G'=H, [ C>=0 && -1+A>=0 && H>=C ], cost: 6-C+H

     83: start0 -> cut : B'=1+H, D'=-3+C+A-H, E'=H, G'=H, [ C>=0 && H>=-1+C && -1+A>=0 && -2+C+A-H>=0 ], cost: 7-2*C+2*H

     93: start0 -> cut : B'=1+H, D'=-3+A-H, E'=H, G'=H, [ -1+C>=0 && H>=-1 && -1+A>=0 && -2+A-H>=0 ], cost: 7+C+2*H



Chained accelerated rules (with incoming rules):

   Start location: start0

     41: start0 -> cut : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && H>=1+C ], cost: 3-C+H

     79: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ C>=0 && H>=C && -1+A>=0 ], cost: 5-C+A+H

     81: start0 -> cut : B'=1+H, D'=-2+A, E'=H, G'=H, [ C>=0 && -1+A>=0 && H>=C ], cost: 6-C+H

     83: start0 -> cut : B'=1+H, D'=-3+C+A-H, E'=H, G'=H, [ C>=0 && H>=-1+C && -1+A>=0 && -2+C+A-H>=0 ], cost: 7-2*C+2*H

     93: start0 -> cut : B'=1+H, D'=-3+A-H, E'=H, G'=H, [ -1+C>=0 && H>=-1 && -1+A>=0 && -2+A-H>=0 ], cost: 7+C+2*H

     97: start0 -> cut : B'=-1+A+H, D'=-1, E'=-2+A+H, G'=H, [ H>=1+C && 1+H>=0 && 2-A==0 ], cost: 3-C+2*A+H

     98: start0 -> cut : B'=-2+A+H, D'=-1, E'=-3+A+H, G'=H, [ C>=0 && H>=C && 1+H>=0 && 3-A==0 ], cost: 4-C+2*A+H

     99: start0 -> cut : B'=-3+C+A, D'=-1, E'=-4+C+A, G'=H, [ C>=0 && H>=-1+C && -1+A>=0 && 1+H>=0 && 4-C-A+H==0 ], cost: 3+2*A

    100: start0 -> cut : B'=-3+A, D'=-1, E'=-4+A, G'=H, [ -1+C>=0 && H>=-1 && -1+A>=0 && 4-A+H==0 ], cost: 3+C+2*A

    101: start0 -> cut : B'=1+H, D'=-1-2*meter+A, E'=H, G'=H, [ H>=1+C && 1+H>=0 && -2+A>=0 && 2*meter==-1+A && meter>=1 ], cost: 3-C+4*meter+H

    102: start0 -> cut : B'=1+H, D'=-2-2*meter+A, E'=H, G'=H, [ C>=0 && H>=C && 1+H>=0 && -3+A>=0 && 2*meter==-2+A && meter>=1 ], cost: 6-C+4*meter+H

    103: start0 -> cut : B'=1+H, D'=-3+C-2*meter+A-H, E'=H, G'=H, [ C>=0 && H>=-1+C && -1+A>=0 && 1+H>=0 && -4+C+A-H>=0 && 2*meter==-3+C+A-H && meter>=1 ], cost: 7-2*C+4*meter+2*H

    104: start0 -> cut : B'=1+H, D'=-3-2*meter+A-H, E'=H, G'=H, [ -1+C>=0 && H>=-1 && -1+A>=0 && -4+A-H>=0 && 2*meter==-3+A-H && meter>=1 ], cost: 7+C+4*meter+2*H



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: start0

     41: start0 -> cut : B'=1+H, D'=-1+A, E'=H, G'=H, [ A>=0 && H>=1+C ], cost: 3-C+H

     79: start0 -> cut : B'=1+H, D'=-1, E'=H, G'=H, [ C>=0 && H>=C && -1+A>=0 ], cost: 5-C+A+H

