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Complexity_C_Integer 2019-03-21 04.38 pair #429989392
details
property
value
status
complete
benchmark
NoriSharma-FSE2013-Fig7_true-termination.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n157.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.31515 seconds
cpu usage
2.33529
user time
2.16827
system time
0.167022
max virtual memory
1.8393436E7
max residence set size
181580.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.26/1.26 WORST_CASE(?, O(n^1)) 2.26/1.27 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.26/1.27 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.26/1.27 2.26/1.27 2.26/1.27 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.26/1.27 2.26/1.27 (0) CpxIntTrs 2.26/1.27 (1) Koat Proof [FINISHED, 76 ms] 2.26/1.27 (2) BOUNDS(1, n^1) 2.26/1.27 2.26/1.27 2.26/1.27 ---------------------------------------- 2.26/1.27 2.26/1.27 (0) 2.26/1.27 Obligation: 2.26/1.27 Complexity Int TRS consisting of the following rules: 2.26/1.27 eval_foo_start(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j) -> Com_1(eval_foo_bb0_in(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j)) :|: TRUE 2.26/1.27 eval_foo_bb0_in(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_i, v_j, v_M, v_N, v_a, v_b, v_c, v_i, v_j)) :|: TRUE 2.26/1.27 eval_foo_bb1_in(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j)) :|: v_.01 < v_M 2.26/1.27 eval_foo_bb1_in(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j)) :|: v_.02 < v_N 2.26/1.27 eval_foo_bb1_in(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j) -> Com_1(eval_foo_bb3_in(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j)) :|: v_.01 >= v_M && v_.02 >= v_N 2.26/1.27 eval_foo_bb2_in(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j) -> Com_1(eval_foo_bb1_in(v_.01 + 1, v_.02 + 1, v_M, v_N, v_a, v_b, v_c, v_i, v_j)) :|: TRUE 2.26/1.27 eval_foo_bb3_in(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j) -> Com_1(eval_foo_stop(v_.01, v_.02, v_M, v_N, v_a, v_b, v_c, v_i, v_j)) :|: TRUE 2.26/1.27 2.26/1.27 The start-symbols are:[eval_foo_start_9] 2.26/1.27 2.26/1.27 2.26/1.27 ---------------------------------------- 2.26/1.27 2.26/1.27 (1) Koat Proof (FINISHED) 2.26/1.27 YES(?, 2*ar_1 + 2*ar_4 + 2*ar_3 + 2*ar_5 + 10) 2.26/1.27 2.26/1.27 2.26/1.27 2.26/1.27 Initial complexity problem: 2.26/1.27 2.26/1.27 1: T: 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 /\ ar_2 >= ar_5 ] 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.26/1.27 2.26/1.27 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.26/1.27 2.26/1.27 start location: koat_start 2.26/1.27 2.26/1.27 leaf cost: 0 2.26/1.27 2.26/1.27 2.26/1.27 2.26/1.27 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.26/1.27 2.26/1.27 2: T: 2.26/1.27 2.26/1.27 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.26/1.27 2.26/1.27 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5)) 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= ar_0 + 1 ] 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_4 /\ ar_2 >= ar_5 ] 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) 2.26/1.27 2.26/1.27 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 2.26/1.27 2.26/1.27 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 2.26/1.27 2.26/1.27 start location: koat_start 2.26/1.27 2.26/1.27 leaf cost: 0 2.26/1.27 2.26/1.27 2.26/1.27 2.26/1.27 A polynomial rank function with 2.26/1.27 2.26/1.27 Pol(evalfoostart) = 2 2.26/1.27 2.26/1.27 Pol(evalfoobb0in) = 2 2.26/1.27 2.26/1.27 Pol(evalfoobb1in) = 2 2.26/1.27 2.26/1.27 Pol(evalfoobb2in) = 2 2.26/1.27 2.26/1.27 Pol(evalfoobb3in) = 1 2.26/1.27 2.26/1.27 Pol(evalfoostop) = 0
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