details

property	value
status	complete
benchmark	ax.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n122.star.cs.uiowa.edu
space	WTC_V2

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	1.3374 seconds
cpu usage	2.26703
user time	2.11234
system time	0.154691
max virtual memory	1.8273556E7
max residence set size	178776.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^2))

output

2.09/1.31 WORST_CASE(?, O(n^2)) 2.09/1.32 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.09/1.32 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.09/1.32 2.09/1.32 2.09/1.32 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 2.09/1.32 2.09/1.32 (0) CpxIntTrs 2.09/1.32 (1) Koat Proof [FINISHED, 79 ms] 2.09/1.32 (2) BOUNDS(1, n^2) 2.09/1.32 2.09/1.32 2.09/1.32 ---------------------------------------- 2.09/1.32 2.09/1.32 (0) 2.09/1.32 Obligation: 2.09/1.32 Complexity Int TRS consisting of the following rules: 2.09/1.32 eval_ax_start(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb0_in(v_.0, v_.01, v_i, v_j, v_n)) :|: TRUE 2.09/1.32 eval_ax_bb0_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb1_in(0, v_.01, v_i, v_j, v_n)) :|: TRUE 2.09/1.32 eval_ax_bb1_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb2_in(v_.0, 0, v_i, v_j, v_n)) :|: TRUE 2.09/1.32 eval_ax_bb2_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb3_in(v_.0, v_.01, v_i, v_j, v_n)) :|: v_.01 < v_n - 1 2.09/1.32 eval_ax_bb2_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb4_in(v_.0, v_.01, v_i, v_j, v_n)) :|: v_.01 >= v_n - 1 2.09/1.32 eval_ax_bb3_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb2_in(v_.0, v_.01 + 1, v_i, v_j, v_n)) :|: TRUE 2.09/1.32 eval_ax_bb4_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_bb1_in(v_.0 + 1, v_.01, v_i, v_j, v_n)) :|: v_.01 >= v_n - 1 && v_.0 + 1 < v_n - 1 2.09/1.32 eval_ax_bb4_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_.critedge_in(v_.0, v_.01, v_i, v_j, v_n)) :|: v_.01 < v_n - 1 2.09/1.32 eval_ax_bb4_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_.critedge_in(v_.0, v_.01, v_i, v_j, v_n)) :|: v_.0 + 1 >= v_n - 1 2.09/1.32 eval_ax_.critedge_in(v_.0, v_.01, v_i, v_j, v_n) -> Com_1(eval_ax_stop(v_.0, v_.01, v_i, v_j, v_n)) :|: TRUE 2.09/1.32 2.09/1.32 The start-symbols are:[eval_ax_start_5] 2.09/1.32 2.09/1.32 2.09/1.32 ---------------------------------------- 2.09/1.32 2.09/1.32 (1) Koat Proof (FINISHED) 2.09/1.32 YES(?, 7*ar_2 + 2*ar_2^2 + 10) 2.09/1.32 2.09/1.32 2.09/1.32 2.09/1.32 Initial complexity problem: 2.09/1.32 2.09/1.32 1: T: 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxstart(ar_0, ar_1, ar_2) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2)) 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb0in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb1in(0, ar_1, ar_2)) 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb1in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, 0, ar_2)) 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 ] 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb3in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2)) 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb1in(ar_0 + 1, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_0 + 3 ] 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxcritedgein(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxcritedgein(ar_0, ar_1, ar_2)) [ ar_0 + 2 >= ar_2 ] 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxcritedgein(ar_0, ar_1, ar_2) -> Com_1(evalaxstop(ar_0, ar_1, ar_2)) 2.09/1.32 2.09/1.32 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalaxstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.09/1.32 2.09/1.32 start location: koat_start 2.09/1.32 2.09/1.32 leaf cost: 0 2.09/1.32 2.09/1.32 2.09/1.32 2.09/1.32 Testing for reachability in the complexity graph removes the following transition from problem 1: 2.09/1.32 2.09/1.32 evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxcritedgein(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] 2.09/1.32 2.09/1.32 We thus obtain the following problem: 2.09/1.32 2.09/1.32 2: T: 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxcritedgein(ar_0, ar_1, ar_2) -> Com_1(evalaxstop(ar_0, ar_1, ar_2)) 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxcritedgein(ar_0, ar_1, ar_2)) [ ar_0 + 2 >= ar_2 ] 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb4in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb1in(ar_0 + 1, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 /\ ar_2 >= ar_0 + 3 ] 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb3in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, ar_1 + 1, ar_2)) 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb4in(ar_0, ar_1, ar_2)) [ ar_1 + 1 >= ar_2 ] 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb2in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 2 ] 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb1in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb2in(ar_0, 0, ar_2)) 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxbb0in(ar_0, ar_1, ar_2) -> Com_1(evalaxbb1in(0, ar_1, ar_2)) 2.09/1.32 2.09/1.32 (Comp: ?, Cost: 1) evalaxstart(ar_0, ar_1, ar_2) -> Com_1(evalaxbb0in(ar_0, ar_1, ar_2)) 2.09/1.32 2.09/1.32 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalaxstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.09/1.32 2.09/1.32 start location: koat_start 2.09/1.32 popout

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all output return to Complexity_C_Integer 2019-03-21 04.38