Compl Integ Trans Syste 26843 pair #381744376

details
property	value
status	complete
benchmark	serpent.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n034.star.cs.uiowa.edu
space	Flores-Montoya_16
run statistics
property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	24.145138979 seconds
cpu usage	35.461665704
max memory	4.88538112E8
stage attributes
key	value
output-size	25059
starexec-result	WORST_CASE(Omega(n^2), ?)
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^2), ?)
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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^2, INF).

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 2686 ms]
(2) BOUNDS(n^2, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval_serpent_start(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_bb0_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_serpent_bb0_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_0(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_serpent_0(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_1(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_serpent_1(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_bb7_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: v_n <= 0
eval_serpent_1(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent__critedge1_in(v_3, v_6, v_8, v_n, v_n, v_n, v_y_1, v_y_2)) :|: v_n > 0
eval_serpent__critedge1_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_bb1_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_0, v_y_2)) :|: v_x_0 >= 0
eval_serpent__critedge1_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_bb7_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: v_x_0 < 0
eval_serpent_bb1_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_bb2_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: v_y_1 >= 0
eval_serpent_bb1_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent__critedge_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: v_y_1 < 0
eval_serpent_bb2_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_2(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_serpent_2(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_3(nondef_0, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_serpent_3(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_bb3_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: v_3 > 0
eval_serpent_3(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent__critedge_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: v_3 <= 0
eval_serpent_bb3_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_bb1_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1 - 1, v_y_2)) :|: TRUE
eval_serpent__critedge_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_7(v_3, v_x_0 - 1, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_serpent_7(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_8(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_serpent_8(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_9(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_serpent_9(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_bb4_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_1)) :|: TRUE
eval_serpent_bb4_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_bb5_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: v_y_2 <= v_n
eval_serpent_bb4_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent__critedge1_in(v_3, v_6, v_8, v_n, v_6, v_y_2, v_y_1, v_y_2)) :|: v_y_2 > v_n
eval_serpent_bb5_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_10(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_serpent_10(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_11(v_3, v_6, nondef_1, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_serpent_11(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_bb6_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: v_8 > 0
eval_serpent_11(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent__critedge1_in(v_3, v_6, v_8, v_n, v_6, v_y_2, v_y_1, v_y_2)) :|: v_8 <= 0
eval_serpent_bb6_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_bb4_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2 + 1)) :|: TRUE
eval_serpent_bb7_in(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2) -> Com_1(eval_serpent_stop(v_3, v_6, v_8, v_n, v_x_0, v_y_0, v_y_1, v_y_2)) :|: TRUE

The start-symbols are:[eval_serpent_start_8]


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(1) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: evalserpentstart

      0: evalserpentstart -> evalserpentbb0in : [], cost: 1

      1: evalserpentbb0in -> evalserpent0 : [], cost: 1

      2: evalserpent0 -> evalserpent1 : [], cost: 1

      3: evalserpent1 -> evalserpentbb7in : [ 0>=A ], cost: 1

      4: evalserpent1 -> evalserpentcritedge1in : B'=A, C'=A, [ A>=1 ], cost: 1

      5: evalserpentcritedge1in -> evalserpentbb1in : D'=C, [ B>=0 ], cost: 1

      6: evalserpentcritedge1in -> evalserpentbb7in : [ 0>=1+B ], cost: 1

      7: evalserpentbb1in -> evalserpentbb2in : [ D>=0 ], cost: 1

      8: evalserpentbb1in -> evalserpentcritedgein : [ 0>=1+D ], cost: 1

      9: evalserpentbb2in -> evalserpent2 : [], cost: 1

     10: evalserpent2 -> evalserpent3 : E'=free, [], cost: 1

     11: evalserpent3 -> evalserpentbb3in : [ E>=1 ], cost: 1

     12: evalserpent3 -> evalserpentcritedgein : [ 0>=E ], cost: 1

     13: evalserpentbb3in -> evalserpentbb1in : D'=-1+D, [], cost: 1

     14: evalserpentcritedgein -> evalserpent7 : F'=-1+B, [], cost: 1

     15: evalserpent7 -> evalserpent8 : [], cost: 1

     16: evalserpent8 -> evalserpent9 : [], cost: 1
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