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Complexity_C_Integer 2019-03-21 04.38 pair #429989270
details
property
value
status
complete
benchmark
Parallel_true-termination.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n102.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.75153 seconds
cpu usage
2.70969
user time
2.4682
system time
0.241491
max virtual memory
1.8454884E7
max residence set size
181128.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.61/1.72 WORST_CASE(?, O(n^1)) 2.61/1.73 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.61/1.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.61/1.73 2.61/1.73 2.61/1.73 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.61/1.73 2.61/1.73 (0) CpxIntTrs 2.61/1.73 (1) Koat Proof [FINISHED, 478 ms] 2.61/1.73 (2) BOUNDS(1, n^1) 2.61/1.73 2.61/1.73 2.61/1.73 ---------------------------------------- 2.61/1.73 2.61/1.73 (0) 2.61/1.73 Obligation: 2.61/1.73 Complexity Int TRS consisting of the following rules: 2.61/1.73 eval_foo_start(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.61/1.73 eval_foo_bb0_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_x, v_y)) :|: TRUE 2.61/1.73 eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= 0 2.61/1.73 eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_x, v_y)) :|: v_.01 >= 0 2.61/1.73 eval_foo_bb1_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 < 0 && v_.01 < 0 2.61/1.73 eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01, v_x, v_y)) :|: v_.0 >= 0 2.61/1.73 eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_x, v_y)) :|: v_.0 >= 0 && v_.0 < 0 2.61/1.73 eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01 - 1, v_x, v_y)) :|: v_.0 < 0 && v_.0 >= 0 2.61/1.73 eval_foo_bb2_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_x, v_y)) :|: v_.0 < 0 2.61/1.73 eval_foo_bb3_in(v_.0, v_.01, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_x, v_y)) :|: TRUE 2.61/1.73 2.61/1.73 The start-symbols are:[eval_foo_start_4] 2.61/1.73 2.61/1.73 2.61/1.73 ---------------------------------------- 2.61/1.73 2.61/1.73 (1) Koat Proof (FINISHED) 2.61/1.73 YES(?, 2*ar_3 + 5*ar_1 + 18) 2.61/1.73 2.61/1.73 2.61/1.73 2.61/1.73 Initial complexity problem: 2.61/1.73 2.61/1.73 1: T: 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ 0 >= ar_0 + 1 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 /\ ar_0 >= 0 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.61/1.73 2.61/1.73 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.61/1.73 2.61/1.73 start location: koat_start 2.61/1.73 2.61/1.73 leaf cost: 0 2.61/1.73 2.61/1.73 2.61/1.73 2.61/1.73 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.61/1.73 2.61/1.73 evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ 0 >= ar_0 + 1 ] 2.61/1.73 2.61/1.73 evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 /\ ar_0 >= 0 ] 2.61/1.73 2.61/1.73 We thus obtain the following problem: 2.61/1.73 2.61/1.73 2: T: 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) [ 0 >= ar_0 + 1 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 + 1 /\ 0 >= ar_2 + 1 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 ] 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.61/1.73 2.61/1.73 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.61/1.73 2.61/1.73 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.61/1.73 2.61/1.73 start location: koat_start 2.61/1.73
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return to Complexity_C_Integer 2019-03-21 04.38