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Compl Integ Trans Syste 26843 pair #381744805
details
property
value
status
complete
benchmark
ndecr.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n084.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.21999597549 seconds
cpu usage
4.433052634
max memory
2.52235776E8
stage attributes
key
value
output-size
13310
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 20 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 400 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_ndecr_start(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_bb0_in(v_0, v_i_0, v_n)) :|: TRUE eval_ndecr_bb0_in(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_0(v_0, v_i_0, v_n)) :|: TRUE eval_ndecr_0(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_1(v_0, v_i_0, v_n)) :|: TRUE eval_ndecr_1(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_2(v_n - 1, v_i_0, v_n)) :|: TRUE eval_ndecr_2(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_3(v_0, v_i_0, v_n)) :|: TRUE eval_ndecr_3(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_4(v_0, v_i_0, v_n)) :|: TRUE eval_ndecr_4(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_bb1_in(v_0, v_0, v_n)) :|: TRUE eval_ndecr_bb1_in(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_bb2_in(v_0, v_i_0, v_n)) :|: v_i_0 > 1 eval_ndecr_bb1_in(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_bb3_in(v_0, v_i_0, v_n)) :|: v_i_0 <= 1 eval_ndecr_bb2_in(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_bb1_in(v_0, v_i_0 - 1, v_n)) :|: TRUE eval_ndecr_bb3_in(v_0, v_i_0, v_n) -> Com_1(eval_ndecr_stop(v_0, v_i_0, v_n)) :|: TRUE The start-symbols are:[eval_ndecr_start_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2*ar_1 + 11) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalndecrstart(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb0in(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalndecrbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndecr0(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalndecr0(ar_0, ar_1, ar_2) -> Com_1(evalndecr1(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalndecr1(ar_0, ar_1, ar_2) -> Com_1(evalndecr2(ar_1 - 1, ar_1, ar_2)) (Comp: ?, Cost: 1) evalndecr2(ar_0, ar_1, ar_2) -> Com_1(evalndecr3(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalndecr3(ar_0, ar_1, ar_2) -> Com_1(evalndecr4(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalndecr4(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_0)) (Comp: ?, Cost: 1) evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ] (Comp: ?, Cost: 1) evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb3in(ar_0, ar_1, ar_2)) [ 1 >= ar_2 ] (Comp: ?, Cost: 1) evalndecrbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_2 - 1)) (Comp: ?, Cost: 1) evalndecrbb3in(ar_0, ar_1, ar_2) -> Com_1(evalndecrstop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndecrstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalndecrstart(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalndecrbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndecr0(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalndecr0(ar_0, ar_1, ar_2) -> Com_1(evalndecr1(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalndecr1(ar_0, ar_1, ar_2) -> Com_1(evalndecr2(ar_1 - 1, ar_1, ar_2)) (Comp: 1, Cost: 1) evalndecr2(ar_0, ar_1, ar_2) -> Com_1(evalndecr3(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalndecr3(ar_0, ar_1, ar_2) -> Com_1(evalndecr4(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalndecr4(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb1in(ar_0, ar_1, ar_0)) (Comp: ?, Cost: 1) evalndecrbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndecrbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 2 ]
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