     81: start0 -> cut : B'=1+H, D'=-2+A, E'=H, G'=H, [ C>=0 && -1+A>=0 && H>=C ], cost: 6-C+H

     83: start0 -> cut : B'=1+H, D'=-3+C+A-H, E'=H, G'=H, [ C>=0 && H>=-1+C && -1+A>=0 && -2+C+A-H>=0 ], cost: 7-2*C+2*H

     93: start0 -> cut : B'=1+H, D'=-3+A-H, E'=H, G'=H, [ -1+C>=0 && H>=-1 && -1+A>=0 && -2+A-H>=0 ], cost: 7+C+2*H

     97: start0 -> cut : B'=-1+A+H, D'=-1, E'=-2+A+H, G'=H, [ H>=1+C && 1+H>=0 && 2-A==0 ], cost: 3-C+2*A+H

     98: start0 -> cut : B'=-2+A+H, D'=-1, E'=-3+A+H, G'=H, [ C>=0 && H>=C && 1+H>=0 && 3-A==0 ], cost: 4-C+2*A+H

     99: start0 -> cut : B'=-3+C+A, D'=-1, E'=-4+C+A, G'=H, [ C>=0 && H>=-1+C && -1+A>=0 && 1+H>=0 && 4-C-A+H==0 ], cost: 3+2*A

    100: start0 -> cut : B'=-3+A, D'=-1, E'=-4+A, G'=H, [ -1+C>=0 && H>=-1 && -1+A>=0 && 4-A+H==0 ], cost: 3+C+2*A

    101: start0 -> cut : B'=1+H, D'=-1-2*meter+A, E'=H, G'=H, [ H>=1+C && 1+H>=0 && -2+A>=0 && 2*meter==-1+A && meter>=1 ], cost: 3-C+4*meter+H

    102: start0 -> cut : B'=1+H, D'=-2-2*meter+A, E'=H, G'=H, [ C>=0 && H>=C && 1+H>=0 && -3+A>=0 && 2*meter==-2+A && meter>=1 ], cost: 6-C+4*meter+H

    103: start0 -> cut : B'=1+H, D'=-3+C-2*meter+A-H, E'=H, G'=H, [ C>=0 && H>=-1+C && -1+A>=0 && 1+H>=0 && -4+C+A-H>=0 && 2*meter==-3+C+A-H && meter>=1 ], cost: 7-2*C+4*meter+2*H

    104: start0 -> cut : B'=1+H, D'=-3-2*meter+A-H, E'=H, G'=H, [ -1+C>=0 && H>=-1 && -1+A>=0 && -4+A-H>=0 && 2*meter==-3+A-H && meter>=1 ], cost: 7+C+4*meter+2*H



Computing asymptotic complexity for rule 41

   Solved the limit problem by the following transformations:

      Created initial limit problem:

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



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



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

      resulting limit problem:

      [solved]



   Solution:

      C / 0

      A / n

      H / n

   Resulting cost 3+n has complexity: Poly(n^1)



Found new complexity Poly(n^1).



Computing asymptotic complexity for rule 101

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      2+2*meter-A (+/+!), -2*meter+A (+/+!), -1+A (+/+!), 3-C+4*meter+H (+), -C+H (+/+!), 2+H (+/+!) [not solved]



      applying transformation rule (C) using substitution {A==1+2*meter}

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 3-C+4*meter+H (+), -C+H (+/+!), 2+H (+/+!) [not solved]



      applying transformation rule (C) using substitution {H==1+C}

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 3+C (+/+!), 4+4*meter (+) [not solved]



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

      resulting limit problem:

      2*meter (+/+!), 3+C (+/+!), 4+4*meter (+) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



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

      resulting limit problem:

      [solved]



   Solved the limit problem by the following transformations:

      Created initial limit problem:

      2+2*meter-A (+/+!), -2*meter+A (+/+!), -1+A (+/+!), 3-C+4*meter+H (+), -C+H (+/+!), 2+H (+/+!) [not solved]



      applying transformation rule (C) using substitution {A==1+2*meter}

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 3-C+4*meter+H (+), -C+H (+/+!), 2+H (+/+!) [not solved]



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

      resulting limit problem:

      2*meter (+/+!), 3-C+4*meter+H (+), -C+H (+/+!), 2+H (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {C==-1,meter==n,H==0}

      resulting limit problem:

      [solved]



   Solution:

      C / 0

      meter / n

      A / 1+2*n

      H / 1

   Resulting cost 4+4*n has complexity: Poly(n^1)



Computing asymptotic complexity for rule 102

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      1+C (+/+!), 3+2*meter-A (+/+!), 1-C+H (+/+!), 6-C+4*meter+H (+), -2+A (+/+!), -1-2*meter+A (+/+!) [not solved]



      applying transformation rule (C) using substitution {A==2+2*meter}

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 1+C (+/+!), 1-C+H (+/+!), 6-C+4*meter+H (+) [not solved]



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

      resulting limit problem:

      1+H (+/+!), 2*meter (+/+!), 1 (+/+!), 6+4*meter+H (+) [not solved]



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

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 1+C (+/+!), 6+C+4*meter (+) [not solved]



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

      resulting limit problem:

      2*meter (+/+!), 1+C (+/+!), 6+C+4*meter (+) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



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

      resulting limit problem:

      [solved]



   Solved the limit problem by the following transformations:

      Created initial limit problem:

      1+C (+/+!), 3+2*meter-A (+/+!), 1-C+H (+/+!), 6-C+4*meter+H (+), -2+A (+/+!), -1-2*meter+A (+/+!) [not solved]



      applying transformation rule (C) using substitution {A==2+2*meter}

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 1+C (+/+!), 1-C+H (+/+!), 6-C+4*meter+H (+) [not solved]



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

      resulting limit problem:

      2*meter (+/+!), 1+C (+/+!), 1-C+H (+/+!), 6-C+4*meter+H (+) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {C==0,meter==n,H==0}

      resulting limit problem:

      [solved]



   Solved the limit problem by the following transformations:

      Created initial limit problem:

      1+C (+/+!), 3+2*meter-A (+/+!), 1-C+H (+/+!), 6-C+4*meter+H (+), -2+A (+/+!), -1-2*meter+A (+/+!) [not solved]



      applying transformation rule (C) using substitution {A==2+2*meter}

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 1+C (+/+!), 1-C+H (+/+!), 6-C+4*meter+H (+) [not solved]



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

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 1+C (+/+!), 6+4*meter (+) [not solved]



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

      resulting limit problem:

      2*meter (+/+!), 1+C (+/+!), 6+4*meter (+) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



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

      resulting limit problem:

      [solved]



   Solved the limit problem by the following transformations:

      Created initial limit problem:

      1+C (+/+!), 3+2*meter-A (+/+!), 1-C+H (+/+!), 6-C+4*meter+H (+), -2+A (+/+!), -1-2*meter+A (+/+!) [not solved]



      applying transformation rule (C) using substitution {A==2+2*meter}

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 1+C (+/+!), 1-C+H (+/+!), 6-C+4*meter+H (+) [not solved]



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

      resulting limit problem:

      1+H (+/+!), 2*meter (+/+!), 1 (+/+!), 6+4*meter+H (+) [not solved]



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

      resulting limit problem:

      1+H (+/+!), 2*meter (+/+!), 6+4*meter+H (+) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {meter==n,H==0}

      resulting limit problem:

      [solved]



   Solution:

      C / 0

      meter / n

      A / 2+2*n

      H / 0

   Resulting cost 6+4*n has complexity: Poly(n^1)



