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Complexity_C_Integer 2019-03-21 04.38 pair #429989688
details
property
value
status
complete
benchmark
speedDis2.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n059.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.59701 seconds
cpu usage
2.46599
user time
2.24892
system time
0.217069
max virtual memory
1.833918E7
max residence set size
182216.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.13/1.53 WORST_CASE(?, O(n^1)) 2.41/1.54 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.41/1.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.41/1.54 2.41/1.54 2.41/1.54 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.41/1.54 2.41/1.54 (0) CpxIntTrs 2.41/1.54 (1) Koat Proof [FINISHED, 268 ms] 2.41/1.54 (2) BOUNDS(1, n^1) 2.41/1.54 2.41/1.54 2.41/1.54 ---------------------------------------- 2.41/1.54 2.41/1.54 (0) 2.41/1.54 Obligation: 2.41/1.54 Complexity Int TRS consisting of the following rules: 2.41/1.54 eval_speedDis2_start(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb0_in(v_.0, v_.01, v_n, v_x, v_z)) :|: TRUE 2.41/1.54 eval_speedDis2_bb0_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb1_in(v_x, v_z, v_n, v_x, v_z)) :|: TRUE 2.41/1.54 eval_speedDis2_bb1_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb2_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.0 < v_n 2.41/1.54 eval_speedDis2_bb1_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb3_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.0 >= v_n 2.41/1.54 eval_speedDis2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb1_in(v_.0 + 1, v_.01, v_n, v_x, v_z)) :|: v_.01 > v_.0 2.41/1.54 eval_speedDis2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb1_in(v_.0, v_.01, v_n, v_x, v_z)) :|: v_.01 > v_.0 && v_.01 <= v_.0 2.41/1.54 eval_speedDis2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb1_in(v_.0 + 1, v_.01 + 1, v_n, v_x, v_z)) :|: v_.01 <= v_.0 && v_.01 > v_.0 2.41/1.54 eval_speedDis2_bb2_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb1_in(v_.0, v_.01 + 1, v_n, v_x, v_z)) :|: v_.01 <= v_.0 2.41/1.54 eval_speedDis2_bb3_in(v_.0, v_.01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_stop(v_.0, v_.01, v_n, v_x, v_z)) :|: TRUE 2.41/1.54 2.41/1.54 The start-symbols are:[eval_speedDis2_start_5] 2.41/1.54 2.41/1.54 2.41/1.54 ---------------------------------------- 2.41/1.54 2.41/1.54 (1) Koat Proof (FINISHED) 2.41/1.54 YES(?, 2*ar_3 + 4*ar_4 + 2*ar_1 + 7) 2.41/1.54 2.41/1.54 2.41/1.54 2.41/1.54 Initial complexity problem: 2.41/1.54 2.41/1.54 1: T: 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ] 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 ] 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 /\ ar_2 >= ar_0 + 1 ] 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ] 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2stop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.41/1.54 2.41/1.54 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.41/1.54 2.41/1.54 start location: koat_start 2.41/1.54 2.41/1.54 leaf cost: 0 2.41/1.54 2.41/1.54 2.41/1.54 2.41/1.54 Testing for reachability in the complexity graph removes the following transitions from problem 1: 2.41/1.54 2.41/1.54 evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 ] 2.41/1.54 2.41/1.54 evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 /\ ar_2 >= ar_0 + 1 ] 2.41/1.54 2.41/1.54 We thus obtain the following problem: 2.41/1.54 2.41/1.54 2: T: 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2stop(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ] 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ] 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) 2.41/1.54 2.41/1.54 (Comp: ?, Cost: 1) evalspeedDis2start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 2.41/1.54 2.41/1.54 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 2.41/1.54 2.41/1.54 start location: koat_start 2.41/1.54 2.41/1.54 leaf cost: 0 2.41/1.54 2.41/1.54 2.41/1.54 2.41/1.54 Repeatedly propagating knowledge in problem 2 produces the following problem:
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