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Complexity_C_Integer 2019-03-21 04.38 pair #429989010
details
property
value
status
complete
benchmark
NoriSharma-FSE2013-Fig8_true-termination.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.40378 seconds
cpu usage
3.42148
user time
3.16992
system time
0.251565
max virtual memory
1.8550784E7
max residence set size
184368.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^3))
output
3.29/2.36 WORST_CASE(?, O(n^3)) 3.29/2.37 proof of /export/starexec/sandbox/output/output_files/bench.koat 3.29/2.37 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.29/2.37 3.29/2.37 3.29/2.37 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3). 3.29/2.37 3.29/2.37 (0) CpxIntTrs 3.29/2.37 (1) Koat Proof [FINISHED, 1078 ms] 3.29/2.37 (2) BOUNDS(1, n^3) 3.29/2.37 3.29/2.37 3.29/2.37 ---------------------------------------- 3.29/2.37 3.29/2.37 (0) 3.29/2.37 Obligation: 3.29/2.37 Complexity Int TRS consisting of the following rules: 3.29/2.37 eval_foo_start(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb0_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: TRUE 3.29/2.37 eval_foo_bb0_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_z, v_y, v_x, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: TRUE 3.29/2.37 eval_foo_bb1_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb2_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: v_.04 >= v_.02 3.29/2.37 eval_foo_bb1_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb5_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: v_.04 < v_.02 3.29/2.37 eval_foo_bb2_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb3_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: v_.01 > 1 3.29/2.37 eval_foo_bb2_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb4_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: v_.01 <= 1 3.29/2.37 eval_foo_bb3_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_.01 - 1, v_.02, v_.04 + v_.01 - 1, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: TRUE 3.29/2.37 eval_foo_bb4_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_bb1_in(v_.01, v_.02 + 1, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: TRUE 3.29/2.37 eval_foo_bb5_in(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z) -> Com_1(eval_foo_stop(v_.01, v_.02, v_.04, v_c, v_u, v_v, v_w, v_x, v_y, v_z)) :|: TRUE 3.29/2.37 3.29/2.37 The start-symbols are:[eval_foo_start_10] 3.29/2.37 3.29/2.37 3.29/2.37 ---------------------------------------- 3.29/2.37 3.29/2.37 (1) Koat Proof (FINISHED) 3.29/2.37 YES(?, 3*ar_1*ar_3 + 9*ar_1^2 + 3*ar_1*ar_5 + 3*ar_1^3 + 6*ar_3 + 12*ar_1 + 6*ar_5 + 20) 3.29/2.37 3.29/2.37 3.29/2.37 3.29/2.37 Initial complexity problem: 3.29/2.37 3.29/2.37 1: T: 3.29/2.37 3.29/2.37 (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)) 3.29/2.37 3.29/2.37 (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_5, ar_5)) 3.29/2.37 3.29/2.37 (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_2 ] 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb2in(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 >= 2 ] 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ] 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb5in(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)) 3.29/2.37 3.29/2.37 (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 ] 3.29/2.37 3.29/2.37 start location: koat_start 3.29/2.37 3.29/2.37 leaf cost: 0 3.29/2.37 3.29/2.37 3.29/2.37 3.29/2.37 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.29/2.37 3.29/2.37 2: T: 3.29/2.37 3.29/2.37 (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)) 3.29/2.37 3.29/2.37 (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_5, ar_5)) 3.29/2.37 3.29/2.37 (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_2 ] 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb2in(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 >= 2 ] 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 1 >= ar_0 ] 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3, ar_4 + ar_0 - 1, ar_5)) 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) 3.29/2.37 3.29/2.37 (Comp: ?, Cost: 1) evalfoobb5in(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)) 3.29/2.37 3.29/2.37 (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 ] 3.29/2.37 3.29/2.37 start location: koat_start 3.29/2.37 3.29/2.37 leaf cost: 0 3.29/2.37 3.29/2.37 3.29/2.37 3.29/2.37 A polynomial rank function with 3.29/2.37 3.29/2.37 Pol(evalfoostart) = 2
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