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Complexity_C_Integer 2019-03-21 04.38 pair #429989682
details
property
value
status
complete
benchmark
easy2.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n014.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.81781 seconds
cpu usage
2.1795
user time
2.02166
system time
0.157832
max virtual memory
1.8273644E7
max residence set size
182100.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.01/1.77 WORST_CASE(?, O(n^1)) 2.01/1.78 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.01/1.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.01/1.78 2.01/1.78 2.01/1.78 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.01/1.78 2.01/1.78 (0) CpxIntTrs 2.01/1.78 (1) Koat Proof [FINISHED, 71 ms] 2.01/1.78 (2) BOUNDS(1, n^1) 2.01/1.78 2.01/1.78 2.01/1.78 ---------------------------------------- 2.01/1.78 2.01/1.78 (0) 2.01/1.78 Obligation: 2.01/1.78 Complexity Int TRS consisting of the following rules: 2.01/1.78 eval_easy2_start(v_.0, v_z) -> Com_1(eval_easy2_bb0_in(v_.0, v_z)) :|: TRUE 2.01/1.78 eval_easy2_bb0_in(v_.0, v_z) -> Com_1(eval_easy2_bb1_in(v_z, v_z)) :|: TRUE 2.01/1.78 eval_easy2_bb1_in(v_.0, v_z) -> Com_1(eval_easy2_bb2_in(v_.0, v_z)) :|: v_.0 > 0 2.01/1.78 eval_easy2_bb1_in(v_.0, v_z) -> Com_1(eval_easy2_bb3_in(v_.0, v_z)) :|: v_.0 <= 0 2.01/1.78 eval_easy2_bb2_in(v_.0, v_z) -> Com_1(eval_easy2_bb1_in(v_.0 - 1, v_z)) :|: TRUE 2.01/1.78 eval_easy2_bb3_in(v_.0, v_z) -> Com_1(eval_easy2_stop(v_.0, v_z)) :|: TRUE 2.01/1.78 2.01/1.78 The start-symbols are:[eval_easy2_start_2] 2.01/1.78 2.01/1.78 2.01/1.78 ---------------------------------------- 2.01/1.78 2.01/1.78 (1) Koat Proof (FINISHED) 2.01/1.78 YES(?, 2*ar_1 + 8) 2.01/1.78 2.01/1.78 2.01/1.78 2.01/1.78 Initial complexity problem: 2.01/1.78 2.01/1.78 1: T: 2.01/1.78 2.01/1.78 (Comp: ?, Cost: 1) evaleasy2start(ar_0, ar_1) -> Com_1(evaleasy2bb0in(ar_0, ar_1)) 2.01/1.78 2.01/1.78 (Comp: ?, Cost: 1) evaleasy2bb0in(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_1, ar_1)) 2.01/1.78 2.01/1.78 (Comp: ?, Cost: 1) evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb2in(ar_0, ar_1)) [ ar_0 >= 1 ] 2.01/1.78 2.01/1.78 (Comp: ?, Cost: 1) evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb3in(ar_0, ar_1)) [ 0 >= ar_0 ] 2.01/1.78 2.01/1.78 (Comp: ?, Cost: 1) evaleasy2bb2in(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_0 - 1, ar_1)) 2.01/1.78 2.01/1.78 (Comp: ?, Cost: 1) evaleasy2bb3in(ar_0, ar_1) -> Com_1(evaleasy2stop(ar_0, ar_1)) 2.01/1.78 2.01/1.78 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1) -> Com_1(evaleasy2start(ar_0, ar_1)) [ 0 <= 0 ] 2.01/1.78 2.01/1.78 start location: koat_start 2.01/1.78 2.01/1.78 leaf cost: 0 2.01/1.78 2.01/1.78 2.01/1.78 2.01/1.78 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.01/1.78 2.01/1.78 2: T: 2.01/1.78 2.01/1.78 (Comp: 1, Cost: 1) evaleasy2start(ar_0, ar_1) -> Com_1(evaleasy2bb0in(ar_0, ar_1)) 2.01/1.78 2.01/1.78 (Comp: 1, Cost: 1) evaleasy2bb0in(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_1, ar_1)) 2.01/1.78 2.01/1.78 (Comp: ?, Cost: 1) evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb2in(ar_0, ar_1)) [ ar_0 >= 1 ] 2.01/1.78 2.01/1.78 (Comp: ?, Cost: 1) evaleasy2bb1in(ar_0, ar_1) -> Com_1(evaleasy2bb3in(ar_0, ar_1)) [ 0 >= ar_0 ] 2.01/1.78 2.01/1.78 (Comp: ?, Cost: 1) evaleasy2bb2in(ar_0, ar_1) -> Com_1(evaleasy2bb1in(ar_0 - 1, ar_1)) 2.01/1.78 2.01/1.78 (Comp: ?, Cost: 1) evaleasy2bb3in(ar_0, ar_1) -> Com_1(evaleasy2stop(ar_0, ar_1)) 2.01/1.78 2.01/1.78 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1) -> Com_1(evaleasy2start(ar_0, ar_1)) [ 0 <= 0 ] 2.01/1.78 2.01/1.78 start location: koat_start 2.01/1.78 2.01/1.78 leaf cost: 0 2.01/1.78 2.01/1.78 2.01/1.78 2.01/1.78 A polynomial rank function with 2.01/1.78 2.01/1.78 Pol(evaleasy2start) = 2 2.01/1.78 2.01/1.78 Pol(evaleasy2bb0in) = 2 2.01/1.78 2.01/1.78 Pol(evaleasy2bb1in) = 2 2.01/1.78 2.01/1.78 Pol(evaleasy2bb2in) = 2 2.01/1.78 2.01/1.78 Pol(evaleasy2bb3in) = 1 2.01/1.78 2.01/1.78 Pol(evaleasy2stop) = 0 2.01/1.78 2.01/1.78 Pol(koat_start) = 2 2.01/1.78 2.01/1.78 orients all transitions weakly and the transitions 2.01/1.78
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