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Complexity_C_Integer 2019-03-21 04.38 pair #429989672
details
property
value
status
complete
benchmark
ndecr.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n133.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.33805 seconds
cpu usage
2.24839
user time
2.0784
system time
0.169988
max virtual memory
1.8273416E7
max residence set size
186652.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.12/1.29 WORST_CASE(?, O(n^1)) 2.12/1.30 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.12/1.30 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.12/1.30 2.12/1.30 2.12/1.30 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.12/1.30 2.12/1.30 (0) CpxIntTrs 2.12/1.30 (1) Koat Proof [FINISHED, 82 ms] 2.12/1.30 (2) BOUNDS(1, n^1) 2.12/1.30 2.12/1.30 2.12/1.30 ---------------------------------------- 2.12/1.30 2.12/1.30 (0) 2.12/1.30 Obligation: 2.12/1.30 Complexity Int TRS consisting of the following rules: 2.12/1.30 eval_ndecr_start(v_i.0, v_n) -> Com_1(eval_ndecr_bb0_in(v_i.0, v_n)) :|: TRUE 2.12/1.30 eval_ndecr_bb0_in(v_i.0, v_n) -> Com_1(eval_ndecr_bb1_in(v_n - 1, v_n)) :|: TRUE 2.12/1.30 eval_ndecr_bb1_in(v_i.0, v_n) -> Com_1(eval_ndecr_bb2_in(v_i.0, v_n)) :|: v_i.0 > 1 2.12/1.30 eval_ndecr_bb1_in(v_i.0, v_n) -> Com_1(eval_ndecr_bb3_in(v_i.0, v_n)) :|: v_i.0 <= 1 2.12/1.30 eval_ndecr_bb2_in(v_i.0, v_n) -> Com_1(eval_ndecr_bb1_in(v_i.0 - 1, v_n)) :|: TRUE 2.12/1.30 eval_ndecr_bb3_in(v_i.0, v_n) -> Com_1(eval_ndecr_stop(v_i.0, v_n)) :|: TRUE 2.12/1.30 2.12/1.30 The start-symbols are:[eval_ndecr_start_2] 2.12/1.30 2.12/1.30 2.12/1.30 ---------------------------------------- 2.12/1.30 2.12/1.30 (1) Koat Proof (FINISHED) 2.12/1.30 YES(?, 2*ar_1 + 6) 2.12/1.30 2.12/1.30 2.12/1.30 2.12/1.30 Initial complexity problem: 2.12/1.30 2.12/1.30 1: T: 2.12/1.30 2.12/1.30 (Comp: ?, Cost: 1) evalndecrstart(ar_0, ar_1) -> Com_1(evalndecrbb0in(ar_0, ar_1)) 2.12/1.30 2.12/1.30 (Comp: ?, Cost: 1) evalndecrbb0in(ar_0, ar_1) -> Com_1(evalndecrbb1in(ar_1 - 1, ar_1)) 2.12/1.30 2.12/1.30 (Comp: ?, Cost: 1) evalndecrbb1in(ar_0, ar_1) -> Com_1(evalndecrbb2in(ar_0, ar_1)) [ ar_0 >= 2 ] 2.12/1.30 2.12/1.30 (Comp: ?, Cost: 1) evalndecrbb1in(ar_0, ar_1) -> Com_1(evalndecrbb3in(ar_0, ar_1)) [ 1 >= ar_0 ] 2.12/1.30 2.12/1.30 (Comp: ?, Cost: 1) evalndecrbb2in(ar_0, ar_1) -> Com_1(evalndecrbb1in(ar_0 - 1, ar_1)) 2.12/1.30 2.12/1.30 (Comp: ?, Cost: 1) evalndecrbb3in(ar_0, ar_1) -> Com_1(evalndecrstop(ar_0, ar_1)) 2.12/1.30 2.12/1.30 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1) -> Com_1(evalndecrstart(ar_0, ar_1)) [ 0 <= 0 ] 2.12/1.30 2.12/1.30 start location: koat_start 2.12/1.30 2.12/1.30 leaf cost: 0 2.12/1.30 2.12/1.30 2.12/1.30 2.12/1.30 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.12/1.30 2.12/1.30 2: T: 2.12/1.30 2.12/1.30 (Comp: 1, Cost: 1) evalndecrstart(ar_0, ar_1) -> Com_1(evalndecrbb0in(ar_0, ar_1)) 2.12/1.30 2.12/1.30 (Comp: 1, Cost: 1) evalndecrbb0in(ar_0, ar_1) -> Com_1(evalndecrbb1in(ar_1 - 1, ar_1)) 2.12/1.30 2.12/1.30 (Comp: ?, Cost: 1) evalndecrbb1in(ar_0, ar_1) -> Com_1(evalndecrbb2in(ar_0, ar_1)) [ ar_0 >= 2 ] 2.12/1.30 2.12/1.30 (Comp: ?, Cost: 1) evalndecrbb1in(ar_0, ar_1) -> Com_1(evalndecrbb3in(ar_0, ar_1)) [ 1 >= ar_0 ] 2.12/1.30 2.12/1.30 (Comp: ?, Cost: 1) evalndecrbb2in(ar_0, ar_1) -> Com_1(evalndecrbb1in(ar_0 - 1, ar_1)) 2.12/1.30 2.12/1.30 (Comp: ?, Cost: 1) evalndecrbb3in(ar_0, ar_1) -> Com_1(evalndecrstop(ar_0, ar_1)) 2.12/1.30 2.12/1.30 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1) -> Com_1(evalndecrstart(ar_0, ar_1)) [ 0 <= 0 ] 2.12/1.30 2.12/1.30 start location: koat_start 2.12/1.30 2.12/1.30 leaf cost: 0 2.12/1.30 2.12/1.30 2.12/1.30 2.12/1.30 A polynomial rank function with 2.12/1.30 2.12/1.30 Pol(evalndecrstart) = 2 2.12/1.30 2.12/1.30 Pol(evalndecrbb0in) = 2 2.12/1.30 2.12/1.30 Pol(evalndecrbb1in) = 2 2.12/1.30 2.12/1.30 Pol(evalndecrbb2in) = 2 2.12/1.30 2.12/1.30 Pol(evalndecrbb3in) = 1 2.12/1.30 2.12/1.30 Pol(evalndecrstop) = 0 2.12/1.30 2.12/1.30 Pol(koat_start) = 2 2.12/1.30 2.12/1.30 orients all transitions weakly and the transitions 2.12/1.30
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