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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 597 ms]
(2) BOUNDS(INF, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f18(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f24(A, B, C, D, E, F, G, H, I, J, K)) :|: 0 >= A
f32(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f32(A, B, C, D, E, F, G, H, I, J, K)) :|: TRUE
f34(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f37(A, B, C, D, E, F, G, H, I, J, K)) :|: TRUE
f24(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f32(A, L, C, D, E, F, G, H, I, J, K)) :|: A >= 1
f24(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f32(A, M, C, L, L, F, G, H, I, J, K)) :|: 0 >= A && 999 + C >= L
f24(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f32(1, M, C, L, L, F, G, H, I, J, K)) :|: 0 >= A && L >= C + 1000
f18(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f24(0, B, L, D, E, L, G, H, I, J, K)) :|: A >= 1
f0(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f18(1, B, C, D, E, F, L, M, I, J, K)) :|: 0 >= M
f0(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f18(1, B, C, D, E, F, L, 0, 1, M, M)) :|: M >= 1 && N >= 1
f0(A, B, C, D, E, F, G, H, I, J, K) -> Com_1(f32(1, B, C, D, E, F, L, 0, 1, M, M)) :|: 0 >= M && N >= 1

The start-symbols are:[f0_11]


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

(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: f0

      0: f18 -> f24 : [ 0>=A ], cost: 1

      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1

      1: f32 -> f32 : [], cost: 1

      2: f34 -> f37 : [], cost: 1

      3: f24 -> f32 : B'=free, [ A>=1 ], cost: 1

      4: f24 -> f32 : B'=free_2, D'=free_1, E'=free_1, [ 0>=A && 999+C>=free_1 ], cost: 1

      5: f24 -> f32 : A'=1, B'=free_4, D'=free_3, E'=free_3, [ 0>=A && free_3>=1000+C ], cost: 1

      7: f0 -> f18 : A'=1, G'=free_7, H'=free_6, [ 0>=free_6 ], cost: 1

      8: f0 -> f18 : A'=1, G'=free_10, H'=0, Q'=1, J'=free_8, K'=free_8, [ free_8>=1 && free_9>=1 ], cost: 1

      9: f0 -> f32 : A'=1, G'=free_13, H'=0, Q'=1, J'=free_11, K'=free_11, [ 0>=free_11 && free_12>=1 ], cost: 1



Checking for constant complexity:

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

      7: f0 -> f18 : A'=1, G'=free_7, H'=free_6, [ 0>=free_6 ], cost: 1



Removed unreachable and leaf rules:

   Start location: f0

      0: f18 -> f24 : [ 0>=A ], cost: 1

      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1

      1: f32 -> f32 : [], cost: 1

      3: f24 -> f32 : B'=free, [ A>=1 ], cost: 1

      4: f24 -> f32 : B'=free_2, D'=free_1, E'=free_1, [ 0>=A && 999+C>=free_1 ], cost: 1

      5: f24 -> f32 : A'=1, B'=free_4, D'=free_3, E'=free_3, [ 0>=A && free_3>=1000+C ], cost: 1

      7: f0 -> f18 : A'=1, G'=free_7, H'=free_6, [ 0>=free_6 ], cost: 1

      8: f0 -> f18 : A'=1, G'=free_10, H'=0, Q'=1, J'=free_8, K'=free_8, [ free_8>=1 && free_9>=1 ], cost: 1

      9: f0 -> f32 : A'=1, G'=free_13, H'=0, Q'=1, J'=free_11, K'=free_11, [ 0>=free_11 && free_12>=1 ], cost: 1



Simplified all rules, resulting in:

   Start location: f0

      0: f18 -> f24 : [ 0>=A ], cost: 1

      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1

      1: f32 -> f32 : [], cost: 1

      3: f24 -> f32 : B'=free, [ A>=1 ], cost: 1

      4: f24 -> f32 : B'=free_2, D'=free_1, E'=free_1, [ 0>=A && 999+C>=free_1 ], cost: 1

      5: f24 -> f32 : A'=1, B'=free_4, D'=free_3, E'=free_3, [ 0>=A && free_3>=1000+C ], cost: 1

      7: f0 -> f18 : A'=1, G'=free_7, H'=free_6, [ 0>=free_6 ], cost: 1

      8: f0 -> f18 : A'=1, G'=free_10, H'=0, Q'=1, J'=free_8, K'=free_8, [ free_8>=1 ], cost: 1

      9: f0 -> f32 : A'=1, G'=free_13, H'=0, Q'=1, J'=free_11, K'=free_11, [ 0>=free_11 ], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      1: f32 -> f32 : [], cost: 1



   Accelerated rule 1 with NONTERM, yielding the new rule 10.

