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Complexity_C_Integer 2019-03-21 04.38 pair #429989728
details
property
value
status
complete
benchmark
nd_loop.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n098.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.75472 seconds
cpu usage
2.5617
user time
2.33166
system time
0.230042
max virtual memory
1.8445336E7
max residence set size
181536.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
2.46/1.65 WORST_CASE(?, O(1)) 2.46/1.66 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.46/1.66 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.46/1.66 2.46/1.66 2.46/1.66 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 2.46/1.66 2.46/1.66 (0) CpxIntTrs 2.46/1.66 (1) Koat Proof [FINISHED, 378 ms] 2.46/1.66 (2) BOUNDS(1, 1) 2.46/1.66 2.46/1.66 2.46/1.66 ---------------------------------------- 2.46/1.66 2.46/1.66 (0) 2.46/1.66 Obligation: 2.46/1.66 Complexity Int TRS consisting of the following rules: 2.46/1.66 eval_nd_loop_start(v_0, v_x.0) -> Com_1(eval_nd_loop_bb0_in(v_0, v_x.0)) :|: TRUE 2.46/1.66 eval_nd_loop_bb0_in(v_0, v_x.0) -> Com_1(eval_nd_loop_bb1_in(v_0, 0)) :|: TRUE 2.46/1.66 eval_nd_loop_bb1_in(v_0, v_x.0) -> Com_1(eval_nd_loop_0(v_0, v_x.0)) :|: TRUE 2.46/1.66 eval_nd_loop_0(v_0, v_x.0) -> Com_2(eval_nondet_start(v_0, v_x.0), eval_nd_loop_1(nondef.0, v_x.0)) :|: TRUE 2.46/1.66 eval_nd_loop_1(v_0, v_x.0) -> Com_1(eval_nd_loop_bb1_in(v_0, v_0)) :|: v_0 - v_x.0 <= 2 && v_0 - v_x.0 >= 1 && v_0 < 10 2.46/1.66 eval_nd_loop_1(v_0, v_x.0) -> Com_1(eval_nd_loop_bb2_in(v_0, v_x.0)) :|: v_0 - v_x.0 > 2 2.46/1.66 eval_nd_loop_1(v_0, v_x.0) -> Com_1(eval_nd_loop_bb2_in(v_0, v_x.0)) :|: v_0 - v_x.0 < 1 2.46/1.66 eval_nd_loop_1(v_0, v_x.0) -> Com_1(eval_nd_loop_bb2_in(v_0, v_x.0)) :|: v_0 >= 10 2.46/1.66 eval_nd_loop_bb2_in(v_0, v_x.0) -> Com_1(eval_nd_loop_stop(v_0, v_x.0)) :|: TRUE 2.46/1.66 2.46/1.66 The start-symbols are:[eval_nd_loop_start_2] 2.46/1.66 2.46/1.66 2.46/1.66 ---------------------------------------- 2.46/1.66 2.46/1.66 (1) Koat Proof (FINISHED) 2.46/1.66 YES(?, 108) 2.46/1.66 2.46/1.66 2.46/1.66 2.46/1.66 Initial complexity problem: 2.46/1.66 2.46/1.66 1: T: 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloopstart(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2)) 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2)) 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2)) 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2)) 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d)) 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(ar_1, ar_1, ar_2)) [ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 ] 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 3 ] 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ] 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 10 ] 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2)) 2.46/1.66 2.46/1.66 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.46/1.66 2.46/1.66 start location: koat_start 2.46/1.66 2.46/1.66 leaf cost: 0 2.46/1.66 2.46/1.66 2.46/1.66 2.46/1.66 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.46/1.66 2.46/1.66 2: T: 2.46/1.66 2.46/1.66 (Comp: 1, Cost: 1) evalndloopstart(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb0in(ar_0, ar_1, ar_2)) 2.46/1.66 2.46/1.66 (Comp: 1, Cost: 1) evalndloopbb0in(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(0, ar_1, ar_2)) 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloopbb1in(ar_0, ar_1, ar_2) -> Com_1(evalndloop0(ar_0, ar_1, ar_2)) 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop00(ar_0, ar_1, ar_2) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2)) 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop01(ar_0, ar_1, ar_2) -> Com_1(evalndloop1(ar_0, ar_2, ar_2)) 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop0(ar_0, ar_1, ar_2) -> Com_2(evalndloop00(ar_0, ar_1, d), evalndloop01(ar_0, ar_1, d)) 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb1in(ar_1, ar_1, ar_2)) [ ar_0 + 2 >= ar_1 /\ ar_1 >= ar_0 + 1 /\ 9 >= ar_1 ] 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_0 + 3 ] 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 ] 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloop1(ar_0, ar_1, ar_2) -> Com_1(evalndloopbb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 10 ] 2.46/1.66 2.46/1.66 (Comp: ?, Cost: 1) evalndloopbb2in(ar_0, ar_1, ar_2) -> Com_1(evalndloopstop(ar_0, ar_1, ar_2)) 2.46/1.66 2.46/1.66 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalndloopstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.46/1.66 2.46/1.66 start location: koat_start
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