Computing asymptotic complexity for rule 103

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      2-C+H (+/+!), 4-C+2*meter-A+H (+/+!), 7-2*C+4*meter+2*H (+), 1+C (+/+!), -3+C+A-H (+/+!), A (+/+!), -2+C-2*meter+A-H (+/+!) [not solved]



      applying transformation rule (C) using substitution {C==3+2*meter-A+H}

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 1+2*A (+), A (+/+!), -1-2*meter+A (+/+!), 4+2*meter-A+H (+/+!) [not solved]



      applying transformation rule (C) using substitution {H==-1+C}

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 1+2*A (+), A (+/+!), 3+C+2*meter-A (+/+!), -1-2*meter+A (+/+!) [not solved]



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

      resulting limit problem:

      2*meter (+/+!), 1+2*A (+), A (+/+!), 3+C+2*meter-A (+/+!), -1-2*meter+A (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {C==0,meter==n,A==2+2*n}

      resulting limit problem:

      [solved]



   Solved the limit problem by the following transformations:

      Created initial limit problem:

      2-C+H (+/+!), 4-C+2*meter-A+H (+/+!), 7-2*C+4*meter+2*H (+), 1+C (+/+!), -3+C+A-H (+/+!), A (+/+!), -2+C-2*meter+A-H (+/+!) [not solved]



      applying transformation rule (C) using substitution {C==3+2*meter-A+H}

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), 1+2*A (+), A (+/+!), -1-2*meter+A (+/+!), 4+2*meter-A+H (+/+!) [not solved]



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

      resulting limit problem:

      2*meter (+/+!), 1+2*A (+), A (+/+!), -1-2*meter+A (+/+!), 4+2*meter-A+H (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {meter==n,A==2+2*n,H==0}

      resulting limit problem:

      [solved]



   Solution:

      C / 0

      meter / n

      A / 2+2*n

      H / -1

   Resulting cost 5+4*n has complexity: Poly(n^1)



Computing asymptotic complexity for rule 104

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      -2-2*meter+A-H (+/+!), C (+/+!), 2+H (+/+!), A (+/+!), -3+A-H (+/+!), 4+2*meter-A+H (+/+!), 7+C+4*meter+2*H (+) [not solved]



      applying transformation rule (C) using substitution {A==3+2*meter+H}

      resulting limit problem:

      3+2*meter+H (+/+!), 2*meter (+/+!), 1 (+/+!), C (+/+!), 2+H (+/+!), 7+C+4*meter+2*H (+) [not solved]



      applying transformation rule (C) using substitution {H==-1}

      resulting limit problem:

      2*meter (+/+!), 1 (+/+!), C (+/+!), 5+C+4*meter (+), 2+2*meter (+/+!) [not solved]



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

      resulting limit problem:

      2*meter (+/+!), C (+/+!), 5+C+4*meter (+), 2+2*meter (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {C==1,meter==n}

      resulting limit problem:

      [solved]



   Solved the limit problem by the following transformations:

      Created initial limit problem:

      -2-2*meter+A-H (+/+!), C (+/+!), 2+H (+/+!), A (+/+!), -3+A-H (+/+!), 4+2*meter-A+H (+/+!), 7+C+4*meter+2*H (+) [not solved]



      applying transformation rule (C) using substitution {A==3+2*meter+H}

      resulting limit problem:

      3+2*meter+H (+/+!), 2*meter (+/+!), 1 (+/+!), C (+/+!), 2+H (+/+!), 7+C+4*meter+2*H (+) [not solved]



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

      resulting limit problem:

      3+2*meter+H (+/+!), 2*meter (+/+!), C (+/+!), 2+H (+/+!), 7+C+4*meter+2*H (+) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {C==1,meter==n,H==0}

      resulting limit problem:

      [solved]



   Solution:

      C / 1

      meter / n

      A / 2+2*n

      H / -1

   Resulting cost 6+4*n has 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: 3+n

   Rule cost:   3-C+H

   Rule guard:  [ A>=0 && H>=1+C ]



WORST_CASE(Omega(n^1),?)


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

(2)
BOUNDS(n^1, INF)