   Removing the simple loops: 1.



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

   Start location: f0

      0: f18 -> f24 : [ 0>=A ], cost: 1

      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1

     10: f32 -> [6] : [], cost: NONTERM

      3: f24 -> f32 : B'=free, [ A>=1 ], cost: 1

      4: f24 -> f32 : B'=free_2, D'=free_1, E'=free_1, [ 0>=A && 999+C>=free_1 ], cost: 1

      5: f24 -> f32 : A'=1, B'=free_4, D'=free_3, E'=free_3, [ 0>=A && free_3>=1000+C ], cost: 1

      7: f0 -> f18 : A'=1, G'=free_7, H'=free_6, [ 0>=free_6 ], cost: 1

      8: f0 -> f18 : A'=1, G'=free_10, H'=0, Q'=1, J'=free_8, K'=free_8, [ free_8>=1 ], cost: 1

      9: f0 -> f32 : A'=1, G'=free_13, H'=0, Q'=1, J'=free_11, K'=free_11, [ 0>=free_11 ], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: f0

      0: f18 -> f24 : [ 0>=A ], cost: 1

      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1

      3: f24 -> f32 : B'=free, [ A>=1 ], cost: 1

      4: f24 -> f32 : B'=free_2, D'=free_1, E'=free_1, [ 0>=A && 999+C>=free_1 ], cost: 1

      5: f24 -> f32 : A'=1, B'=free_4, D'=free_3, E'=free_3, [ 0>=A && free_3>=1000+C ], cost: 1

     11: f24 -> [6] : B'=free, [ A>=1 ], cost: NONTERM

     12: f24 -> [6] : B'=free_2, D'=free_1, E'=free_1, [ 0>=A && 999+C>=free_1 ], cost: NONTERM

     13: f24 -> [6] : A'=1, B'=free_4, D'=free_3, E'=free_3, [ 0>=A && free_3>=1000+C ], cost: NONTERM

      7: f0 -> f18 : A'=1, G'=free_7, H'=free_6, [ 0>=free_6 ], cost: 1

      8: f0 -> f18 : A'=1, G'=free_10, H'=0, Q'=1, J'=free_8, K'=free_8, [ free_8>=1 ], cost: 1

      9: f0 -> f32 : A'=1, G'=free_13, H'=0, Q'=1, J'=free_11, K'=free_11, [ 0>=free_11 ], cost: 1

     14: f0 -> [6] : A'=1, G'=free_13, H'=0, Q'=1, J'=free_11, K'=free_11, [ 0>=free_11 ], cost: NONTERM



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

   Start location: f0

      0: f18 -> f24 : [ 0>=A ], cost: 1

      6: f18 -> f24 : A'=0, C'=free_5, F'=free_5, [ A>=1 ], cost: 1

     11: f24 -> [6] : B'=free, [ A>=1 ], cost: NONTERM

     12: f24 -> [6] : B'=free_2, D'=free_1, E'=free_1, [ 0>=A && 999+C>=free_1 ], cost: NONTERM

     13: f24 -> [6] : A'=1, B'=free_4, D'=free_3, E'=free_3, [ 0>=A && free_3>=1000+C ], cost: NONTERM

      7: f0 -> f18 : A'=1, G'=free_7, H'=free_6, [ 0>=free_6 ], cost: 1

      8: f0 -> f18 : A'=1, G'=free_10, H'=0, Q'=1, J'=free_8, K'=free_8, [ free_8>=1 ], cost: 1

