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Complexity_C_Integer 2019-03-21 04.38 pair #429988866
details
property
value
status
complete
benchmark
t47.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n017.star.cs.uiowa.edu
space
C4B_examples
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.32828 seconds
cpu usage
2.32236
user time
2.13579
system time
0.186577
max virtual memory
1.83444E7
max residence set size
181056.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.15/1.28 WORST_CASE(?, O(n^1)) 2.15/1.29 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.15/1.29 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.15/1.29 2.15/1.29 2.15/1.29 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.15/1.29 2.15/1.29 (0) CpxIntTrs 2.15/1.29 (1) Koat Proof [FINISHED, 67 ms] 2.15/1.29 (2) BOUNDS(1, n^1) 2.15/1.29 2.15/1.29 2.15/1.29 ---------------------------------------- 2.15/1.29 2.15/1.29 (0) 2.15/1.29 Obligation: 2.15/1.29 Complexity Int TRS consisting of the following rules: 2.15/1.29 eval_t47_start(v_.0, v_flag.0, v_n) -> Com_1(eval_t47_bb0_in(v_.0, v_flag.0, v_n)) :|: TRUE 2.15/1.29 eval_t47_bb0_in(v_.0, v_flag.0, v_n) -> Com_1(eval_t47_bb1_in(v_n, 1, v_n)) :|: TRUE 2.15/1.29 eval_t47_bb1_in(v_.0, v_flag.0, v_n) -> Com_1(eval_t47_bb2_in(v_.0, v_flag.0, v_n)) :|: v_flag.0 > 0 2.15/1.29 eval_t47_bb1_in(v_.0, v_flag.0, v_n) -> Com_1(eval_t47_bb3_in(v_.0, v_flag.0, v_n)) :|: v_flag.0 <= 0 2.15/1.29 eval_t47_bb2_in(v_.0, v_flag.0, v_n) -> Com_1(eval_t47_bb1_in(v_.0 - 1, 1, v_n)) :|: v_.0 > 0 2.15/1.29 eval_t47_bb2_in(v_.0, v_flag.0, v_n) -> Com_1(eval_t47_bb1_in(v_.0, 1, v_n)) :|: v_.0 > 0 && v_.0 <= 0 2.15/1.29 eval_t47_bb2_in(v_.0, v_flag.0, v_n) -> Com_1(eval_t47_bb1_in(v_.0 - 1, 0, v_n)) :|: v_.0 <= 0 && v_.0 > 0 2.15/1.29 eval_t47_bb2_in(v_.0, v_flag.0, v_n) -> Com_1(eval_t47_bb1_in(v_.0, 0, v_n)) :|: v_.0 <= 0 2.15/1.29 eval_t47_bb3_in(v_.0, v_flag.0, v_n) -> Com_1(eval_t47_stop(v_.0, v_flag.0, v_n)) :|: TRUE 2.15/1.29 2.15/1.29 The start-symbols are:[eval_t47_start_3] 2.15/1.29 2.15/1.29 2.15/1.29 ---------------------------------------- 2.15/1.29 2.15/1.29 (1) Koat Proof (FINISHED) 2.15/1.29 YES(?, 2*ar_1 + 8) 2.15/1.29 2.15/1.29 2.15/1.29 2.15/1.29 Initial complexity problem: 2.15/1.29 2.15/1.29 1: T: 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47start(ar_0, ar_1, ar_2) -> Com_1(evalt47bb0in(ar_0, ar_1, ar_2)) 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb0in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb1in(ar_1, ar_1, 1)) 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb1in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb1in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb2in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb1in(ar_0 - 1, ar_1, 1)) [ ar_0 >= 1 ] 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb2in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb1in(ar_0, ar_1, 1)) [ ar_0 >= 1 /\ 0 >= ar_0 ] 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb2in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb1in(ar_0 - 1, ar_1, 0)) [ 0 >= ar_0 /\ ar_0 >= 1 ] 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb2in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb1in(ar_0, ar_1, 0)) [ 0 >= ar_0 ] 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb3in(ar_0, ar_1, ar_2) -> Com_1(evalt47stop(ar_0, ar_1, ar_2)) 2.15/1.29 2.15/1.29 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalt47start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.15/1.29 2.15/1.29 start location: koat_start 2.15/1.29 2.15/1.29 leaf cost: 0 2.15/1.29 2.15/1.29 2.15/1.29 2.15/1.29 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.15/1.29 2.15/1.29 evalt47bb2in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb1in(ar_0, ar_1, 1)) [ ar_0 >= 1 /\ 0 >= ar_0 ] 2.15/1.29 2.15/1.29 evalt47bb2in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb1in(ar_0 - 1, ar_1, 0)) [ 0 >= ar_0 /\ ar_0 >= 1 ] 2.15/1.29 2.15/1.29 We thus obtain the following problem: 2.15/1.29 2.15/1.29 2: T: 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb3in(ar_0, ar_1, ar_2) -> Com_1(evalt47stop(ar_0, ar_1, ar_2)) 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb1in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ] 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb2in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb1in(ar_0, ar_1, 0)) [ 0 >= ar_0 ] 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb2in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb1in(ar_0 - 1, ar_1, 1)) [ ar_0 >= 1 ] 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb1in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 1 ] 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47bb0in(ar_0, ar_1, ar_2) -> Com_1(evalt47bb1in(ar_1, ar_1, 1)) 2.15/1.29 2.15/1.29 (Comp: ?, Cost: 1) evalt47start(ar_0, ar_1, ar_2) -> Com_1(evalt47bb0in(ar_0, ar_1, ar_2)) 2.15/1.29 2.15/1.29 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalt47start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] 2.15/1.29 2.15/1.29 start location: koat_start 2.15/1.29 2.15/1.29 leaf cost: 0 2.15/1.29 2.15/1.29 2.15/1.29 2.15/1.29 Repeatedly propagating knowledge in problem 2 produces the following problem:
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