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Complexity_C_Integer 2019-03-21 04.38 pair #429988836
details
property
value
status
complete
benchmark
t10.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n166.star.cs.uiowa.edu
space
C4B_examples
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.65524 seconds
cpu usage
2.54286
user time
2.30224
system time
0.240629
max virtual memory
1.8273644E7
max residence set size
180948.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.07/1.61 WORST_CASE(?, O(n^1)) 2.07/1.62 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.07/1.62 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.07/1.62 2.07/1.62 2.07/1.62 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.07/1.62 2.07/1.62 (0) CpxIntTrs 2.07/1.62 (1) Koat Proof [FINISHED, 371 ms] 2.07/1.62 (2) BOUNDS(1, n^1) 2.07/1.62 2.07/1.62 2.07/1.62 ---------------------------------------- 2.07/1.62 2.07/1.62 (0) 2.07/1.62 Obligation: 2.07/1.62 Complexity Int TRS consisting of the following rules: 2.07/1.62 eval_t10_start(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb0_in(v_.0, v_.01, v_1, v_x, v_y)) :|: TRUE 2.07/1.62 eval_t10_bb0_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb1_in(v_x, v_y, v_1, v_x, v_y)) :|: TRUE 2.07/1.62 eval_t10_bb1_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb2_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_.0 > v_.01 2.07/1.62 eval_t10_bb1_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb3_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_.0 <= v_.01 2.07/1.62 eval_t10_bb2_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_0(v_.0, v_.01, v_1, v_x, v_y)) :|: TRUE 2.07/1.62 eval_t10_0(v_.0, v_.01, v_1, v_x, v_y) -> Com_2(eval_nondet_start(v_.0, v_.01, v_1, v_x, v_y), eval_t10_1(v_.0, v_.01, nondef.0, v_x, v_y)) :|: TRUE 2.07/1.62 eval_t10_1(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb1_in(v_.0, v_.01 + 1, v_1, v_x, v_y)) :|: v_1 > 0 2.07/1.62 eval_t10_1(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb1_in(v_.0 - 1, v_.01 + 1, v_1, v_x, v_y)) :|: v_1 > 0 && v_1 <= 0 2.07/1.62 eval_t10_1(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb1_in(v_.0, v_.01, v_1, v_x, v_y)) :|: v_1 <= 0 && v_1 > 0 2.07/1.62 eval_t10_1(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_bb1_in(v_.0 - 1, v_.01, v_1, v_x, v_y)) :|: v_1 <= 0 2.07/1.62 eval_t10_bb3_in(v_.0, v_.01, v_1, v_x, v_y) -> Com_1(eval_t10_stop(v_.0, v_.01, v_1, v_x, v_y)) :|: TRUE 2.07/1.62 2.07/1.62 The start-symbols are:[eval_t10_start_5] 2.07/1.62 2.07/1.62 2.07/1.62 ---------------------------------------- 2.07/1.62 2.07/1.62 (1) Koat Proof (FINISHED) 2.07/1.62 YES(?, 42*ar_1 + 42*ar_3 + 6) 2.07/1.62 2.07/1.62 2.07/1.62 2.07/1.62 Initial complexity problem: 2.07/1.62 2.07/1.62 1: T: 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt10bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 1 ] 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 ] 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt101(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5)) 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, g)) 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 >= 1 /\ 0 >= ar_4 ] 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 /\ ar_4 >= 1 ] 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 ] 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.07/1.62 2.07/1.62 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.07/1.62 2.07/1.62 start location: koat_start 2.07/1.62 2.07/1.62 leaf cost: 0 2.07/1.62 2.07/1.62 2.07/1.62 2.07/1.62 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.07/1.62 2.07/1.62 evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 >= 1 /\ 0 >= ar_4 ] 2.07/1.62 2.07/1.62 evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 /\ ar_4 >= 1 ] 2.07/1.62 2.07/1.62 We thus obtain the following problem: 2.07/1.62 2.07/1.62 2: T: 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 ] 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt101(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt101(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5)) 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalt1000(ar_0, ar_1, ar_2, ar_3, ar_4, g), evalt1001(ar_0, ar_1, ar_2, ar_3, ar_4, g)) 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt10bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt10stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.07/1.62 2.07/1.62 (Comp: ?, Cost: 1) evalt10bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalt100(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5))
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