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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308199
details
property
value
status
complete
benchmark
ExIntrod_GM01_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.49157 seconds
cpu usage
10.6131
user time
10.0936
system time
0.519432
max virtual memory
1.857952E7
max residence set size
1515964.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
10.26/3.43 WORST_CASE(NON_POLY, ?) 10.26/3.45 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 10.26/3.45 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.26/3.45 10.26/3.45 10.26/3.45 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 10.26/3.45 10.26/3.45 (0) CpxTRS 10.26/3.45 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 10.26/3.45 (2) TRS for Loop Detection 10.26/3.45 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 10.26/3.45 (4) BEST 10.26/3.45 (5) proven lower bound 10.26/3.45 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 10.26/3.45 (7) BOUNDS(n^1, INF) 10.26/3.45 (8) TRS for Loop Detection 10.26/3.45 (9) InfiniteLowerBoundProof [FINISHED, 1265 ms] 10.26/3.45 (10) BOUNDS(INF, INF) 10.26/3.45 10.26/3.45 10.26/3.45 ---------------------------------------- 10.26/3.45 10.26/3.45 (0) 10.26/3.45 Obligation: 10.26/3.45 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 10.26/3.45 10.26/3.45 10.26/3.45 The TRS R consists of the following rules: 10.26/3.45 10.26/3.45 incr(nil) -> nil 10.26/3.45 incr(cons(X, L)) -> cons(s(X), n__incr(activate(L))) 10.26/3.45 adx(nil) -> nil 10.26/3.45 adx(cons(X, L)) -> incr(cons(X, n__adx(activate(L)))) 10.26/3.45 nats -> adx(zeros) 10.26/3.45 zeros -> cons(0, n__zeros) 10.26/3.45 head(cons(X, L)) -> X 10.26/3.45 tail(cons(X, L)) -> activate(L) 10.26/3.45 incr(X) -> n__incr(X) 10.26/3.45 adx(X) -> n__adx(X) 10.26/3.45 zeros -> n__zeros 10.26/3.45 activate(n__incr(X)) -> incr(activate(X)) 10.26/3.45 activate(n__adx(X)) -> adx(activate(X)) 10.26/3.45 activate(n__zeros) -> zeros 10.26/3.45 activate(X) -> X 10.26/3.45 10.26/3.45 S is empty. 10.26/3.45 Rewrite Strategy: FULL 10.26/3.45 ---------------------------------------- 10.26/3.45 10.26/3.45 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 10.26/3.45 Transformed a relative TRS into a decreasing-loop problem. 10.26/3.45 ---------------------------------------- 10.26/3.45 10.26/3.45 (2) 10.26/3.45 Obligation: 10.26/3.45 Analyzing the following TRS for decreasing loops: 10.26/3.45 10.26/3.45 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 10.26/3.45 10.26/3.45 10.26/3.45 The TRS R consists of the following rules: 10.26/3.45 10.26/3.45 incr(nil) -> nil 10.26/3.45 incr(cons(X, L)) -> cons(s(X), n__incr(activate(L))) 10.26/3.45 adx(nil) -> nil 10.26/3.45 adx(cons(X, L)) -> incr(cons(X, n__adx(activate(L)))) 10.26/3.45 nats -> adx(zeros) 10.26/3.45 zeros -> cons(0, n__zeros) 10.26/3.45 head(cons(X, L)) -> X 10.26/3.45 tail(cons(X, L)) -> activate(L) 10.26/3.45 incr(X) -> n__incr(X) 10.26/3.45 adx(X) -> n__adx(X) 10.26/3.45 zeros -> n__zeros 10.26/3.45 activate(n__incr(X)) -> incr(activate(X)) 10.26/3.45 activate(n__adx(X)) -> adx(activate(X)) 10.26/3.45 activate(n__zeros) -> zeros 10.26/3.45 activate(X) -> X 10.26/3.45 10.26/3.45 S is empty. 10.26/3.45 Rewrite Strategy: FULL 10.26/3.45 ---------------------------------------- 10.26/3.45 10.26/3.45 (3) DecreasingLoopProof (LOWER BOUND(ID)) 10.26/3.45 The following loop(s) give(s) rise to the lower bound Omega(n^1): 10.26/3.45 10.26/3.45 The rewrite sequence 10.26/3.45 10.26/3.45 activate(n__adx(X)) ->^+ adx(activate(X)) 10.26/3.45 10.26/3.45 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 10.26/3.45 10.26/3.45 The pumping substitution is [X / n__adx(X)]. 10.26/3.45 10.26/3.45 The result substitution is [ ]. 10.26/3.45 10.26/3.45 10.26/3.45 10.26/3.45 10.26/3.45 ---------------------------------------- 10.26/3.45
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