details

property	value
status	complete
benchmark	jama_ex6.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n067.star.cs.uiowa.edu
space	Flores-Montoya_16

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	16.2971 seconds
cpu usage	22.3847
user time	20.6713
system time	1.7134
max virtual memory	1.886142E7
max residence set size	241636.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^3), O(n^4))

output

22.31/16.25 WORST_CASE(Omega(n^3), O(n^4)) 22.31/16.26 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 22.31/16.26 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 22.31/16.26 22.31/16.26 22.31/16.26 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^3, n^4). 22.31/16.26 22.31/16.26 (0) CpxIntTrs 22.31/16.26 (1) Koat Proof [FINISHED, 1032 ms] 22.31/16.26 (2) BOUNDS(1, n^4) 22.31/16.26 (3) Loat Proof [FINISHED, 2705 ms] 22.31/16.26 (4) BOUNDS(n^3, INF) 22.31/16.26 22.31/16.26 22.31/16.26 ---------------------------------------- 22.31/16.26 22.31/16.26 (0) 22.31/16.26 Obligation: 22.31/16.26 Complexity Int TRS consisting of the following rules: 22.31/16.26 eval_abc_start(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb0_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_bb0_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_0(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_0(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_1(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_1(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_2(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_2(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_3(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_3(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_4(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_4(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_5(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_5(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_6(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_6(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_7(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_7(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_8(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_8(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb1_in(v_6, v_7, v_a, v_b, v_c, v_d, v_a, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_bb1_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb2_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_c, v_k_0)) :|: v_i_0 <= v_b 22.31/16.26 eval_abc_bb1_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb8_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: v_i_0 > v_b 22.31/16.26 eval_abc_bb2_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb3_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: v_j_0 <= v_d 22.31/16.26 eval_abc_bb2_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb7_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: v_j_0 > v_d 22.31/16.26 eval_abc_bb3_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb4_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_i_0 - v_j_0)) :|: TRUE 22.31/16.26 eval_abc_bb4_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb5_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: v_k_0 <= v_i_0 + v_j_0 22.31/16.26 eval_abc_bb4_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb6_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: v_k_0 > v_i_0 + v_j_0 22.31/16.26 eval_abc_bb5_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb4_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0 + 1)) :|: TRUE 22.31/16.26 eval_abc_bb6_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_16(v_j_0 + 1, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_16(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_17(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_17(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb2_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_6, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_bb7_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_19(v_6, v_i_0 + 1, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_19(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_20(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_20(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_bb1_in(v_6, v_7, v_a, v_b, v_c, v_d, v_7, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 eval_abc_bb8_in(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0) -> Com_1(eval_abc_stop(v_6, v_7, v_a, v_b, v_c, v_d, v_i_0, v_j_0, v_k_0)) :|: TRUE 22.31/16.26 22.31/16.26 The start-symbols are:[eval_abc_start_9] 22.31/16.26 22.31/16.26 22.31/16.26 ---------------------------------------- 22.31/16.26 22.31/16.26 (1) Koat Proof (FINISHED) 22.31/16.26 YES(?, 489*ar_1 + 489*ar_2 + 508*ar_1*ar_4 + 508*ar_2*ar_4 + 504*ar_1*ar_5 + 504*ar_2*ar_5 + 456*ar_4 + 452*ar_5 + 52*ar_1^2*ar_4 + 104*ar_1*ar_2*ar_4 + 52*ar_1^2*ar_5 + 104*ar_1*ar_2*ar_5 + 36*ar_1^2 + 72*ar_1*ar_2 + 52*ar_2^2*ar_4 + 52*ar_2^2*ar_5 + 36*ar_2^2 + 36*ar_1*ar_4^2 + 36*ar_2*ar_4^2 + 68*ar_1*ar_4*ar_5 + 68*ar_2*ar_4*ar_5 + 20*ar_4^2 + 36*ar_4*ar_5 + 16*ar_1^2*ar_4^2 + 32*ar_1*ar_2*ar_4^2 + 32*ar_1^2*ar_4*ar_5 + 64*ar_1*ar_2*ar_4*ar_5 + 16*ar_2^2*ar_4^2 + 32*ar_2^2*ar_4*ar_5 + 16*ar_1^2*ar_5^2 + 32*ar_1*ar_2*ar_5^2 + 32*ar_1*ar_5^2 + 16*ar_2^2*ar_5^2 + 32*ar_2*ar_5^2 + 16*ar_5^2 + 468) 22.31/16.26 22.31/16.26 22.31/16.26 22.31/16.26 Initial complexity problem: 22.31/16.26 22.31/16.26 1: T: 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabcstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabcbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabc0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabc1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabc2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabc3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabc4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabc5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabc6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabc6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabc7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabc7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabc8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabc8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabcbb1in(ar_1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabcbb2in(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_2 >= ar_0 ] 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabcbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabcbb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= ar_2 + 1 ] 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_5 >= ar_3 ] 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabcbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabcbb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_3 >= ar_5 + 1 ] 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabcbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_0 - ar_3, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 + ar_3 >= ar_6 ] 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabcbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_6 >= ar_0 + ar_3 + 1 ] 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabcbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabcbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8)) 22.31/16.26 22.31/16.26 (Comp: ?, Cost: 1) evalabcbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalabc16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_3 + 1, ar_8)) 22.31/16.26 popout

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all output return to Complexity_ITS 2019-03-21 04.46