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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307680
details
property
value
status
complete
benchmark
Liveness8.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.594 seconds
cpu usage
1046.59
user time
1029.42
system time
17.1677
max virtual memory
5.7108664E7
max residence set size
1.5135152E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
1046.43/291.52 WORST_CASE(Omega(n^1), O(n^1)) 1046.43/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1046.43/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1046.43/291.53 1046.43/291.53 1046.43/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 1046.43/291.53 1046.43/291.53 (0) CpxTRS 1046.43/291.53 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 1046.43/291.53 (2) CpxTRS 1046.43/291.53 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 1046.43/291.53 (4) CpxTRS 1046.43/291.53 (5) CpxTrsMatchBoundsTAProof [FINISHED, 62 ms] 1046.43/291.53 (6) BOUNDS(1, n^1) 1046.43/291.53 (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1046.43/291.53 (8) CpxTRS 1046.43/291.53 (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1046.43/291.53 (10) typed CpxTrs 1046.43/291.53 (11) OrderProof [LOWER BOUND(ID), 0 ms] 1046.43/291.53 (12) typed CpxTrs 1046.43/291.53 (13) RewriteLemmaProof [LOWER BOUND(ID), 471 ms] 1046.43/291.53 (14) BEST 1046.43/291.53 (15) proven lower bound 1046.43/291.53 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1046.43/291.53 (17) BOUNDS(n^1, INF) 1046.43/291.53 (18) typed CpxTrs 1046.43/291.53 1046.43/291.53 1046.43/291.53 ---------------------------------------- 1046.43/291.53 1046.43/291.53 (0) 1046.43/291.53 Obligation: 1046.43/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 1046.43/291.53 1046.43/291.53 1046.43/291.53 The TRS R consists of the following rules: 1046.43/291.53 1046.43/291.53 active(f(x)) -> mark(x) 1046.43/291.53 top(active(c)) -> top(mark(c)) 1046.43/291.53 top(mark(x)) -> top(check(x)) 1046.43/291.53 check(f(x)) -> f(check(x)) 1046.43/291.53 check(x) -> start(match(f(X), x)) 1046.43/291.53 match(f(x), f(y)) -> f(match(x, y)) 1046.43/291.53 match(X, x) -> proper(x) 1046.43/291.53 proper(c) -> ok(c) 1046.43/291.53 proper(f(x)) -> f(proper(x)) 1046.43/291.53 f(ok(x)) -> ok(f(x)) 1046.43/291.53 start(ok(x)) -> found(x) 1046.43/291.53 f(found(x)) -> found(f(x)) 1046.43/291.53 top(found(x)) -> top(active(x)) 1046.43/291.53 active(f(x)) -> f(active(x)) 1046.43/291.53 f(mark(x)) -> mark(f(x)) 1046.43/291.53 1046.43/291.53 S is empty. 1046.43/291.53 Rewrite Strategy: FULL 1046.43/291.53 ---------------------------------------- 1046.43/291.53 1046.43/291.53 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 1046.43/291.53 The following defined symbols can occur below the 0th argument of top: active, start, proper, top, f, check, match 1046.43/291.53 The following defined symbols can occur below the 0th argument of active: active, start, proper, top, f, check, match 1046.43/291.53 The following defined symbols can occur below the 0th argument of f: active, start, proper, top, f, check, match 1046.43/291.53 The following defined symbols can occur below the 0th argument of start: active, start, proper, top, f, check, match 1046.43/291.53 The following defined symbols can occur below the 0th argument of match: active, start, proper, top, f, check, match 1046.43/291.53 The following defined symbols can occur below the 0th argument of check: active, start, proper, top, f, check, match 1046.43/291.53 1046.43/291.53 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 1046.43/291.53 match(f(x), f(y)) -> f(match(x, y)) 1046.43/291.53 proper(f(x)) -> f(proper(x)) 1046.43/291.53 1046.43/291.53 ---------------------------------------- 1046.43/291.53 1046.43/291.53 (2) 1046.43/291.53 Obligation: 1046.43/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 1046.43/291.53 1046.43/291.53 1046.43/291.53 The TRS R consists of the following rules: 1046.43/291.53 1046.43/291.53 active(f(x)) -> mark(x) 1046.43/291.53 top(active(c)) -> top(mark(c)) 1046.43/291.53 top(mark(x)) -> top(check(x)) 1046.43/291.53 check(f(x)) -> f(check(x)) 1046.43/291.53 check(x) -> start(match(f(X), x)) 1046.43/291.53 match(X, x) -> proper(x) 1046.43/291.53 proper(c) -> ok(c) 1046.43/291.53 f(ok(x)) -> ok(f(x)) 1046.43/291.53 start(ok(x)) -> found(x) 1046.43/291.53 f(found(x)) -> found(f(x)) 1046.43/291.53 top(found(x)) -> top(active(x)) 1046.43/291.53 active(f(x)) -> f(active(x)) 1046.43/291.53 f(mark(x)) -> mark(f(x)) 1046.43/291.53 1046.43/291.53 S is empty. 1046.43/291.53 Rewrite Strategy: FULL 1046.43/291.53 ---------------------------------------- 1046.43/291.53 1046.43/291.53 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 1046.43/291.53 transformed relative TRS to TRS 1046.43/291.53 ---------------------------------------- 1046.43/291.53
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