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Complexity_C_Integer 2019-03-21 04.38 pair #429989280
details
property
value
status
complete
benchmark
GCD3.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n037.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.96172 seconds
cpu usage
3.21634
user time
2.95262
system time
0.263722
max virtual memory
1.848508E7
max residence set size
190308.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
3.12/1.93 WORST_CASE(?, O(n^1)) 3.12/1.94 proof of /export/starexec/sandbox2/output/output_files/bench.koat 3.12/1.94 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.12/1.94 3.12/1.94 3.12/1.94 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 3.12/1.94 3.12/1.94 (0) CpxIntTrs 3.12/1.94 (1) Koat Proof [FINISHED, 578 ms] 3.12/1.94 (2) BOUNDS(1, n^1) 3.12/1.94 3.12/1.94 3.12/1.94 ---------------------------------------- 3.12/1.94 3.12/1.94 (0) 3.12/1.94 Obligation: 3.12/1.94 Complexity Int TRS consisting of the following rules: 3.12/1.94 eval_foo_start(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 3.12/1.94 eval_foo_bb0_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 3.12/1.94 eval_foo_bb1_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 > 0 && v_.0 > 0 3.12/1.94 eval_foo_bb1_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb9_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 <= 0 3.12/1.94 eval_foo_bb1_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb9_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.0 <= 0 3.12/1.94 eval_foo_bb2_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.0, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 >= 0 && v_.01 <= 0 3.12/1.94 eval_foo_bb2_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 < 0 3.12/1.94 eval_foo_bb2_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 > 0 3.12/1.94 eval_foo_bb3_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, -(v_.0), v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 < 0 3.12/1.94 eval_foo_bb3_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_.0, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.01 >= 0 3.12/1.94 eval_foo_bb4_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_.13, v_.13, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.13 > 0 3.12/1.94 eval_foo_bb4_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb7_in(v_.0, v_.01, v_.13, v_.24, v_.13, v_tmp, v_x, v_xtmp, v_y)) :|: v_.13 <= 0 3.12/1.94 eval_foo_bb5_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb6_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.24 >= v_.01 3.12/1.94 eval_foo_bb5_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.24, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.24 < v_.01 3.12/1.94 eval_foo_bb6_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb5_in(v_.0, v_.01, v_.13, v_.24 - v_.01, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 3.12/1.94 eval_foo_bb7_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb8_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.3 < 0 3.12/1.94 eval_foo_bb7_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb1_in(v_.01, v_.3, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: v_.3 >= 0 3.12/1.94 eval_foo_bb8_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_bb7_in(v_.0, v_.01, v_.13, v_.24, v_.3 - v_.01, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 3.12/1.94 eval_foo_bb9_in(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_.13, v_.24, v_.3, v_tmp, v_x, v_xtmp, v_y)) :|: TRUE 3.12/1.94 3.12/1.94 The start-symbols are:[eval_foo_start_9] 3.12/1.94 3.12/1.94 3.12/1.94 ---------------------------------------- 3.12/1.94 3.12/1.94 (1) Koat Proof (FINISHED) 3.12/1.94 YES(?, 16*ar_1 + 48*ar_3 + 8) 3.12/1.94 3.12/1.94 3.12/1.94 3.12/1.94 Initial complexity problem: 3.12/1.94 3.12/1.94 1: T: 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 1 /\ ar_0 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_2 = 0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_2 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, -ar_0, ar_5, ar_6)) [ 0 >= ar_2 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_2 >= 0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_6)) [ ar_4 >= 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4)) [ 0 >= ar_4 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= ar_2 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_5, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_5 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_2, ar_6)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_6 + 1 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb1in(ar_2, ar_1, ar_6, ar_3, ar_4, ar_5, ar_6)) [ ar_6 >= 0 ] 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - ar_2)) 3.12/1.94 3.12/1.94 (Comp: ?, Cost: 1) evalfoobb9in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 3.12/1.94 3.12/1.94 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.12/1.94 3.12/1.94 start location: koat_start 3.12/1.94 3.12/1.94 leaf cost: 0 3.12/1.94 3.12/1.94 3.12/1.94 3.12/1.94 Testing for reachability in the complexity graph removes the following transitions from problem 1: 3.12/1.94 3.12/1.94 evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3, ar_0, ar_5, ar_6)) [ ar_2 = 0 ]
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return to Complexity_C_Integer 2019-03-21 04.38