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Complexity_C_Integer 2019-03-21 04.38 pair #429989684
details
property
value
status
complete
benchmark
sipma91.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n107.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
3.36193 seconds
cpu usage
4.52457
user time
4.17575
system time
0.348829
max virtual memory
1.8634528E7
max residence set size
199036.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
4.34/3.30 WORST_CASE(?, O(n^1)) 4.46/3.31 proof of /export/starexec/sandbox/output/output_files/bench.koat 4.46/3.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.46/3.31 4.46/3.31 4.46/3.31 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 4.46/3.31 4.46/3.31 (0) CpxIntTrs 4.46/3.31 (1) Koat Proof [FINISHED, 2083 ms] 4.46/3.31 (2) BOUNDS(1, n^1) 4.46/3.31 4.46/3.31 4.46/3.31 ---------------------------------------- 4.46/3.31 4.46/3.31 (0) 4.46/3.31 Obligation: 4.46/3.31 Complexity Int TRS consisting of the following rules: 4.46/3.31 eval_sipma91_start(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb0_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2)) :|: TRUE 4.46/3.31 eval_sipma91_bb0_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb8_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2)) :|: v_x > 100 4.46/3.31 eval_sipma91_bb0_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb1_in(v_5, v_6, v_x, v_x, v_y1.1, v_y1.2, 1, v_y2.1, v_y2.2)) :|: v_x <= 100 4.46/3.31 eval_sipma91_bb1_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb2_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2)) :|: v_y1.0 <= 100 4.46/3.31 eval_sipma91_bb1_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb3_in(v_5, v_6, v_x, v_y1.0, v_y1.0, v_y1.2, v_y2.0, v_y2.0, v_y2.2)) :|: v_y1.0 > 100 4.46/3.31 eval_sipma91_bb2_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb1_in(v_5, v_6, v_x, v_y1.0 + 11, v_y1.1, v_y1.2, v_y2.0 + 1, v_y2.1, v_y2.2)) :|: TRUE 4.46/3.31 eval_sipma91_bb3_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb4_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2)) :|: v_y2.1 > 1 4.46/3.31 eval_sipma91_bb3_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb8_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2)) :|: v_y2.1 <= 1 4.46/3.31 eval_sipma91_bb4_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb3_in(v_5, v_6, v_x, v_y1.0, v_y1.1 - 10, v_y1.2, v_y2.0, v_y2.1 - 1, v_y2.2)) :|: v_y1.1 - 10 > 100 && v_y2.1 - 1 >= 1 && v_y2.1 - 1 <= 1 4.46/3.31 eval_sipma91_bb4_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb5_in(v_y1.1 - 10, v_y2.1 - 1, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2)) :|: v_y1.1 - 10 <= 100 4.46/3.31 eval_sipma91_bb4_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb5_in(v_y1.1 - 10, v_y2.1 - 1, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2)) :|: v_y2.1 - 1 < 1 4.46/3.31 eval_sipma91_bb4_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb5_in(v_y1.1 - 10, v_y2.1 - 1, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2)) :|: v_y2.1 - 1 > 1 4.46/3.31 eval_sipma91_bb5_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb6_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2)) :|: v_5 > 100 4.46/3.31 eval_sipma91_bb5_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb7_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_5, v_y2.0, v_y2.1, v_6)) :|: v_5 <= 100 4.46/3.31 eval_sipma91_bb6_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb7_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_5 - 10, v_y2.0, v_y2.1, v_6 - 1)) :|: TRUE 4.46/3.31 eval_sipma91_bb7_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_bb3_in(v_5, v_6, v_x, v_y1.0, v_y1.2 + 11, v_y1.2, v_y2.0, v_y2.2 + 1, v_y2.2)) :|: TRUE 4.46/3.31 eval_sipma91_bb8_in(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2) -> Com_1(eval_sipma91_stop(v_5, v_6, v_x, v_y1.0, v_y1.1, v_y1.2, v_y2.0, v_y2.1, v_y2.2)) :|: TRUE 4.46/3.31 4.46/3.31 The start-symbols are:[eval_sipma91_start_9] 4.46/3.31 4.46/3.31 4.46/3.31 ---------------------------------------- 4.46/3.31 4.46/3.31 (1) Koat Proof (FINISHED) 4.46/3.31 YES(?, 365*ar_0 + 40276) 4.46/3.31 4.46/3.31 4.46/3.31 4.46/3.31 Initial complexity problem: 4.46/3.31 4.46/3.31 1: T: 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= 101 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb1in(ar_0, ar_0, 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 100 >= ar_0 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 100 >= ar_1 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb3in(ar_0, ar_1, ar_2, ar_1, ar_2, ar_5, ar_6, ar_7, ar_8)) [ ar_1 >= 101 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb1in(ar_0, ar_1 + 11, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_4 >= 2 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 1 >= ar_4 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb3in(ar_0, ar_1, ar_2, ar_3 - 10, ar_4 - 1, ar_5, ar_6, ar_7, ar_8)) [ ar_3 >= 111 /\ ar_4 = 2 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_3 - 10, ar_4 - 1, ar_7, ar_8)) [ 110 >= ar_3 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_3 - 10, ar_4 - 1, ar_7, ar_8)) [ 1 >= ar_4 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_3 - 10, ar_4 - 1, ar_7, ar_8)) [ ar_4 >= 3 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_5 >= 101 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_5, ar_6)) [ 100 >= ar_5 ] 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_5 - 10, ar_6 - 1)) 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb3in(ar_0, ar_1, ar_2, ar_7 + 11, ar_8 + 1, ar_5, ar_6, ar_7, ar_8)) 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 4.46/3.31 4.46/3.31 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 <= 0 ] 4.46/3.31 4.46/3.31 start location: koat_start 4.46/3.31 4.46/3.31 leaf cost: 0 4.46/3.31 4.46/3.31 4.46/3.31 4.46/3.31 Testing for reachability in the complexity graph removes the following transition from problem 1: 4.46/3.31 4.46/3.31 evalsipma91bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_3 - 10, ar_4 - 1, ar_7, ar_8)) [ 1 >= ar_4 ] 4.46/3.31 4.46/3.31 We thus obtain the following problem: 4.46/3.31 4.46/3.31 2: T: 4.46/3.31 4.46/3.31 (Comp: ?, Cost: 1) evalsipma91bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb3in(ar_0, ar_1, ar_2, ar_7 + 11, ar_8 + 1, ar_5, ar_6, ar_7, ar_8))
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