     14: f0 -> [6] : A'=1, G'=free_13, H'=0, Q'=1, J'=free_11, K'=free_11, [ 0>=free_11 ], cost: NONTERM



Eliminated locations (on tree-shaped paths):

   Start location: f0

     11: f24 -> [6] : B'=free, [ A>=1 ], cost: NONTERM

     12: f24 -> [6] : B'=free_2, D'=free_1, E'=free_1, [ 0>=A && 999+C>=free_1 ], cost: NONTERM

     13: f24 -> [6] : A'=1, B'=free_4, D'=free_3, E'=free_3, [ 0>=A && free_3>=1000+C ], cost: NONTERM

     14: f0 -> [6] : A'=1, G'=free_13, H'=0, Q'=1, J'=free_11, K'=free_11, [ 0>=free_11 ], cost: NONTERM

     15: f0 -> f24 : A'=0, C'=free_5, F'=free_5, G'=free_7, H'=free_6, [ 0>=free_6 ], cost: 2

     16: f0 -> f24 : A'=0, C'=free_5, F'=free_5, G'=free_10, H'=0, Q'=1, J'=free_8, K'=free_8, [ free_8>=1 ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: f0

     14: f0 -> [6] : A'=1, G'=free_13, H'=0, Q'=1, J'=free_11, K'=free_11, [ 0>=free_11 ], cost: NONTERM

     17: f0 -> [6] : A'=0, B'=free_2, C'=free_5, D'=free_1, E'=free_1, F'=free_5, G'=free_7, H'=free_6, [ 0>=free_6 && 999+free_5>=free_1 ], cost: NONTERM

     18: f0 -> [6] : A'=1, B'=free_4, C'=free_5, D'=free_3, E'=free_3, F'=free_5, G'=free_7, H'=free_6, [ 0>=free_6 && free_3>=1000+free_5 ], cost: NONTERM

     19: f0 -> [6] : A'=0, B'=free_2, C'=free_5, D'=free_1, E'=free_1, F'=free_5, G'=free_10, H'=0, Q'=1, J'=free_8, K'=free_8, [ free_8>=1 && 999+free_5>=free_1 ], cost: NONTERM

     20: f0 -> [6] : A'=1, B'=free_4, C'=free_5, D'=free_3, E'=free_3, F'=free_5, G'=free_10, H'=0, Q'=1, J'=free_8, K'=free_8, [ free_8>=1 && free_3>=1000+free_5 ], cost: NONTERM



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: f0

     14: f0 -> [6] : A'=1, G'=free_13, H'=0, Q'=1, J'=free_11, K'=free_11, [ 0>=free_11 ], cost: NONTERM

     17: f0 -> [6] : A'=0, B'=free_2, C'=free_5, D'=free_1, E'=free_1, F'=free_5, G'=free_7, H'=free_6, [ 0>=free_6 && 999+free_5>=free_1 ], cost: NONTERM

     18: f0 -> [6] : A'=1, B'=free_4, C'=free_5, D'=free_3, E'=free_3, F'=free_5, G'=free_7, H'=free_6, [ 0>=free_6 && free_3>=1000+free_5 ], cost: NONTERM

     19: f0 -> [6] : A'=0, B'=free_2, C'=free_5, D'=free_1, E'=free_1, F'=free_5, G'=free_10, H'=0, Q'=1, J'=free_8, K'=free_8, [ free_8>=1 && 999+free_5>=free_1 ], cost: NONTERM

     20: f0 -> [6] : A'=1, B'=free_4, C'=free_5, D'=free_3, E'=free_3, F'=free_5, G'=free_10, H'=0, Q'=1, J'=free_8, K'=free_8, [ free_8>=1 && free_3>=1000+free_5 ], cost: NONTERM



Computing asymptotic complexity for rule 14

   Guard is satisfiable, yielding nontermination

   Resulting cost NONTERM has complexity: Nonterm



Found new complexity Nonterm.



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

   Complexity:  Nonterm

   Cpx degree:  Nonterm

   Solved cost: NONTERM

   Rule cost:   NONTERM

   Rule guard:  [ 0>=free_11 ]



NO


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

(2)
BOUNDS(INF, INF)