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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313307
details
property
value
status
complete
benchmark
aprove08.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n113.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.06 seconds
cpu usage
1149.88
user time
1132.46
system time
17.4248
max virtual memory
5.6807428E7
max residence set size
1.5049544E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1149.56/291.96 WORST_CASE(Omega(n^1), O(n^2)) 1149.70/291.98 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1149.70/291.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1149.70/291.98 1149.70/291.98 1149.70/291.98 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1149.70/291.98 1149.70/291.98 (0) CpxTRS 1149.70/291.98 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1149.70/291.98 (2) CpxWeightedTrs 1149.70/291.98 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1149.70/291.98 (4) CpxTypedWeightedTrs 1149.70/291.98 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1149.70/291.98 (6) CpxTypedWeightedCompleteTrs 1149.70/291.98 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1149.70/291.98 (8) CpxRNTS 1149.70/291.98 (9) CompleteCoflocoProof [FINISHED, 3400 ms] 1149.70/291.98 (10) BOUNDS(1, n^2) 1149.70/291.98 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1149.70/291.98 (12) CpxTRS 1149.70/291.98 (13) SlicingProof [LOWER BOUND(ID), 0 ms] 1149.70/291.98 (14) CpxTRS 1149.70/291.98 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1149.70/291.98 (16) typed CpxTrs 1149.70/291.98 (17) OrderProof [LOWER BOUND(ID), 0 ms] 1149.70/291.98 (18) typed CpxTrs 1149.70/291.98 (19) RewriteLemmaProof [LOWER BOUND(ID), 299 ms] 1149.70/291.98 (20) BEST 1149.70/291.98 (21) proven lower bound 1149.70/291.98 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 1149.70/291.98 (23) BOUNDS(n^1, INF) 1149.70/291.98 (24) typed CpxTrs 1149.70/291.98 (25) RewriteLemmaProof [LOWER BOUND(ID), 38 ms] 1149.70/291.98 (26) typed CpxTrs 1149.70/291.98 (27) RewriteLemmaProof [LOWER BOUND(ID), 54 ms] 1149.70/291.98 (28) typed CpxTrs 1149.70/291.98 1149.70/291.98 1149.70/291.98 ---------------------------------------- 1149.70/291.98 1149.70/291.98 (0) 1149.70/291.98 Obligation: 1149.70/291.98 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1149.70/291.98 1149.70/291.98 1149.70/291.98 The TRS R consists of the following rules: 1149.70/291.98 1149.70/291.98 gcd(x, y) -> gcd2(x, y, 0) 1149.70/291.98 gcd2(x, y, i) -> if1(le(x, 0), le(y, 0), le(x, y), le(y, x), x, y, inc(i)) 1149.70/291.98 if1(true, b1, b2, b3, x, y, i) -> pair(result(y), neededIterations(i)) 1149.70/291.98 if1(false, b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i) 1149.70/291.98 if2(true, b2, b3, x, y, i) -> pair(result(x), neededIterations(i)) 1149.70/291.98 if2(false, b2, b3, x, y, i) -> if3(b2, b3, x, y, i) 1149.70/291.98 if3(false, b3, x, y, i) -> gcd2(minus(x, y), y, i) 1149.70/291.98 if3(true, b3, x, y, i) -> if4(b3, x, y, i) 1149.70/291.98 if4(false, x, y, i) -> gcd2(x, minus(y, x), i) 1149.70/291.98 if4(true, x, y, i) -> pair(result(x), neededIterations(i)) 1149.70/291.98 inc(0) -> 0 1149.70/291.98 inc(s(i)) -> s(inc(i)) 1149.70/291.98 le(s(x), 0) -> false 1149.70/291.98 le(0, y) -> true 1149.70/291.98 le(s(x), s(y)) -> le(x, y) 1149.70/291.98 minus(x, 0) -> x 1149.70/291.98 minus(0, y) -> 0 1149.70/291.98 minus(s(x), s(y)) -> minus(x, y) 1149.70/291.98 a -> b 1149.70/291.98 a -> c 1149.70/291.98 1149.70/291.98 S is empty. 1149.70/291.98 Rewrite Strategy: INNERMOST 1149.70/291.98 ---------------------------------------- 1149.70/291.98 1149.70/291.98 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1149.70/291.98 Transformed relative TRS to weighted TRS 1149.70/291.98 ---------------------------------------- 1149.70/291.98 1149.70/291.98 (2) 1149.70/291.98 Obligation: 1149.70/291.98 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1149.70/291.98 1149.70/291.98 1149.70/291.98 The TRS R consists of the following rules: 1149.70/291.98 1149.70/291.98 gcd(x, y) -> gcd2(x, y, 0) [1] 1149.70/291.98 gcd2(x, y, i) -> if1(le(x, 0), le(y, 0), le(x, y), le(y, x), x, y, inc(i)) [1] 1149.70/291.98 if1(true, b1, b2, b3, x, y, i) -> pair(result(y), neededIterations(i)) [1] 1149.70/291.98 if1(false, b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i) [1] 1149.70/291.98 if2(true, b2, b3, x, y, i) -> pair(result(x), neededIterations(i)) [1] 1149.70/291.98 if2(false, b2, b3, x, y, i) -> if3(b2, b3, x, y, i) [1] 1149.70/291.98 if3(false, b3, x, y, i) -> gcd2(minus(x, y), y, i) [1] 1149.70/291.98 if3(true, b3, x, y, i) -> if4(b3, x, y, i) [1] 1149.70/291.98 if4(false, x, y, i) -> gcd2(x, minus(y, x), i) [1] 1149.70/291.98 if4(true, x, y, i) -> pair(result(x), neededIterations(i)) [1] 1149.70/291.98 inc(0) -> 0 [1] 1149.70/291.98 inc(s(i)) -> s(inc(i)) [1] 1149.70/291.98 le(s(x), 0) -> false [1] 1149.70/291.98 le(0, y) -> true [1] 1149.70/291.98 le(s(x), s(y)) -> le(x, y) [1] 1149.70/291.98 minus(x, 0) -> x [1] 1149.70/291.98 minus(0, y) -> 0 [1]
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