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Complexity_C_Integer 2019-03-21 04.38 pair #429988988
details
property
value
status
complete
benchmark
McCarthyIterative.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n068.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.49076 seconds
cpu usage
2.42971
user time
2.20869
system time
0.221025
max virtual memory
1.8549636E7
max residence set size
180432.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
2.33/1.46 WORST_CASE(?, O(n^2)) 2.33/1.47 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.33/1.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.33/1.47 2.33/1.47 2.33/1.47 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.33/1.47 2.33/1.47 (0) CpxIntTrs 2.33/1.47 (1) Koat Proof [FINISHED, 285 ms] 2.33/1.47 (2) BOUNDS(1, n^2) 2.33/1.47 2.33/1.47 2.33/1.47 ---------------------------------------- 2.33/1.47 2.33/1.47 (0) 2.33/1.47 Obligation: 2.33/1.47 Complexity Int TRS consisting of the following rules: 2.33/1.47 eval_foo_start(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_c, v_x)) :|: TRUE 2.33/1.47 eval_foo_bb0_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb1_in(v_x, 1, v_c, v_x)) :|: TRUE 2.33/1.47 eval_foo_bb1_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_c, v_x)) :|: v_.01 > 0 2.33/1.47 eval_foo_bb1_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_c, v_x)) :|: v_.01 <= 0 2.33/1.47 eval_foo_bb2_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_c, v_x)) :|: v_.0 > 100 2.33/1.47 eval_foo_bb2_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_c, v_x)) :|: v_.0 <= 100 2.33/1.47 eval_foo_bb3_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb1_in(v_.0 - 10, v_.01 - 1, v_c, v_x)) :|: TRUE 2.33/1.47 eval_foo_bb4_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_bb1_in(v_.0 + 11, v_.01 + 1, v_c, v_x)) :|: TRUE 2.33/1.47 eval_foo_bb5_in(v_.0, v_.01, v_c, v_x) -> Com_1(eval_foo_stop(v_.0, v_.01, v_c, v_x)) :|: TRUE 2.33/1.47 2.33/1.47 The start-symbols are:[eval_foo_start_4] 2.33/1.47 2.33/1.47 2.33/1.47 ---------------------------------------- 2.33/1.47 2.33/1.47 (1) Koat Proof (FINISHED) 2.33/1.47 YES(?, 18256*ar_1 + 36*ar_1^2 + 1476635) 2.33/1.47 2.33/1.47 2.33/1.47 2.33/1.47 Initial complexity problem: 2.33/1.47 2.33/1.47 1: T: 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1)) 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ] 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ] 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.33/1.47 2.33/1.47 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.33/1.47 2.33/1.47 start location: koat_start 2.33/1.47 2.33/1.47 leaf cost: 0 2.33/1.47 2.33/1.47 2.33/1.47 2.33/1.47 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.33/1.47 2.33/1.47 2: T: 2.33/1.47 2.33/1.47 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2)) 2.33/1.47 2.33/1.47 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_1, ar_1, 1)) 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 101 ] 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2)) [ 100 >= ar_0 ] 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 - 10, ar_1, ar_2 - 1)) 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2) -> Com_1(evalfoobb1in(ar_0 + 11, ar_1, ar_2 + 1)) 2.33/1.47 2.33/1.47 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2) -> Com_1(evalfoostop(ar_0, ar_1, ar_2)) 2.33/1.47 2.33/1.47 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfoostart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.33/1.47 2.33/1.47 start location: koat_start 2.33/1.47 2.33/1.47 leaf cost: 0 2.33/1.47 2.33/1.47 2.33/1.47 2.33/1.47 A polynomial rank function with 2.33/1.47 2.33/1.47 Pol(evalfoostart) = 2
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