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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308068
details
property
value
status
complete
benchmark
Ex49_GM04_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n111.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
11.721 seconds
cpu usage
29.6241
user time
27.0868
system time
2.53732
max virtual memory
1.9338448E7
max residence set size
3935292.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
29.46/11.67 WORST_CASE(Omega(n^1), O(n^1)) 29.46/11.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 29.46/11.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 29.46/11.67 29.46/11.67 29.46/11.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 29.46/11.67 29.46/11.67 (0) CpxTRS 29.46/11.67 (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] 29.46/11.67 (2) CpxTRS 29.46/11.67 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 29.46/11.67 (4) CpxTRS 29.46/11.67 (5) CpxTrsMatchBoundsTAProof [FINISHED, 290 ms] 29.46/11.67 (6) BOUNDS(1, n^1) 29.46/11.67 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 29.46/11.67 (8) TRS for Loop Detection 29.46/11.67 (9) DecreasingLoopProof [LOWER BOUND(ID), 63 ms] 29.46/11.67 (10) BEST 29.46/11.67 (11) proven lower bound 29.46/11.67 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 29.46/11.67 (13) BOUNDS(n^1, INF) 29.46/11.67 (14) TRS for Loop Detection 29.46/11.67 29.46/11.67 29.46/11.67 ---------------------------------------- 29.46/11.67 29.46/11.67 (0) 29.46/11.67 Obligation: 29.46/11.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 29.46/11.67 29.46/11.67 29.46/11.67 The TRS R consists of the following rules: 29.46/11.67 29.46/11.67 minus(n__0, Y) -> 0 29.46/11.67 minus(n__s(X), n__s(Y)) -> minus(activate(X), activate(Y)) 29.46/11.67 geq(X, n__0) -> true 29.46/11.67 geq(n__0, n__s(Y)) -> false 29.46/11.67 geq(n__s(X), n__s(Y)) -> geq(activate(X), activate(Y)) 29.46/11.67 div(0, n__s(Y)) -> 0 29.46/11.67 div(s(X), n__s(Y)) -> if(geq(X, activate(Y)), n__s(div(minus(X, activate(Y)), n__s(activate(Y)))), n__0) 29.46/11.67 if(true, X, Y) -> activate(X) 29.46/11.67 if(false, X, Y) -> activate(Y) 29.46/11.67 0 -> n__0 29.46/11.67 s(X) -> n__s(X) 29.46/11.67 activate(n__0) -> 0 29.46/11.67 activate(n__s(X)) -> s(X) 29.46/11.67 activate(X) -> X 29.46/11.67 29.46/11.67 S is empty. 29.46/11.67 Rewrite Strategy: FULL 29.46/11.67 ---------------------------------------- 29.46/11.67 29.46/11.67 (1) DependencyGraphProof (UPPER BOUND(ID)) 29.46/11.67 The following rules are not reachable from basic terms in the dependency graph and can be removed: 29.46/11.67 29.46/11.67 div(0, n__s(Y)) -> 0 29.46/11.67 div(s(X), n__s(Y)) -> if(geq(X, activate(Y)), n__s(div(minus(X, activate(Y)), n__s(activate(Y)))), n__0) 29.46/11.67 29.46/11.67 ---------------------------------------- 29.46/11.67 29.46/11.67 (2) 29.46/11.67 Obligation: 29.46/11.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 29.46/11.67 29.46/11.67 29.46/11.67 The TRS R consists of the following rules: 29.46/11.67 29.46/11.67 minus(n__0, Y) -> 0 29.46/11.67 minus(n__s(X), n__s(Y)) -> minus(activate(X), activate(Y)) 29.46/11.67 geq(X, n__0) -> true 29.46/11.67 geq(n__0, n__s(Y)) -> false 29.46/11.67 geq(n__s(X), n__s(Y)) -> geq(activate(X), activate(Y)) 29.46/11.67 if(true, X, Y) -> activate(X) 29.46/11.67 if(false, X, Y) -> activate(Y) 29.46/11.67 0 -> n__0 29.46/11.67 s(X) -> n__s(X) 29.46/11.67 activate(n__0) -> 0 29.46/11.67 activate(n__s(X)) -> s(X) 29.46/11.67 activate(X) -> X 29.46/11.67 29.46/11.67 S is empty. 29.46/11.67 Rewrite Strategy: FULL 29.46/11.67 ---------------------------------------- 29.46/11.67 29.46/11.67 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 29.46/11.67 transformed relative TRS to TRS 29.46/11.67 ---------------------------------------- 29.46/11.67 29.46/11.67 (4) 29.46/11.67 Obligation: 29.46/11.67 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 29.46/11.67 29.46/11.67 29.46/11.67 The TRS R consists of the following rules: 29.46/11.67 29.46/11.67 minus(n__0, Y) -> 0 29.46/11.67 minus(n__s(X), n__s(Y)) -> minus(activate(X), activate(Y)) 29.46/11.67 geq(X, n__0) -> true 29.46/11.67 geq(n__0, n__s(Y)) -> false 29.46/11.67 geq(n__s(X), n__s(Y)) -> geq(activate(X), activate(Y))
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