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Runtime Complexity: TRS pair #487111286
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
n149.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.853 seconds
cpu usage
1042.99
user time
1025.89
system time
17.1063
max virtual memory
3.798328E7
max residence set size
1.419474E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsMatchBoundsTAProof [FINISHED, 26 ms] (6) BOUNDS(1, n^1) (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (8) TRS for Loop Detection (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (10) BEST (11) proven lower bound (12) LowerBoundPropagationProof [FINISHED, 0 ms] (13) BOUNDS(n^1, INF) (14) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: active(f(x)) -> mark(x) top(active(c)) -> top(mark(c)) top(mark(x)) -> top(check(x)) check(f(x)) -> f(check(x)) check(x) -> start(match(f(X), x)) match(f(x), f(y)) -> f(match(x, y)) match(X, x) -> proper(x) proper(c) -> ok(c) proper(f(x)) -> f(proper(x)) f(ok(x)) -> ok(f(x)) start(ok(x)) -> found(x) f(found(x)) -> found(f(x)) top(found(x)) -> top(active(x)) active(f(x)) -> f(active(x)) f(mark(x)) -> mark(f(x)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of top: active, start, proper, top, f, check, match The following defined symbols can occur below the 0th argument of active: active, start, proper, top, f, check, match The following defined symbols can occur below the 0th argument of f: active, start, proper, top, f, check, match The following defined symbols can occur below the 0th argument of start: active, start, proper, top, f, check, match The following defined symbols can occur below the 0th argument of match: active, start, proper, top, f, check, match The following defined symbols can occur below the 0th argument of check: active, start, proper, top, f, check, match Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: match(f(x), f(y)) -> f(match(x, y)) proper(f(x)) -> f(proper(x)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: active(f(x)) -> mark(x) top(active(c)) -> top(mark(c)) top(mark(x)) -> top(check(x)) check(f(x)) -> f(check(x)) check(x) -> start(match(f(X), x)) match(X, x) -> proper(x) proper(c) -> ok(c) f(ok(x)) -> ok(f(x)) start(ok(x)) -> found(x) f(found(x)) -> found(f(x)) top(found(x)) -> top(active(x)) active(f(x)) -> f(active(x)) f(mark(x)) -> mark(f(x)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
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