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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308029
details
property
value
status
complete
benchmark
PALINDROME_nosorts_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n051.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
11.4639 seconds
cpu usage
22.8537
user time
21.1336
system time
1.72013
max virtual memory
1.9275332E7
max residence set size
3859732.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
22.58/8.22 WORST_CASE(Omega(n^1), O(n^1)) 22.58/8.23 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 22.58/8.23 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 22.58/8.23 22.58/8.23 22.58/8.23 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 22.58/8.23 22.58/8.23 (0) CpxTRS 22.58/8.23 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 22.58/8.23 (2) CpxTRS 22.58/8.23 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 22.58/8.23 (4) CpxTRS 22.58/8.23 (5) CpxTrsMatchBoundsTAProof [FINISHED, 49 ms] 22.58/8.23 (6) BOUNDS(1, n^1) 22.58/8.23 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 22.58/8.23 (8) TRS for Loop Detection 22.58/8.23 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 22.58/8.23 (10) BEST 22.58/8.23 (11) proven lower bound 22.58/8.23 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 22.58/8.23 (13) BOUNDS(n^1, INF) 22.58/8.23 (14) TRS for Loop Detection 22.58/8.23 22.58/8.23 22.58/8.23 ---------------------------------------- 22.58/8.23 22.58/8.23 (0) 22.58/8.23 Obligation: 22.58/8.23 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 22.58/8.23 22.58/8.23 22.58/8.23 The TRS R consists of the following rules: 22.58/8.23 22.58/8.23 active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 22.58/8.23 active(__(X, nil)) -> mark(X) 22.58/8.23 active(__(nil, X)) -> mark(X) 22.58/8.23 active(U11(tt)) -> mark(U12(tt)) 22.58/8.23 active(U12(tt)) -> mark(tt) 22.58/8.23 active(isNePal(__(I, __(P, I)))) -> mark(U11(tt)) 22.58/8.23 active(__(X1, X2)) -> __(active(X1), X2) 22.58/8.23 active(__(X1, X2)) -> __(X1, active(X2)) 22.58/8.23 active(U11(X)) -> U11(active(X)) 22.58/8.23 active(U12(X)) -> U12(active(X)) 22.58/8.23 active(isNePal(X)) -> isNePal(active(X)) 22.58/8.23 __(mark(X1), X2) -> mark(__(X1, X2)) 22.58/8.23 __(X1, mark(X2)) -> mark(__(X1, X2)) 22.58/8.23 U11(mark(X)) -> mark(U11(X)) 22.58/8.23 U12(mark(X)) -> mark(U12(X)) 22.58/8.23 isNePal(mark(X)) -> mark(isNePal(X)) 22.58/8.23 proper(__(X1, X2)) -> __(proper(X1), proper(X2)) 22.58/8.23 proper(nil) -> ok(nil) 22.58/8.23 proper(U11(X)) -> U11(proper(X)) 22.58/8.23 proper(tt) -> ok(tt) 22.58/8.23 proper(U12(X)) -> U12(proper(X)) 22.58/8.23 proper(isNePal(X)) -> isNePal(proper(X)) 22.58/8.23 __(ok(X1), ok(X2)) -> ok(__(X1, X2)) 22.58/8.23 U11(ok(X)) -> ok(U11(X)) 22.58/8.23 U12(ok(X)) -> ok(U12(X)) 22.58/8.23 isNePal(ok(X)) -> ok(isNePal(X)) 22.58/8.23 top(mark(X)) -> top(proper(X)) 22.58/8.23 top(ok(X)) -> top(active(X)) 22.58/8.23 22.58/8.23 S is empty. 22.58/8.23 Rewrite Strategy: FULL 22.58/8.23 ---------------------------------------- 22.58/8.23 22.58/8.23 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 22.58/8.23 The following defined symbols can occur below the 0th argument of top: proper, active 22.58/8.23 The following defined symbols can occur below the 0th argument of proper: proper, active 22.58/8.23 The following defined symbols can occur below the 0th argument of active: proper, active 22.58/8.23 22.58/8.23 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 22.58/8.23 active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 22.58/8.23 active(__(X, nil)) -> mark(X) 22.58/8.23 active(__(nil, X)) -> mark(X) 22.58/8.23 active(U11(tt)) -> mark(U12(tt)) 22.58/8.23 active(U12(tt)) -> mark(tt) 22.58/8.23 active(isNePal(__(I, __(P, I)))) -> mark(U11(tt)) 22.58/8.23 active(__(X1, X2)) -> __(active(X1), X2) 22.58/8.23 active(__(X1, X2)) -> __(X1, active(X2)) 22.58/8.23 active(U11(X)) -> U11(active(X)) 22.58/8.23 active(U12(X)) -> U12(active(X)) 22.58/8.23 active(isNePal(X)) -> isNePal(active(X)) 22.58/8.23 proper(__(X1, X2)) -> __(proper(X1), proper(X2)) 22.58/8.23 proper(U11(X)) -> U11(proper(X)) 22.58/8.23 proper(U12(X)) -> U12(proper(X)) 22.58/8.23 proper(isNePal(X)) -> isNePal(proper(X)) 22.58/8.23 22.58/8.23 ---------------------------------------- 22.58/8.23 22.58/8.23 (2) 22.58/8.23 Obligation: 22.58/8.23 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 22.58/8.23 22.58/8.23 22.58/8.23 The TRS R consists of the following rules: 22.58/8.23 22.58/8.23 __(mark(X1), X2) -> mark(__(X1, X2)) 22.58/8.23 __(X1, mark(X2)) -> mark(__(X1, X2)) 22.58/8.23 U11(mark(X)) -> mark(U11(X))
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