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Complexity_C_Integer 2019-03-21 04.38 pair #429988830
details
property
value
status
complete
benchmark
t20.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n123.star.cs.uiowa.edu
space
C4B_examples
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.34893 seconds
cpu usage
2.29853
user time
2.12543
system time
0.173105
max virtual memory
1.8273644E7
max residence set size
181636.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.11/1.30 WORST_CASE(?, O(n^1)) 2.11/1.31 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.11/1.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.11/1.31 2.11/1.31 2.11/1.31 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.11/1.31 2.11/1.31 (0) CpxIntTrs 2.11/1.31 (1) Koat Proof [FINISHED, 75 ms] 2.11/1.31 (2) BOUNDS(1, n^1) 2.11/1.31 2.11/1.31 2.11/1.31 ---------------------------------------- 2.11/1.31 2.11/1.31 (0) 2.11/1.31 Obligation: 2.11/1.31 Complexity Int TRS consisting of the following rules: 2.11/1.31 eval_t20_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.11/1.31 eval_t20_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb1_in(v_x, v_.01, v_x, v_y)) :|: TRUE 2.11/1.31 eval_t20_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < v_y 2.11/1.31 eval_t20_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb3_in(v_.0, v_y, v_x, v_y)) :|: v_.0 >= v_y 2.11/1.31 eval_t20_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb1_in(v_.0 + 1, v_.01, v_x, v_y)) :|: TRUE 2.11/1.31 eval_t20_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb4_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 < v_.0 2.11/1.31 eval_t20_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb5_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 >= v_.0 2.11/1.31 eval_t20_bb4_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_bb3_in(v_.0, v_.01 + 1, v_x, v_y)) :|: TRUE 2.11/1.31 eval_t20_bb5_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_t20_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.11/1.31 2.11/1.31 The start-symbols are:[eval_t20_start_4] 2.11/1.31 2.11/1.31 2.11/1.31 ---------------------------------------- 2.11/1.31 2.11/1.31 (1) Koat Proof (FINISHED) 2.11/1.31 YES(?, 14*ar_1 + 20*ar_2 + 17) 2.11/1.31 2.11/1.31 2.11/1.31 2.11/1.31 Initial complexity problem: 2.11/1.31 2.11/1.31 1: T: 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3)) 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3)) 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ] 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ] 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ] 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1)) 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3)) 2.11/1.31 2.11/1.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.11/1.31 2.11/1.31 start location: koat_start 2.11/1.31 2.11/1.31 leaf cost: 0 2.11/1.31 2.11/1.31 2.11/1.31 2.11/1.31 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.11/1.31 2.11/1.31 2: T: 2.11/1.31 2.11/1.31 (Comp: 1, Cost: 1) evalt20start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb0in(ar_0, ar_1, ar_2, ar_3)) 2.11/1.31 2.11/1.31 (Comp: 1, Cost: 1) evalt20bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_1, ar_1, ar_2, ar_3)) 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_2)) [ ar_0 >= ar_2 ] 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb1in(ar_0 + 1, ar_1, ar_2, ar_3)) 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 + 1 ] 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 ] 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20bb3in(ar_0, ar_1, ar_2, ar_3 + 1)) 2.11/1.31 2.11/1.31 (Comp: ?, Cost: 1) evalt20bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20stop(ar_0, ar_1, ar_2, ar_3)) 2.11/1.31 2.11/1.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt20start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.11/1.31 2.11/1.31 start location: koat_start 2.11/1.31 2.11/1.31 leaf cost: 0 2.11/1.31 2.11/1.31 2.11/1.31 2.11/1.31 A polynomial rank function with 2.11/1.31 2.11/1.31 Pol(evalt20start) = 3
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