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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313532
details
property
value
status
complete
benchmark
ExIntrod_GM04_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n016.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.43815 seconds
cpu usage
17.7411
user time
17.0117
system time
0.729417
max virtual memory
3.730892E7
max residence set size
2039872.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
17.60/5.36 WORST_CASE(NON_POLY, ?) 17.60/5.37 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 17.60/5.37 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 17.60/5.37 17.60/5.37 17.60/5.37 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 17.60/5.37 17.60/5.37 (0) CpxTRS 17.60/5.37 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 17.60/5.37 (2) TRS for Loop Detection 17.60/5.37 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 17.60/5.37 (4) BEST 17.60/5.37 (5) proven lower bound 17.60/5.37 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 17.60/5.37 (7) BOUNDS(n^1, INF) 17.60/5.37 (8) TRS for Loop Detection 17.60/5.37 (9) InfiniteLowerBoundProof [FINISHED, 2241 ms] 17.60/5.37 (10) BOUNDS(INF, INF) 17.60/5.37 17.60/5.37 17.60/5.37 ---------------------------------------- 17.60/5.37 17.60/5.37 (0) 17.60/5.37 Obligation: 17.60/5.37 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 17.60/5.37 17.60/5.37 17.60/5.37 The TRS R consists of the following rules: 17.60/5.37 17.60/5.37 nats -> adx(zeros) 17.60/5.37 zeros -> cons(n__0, n__zeros) 17.60/5.37 incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) 17.60/5.37 adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) 17.60/5.37 hd(cons(X, Y)) -> activate(X) 17.60/5.37 tl(cons(X, Y)) -> activate(Y) 17.60/5.37 0 -> n__0 17.60/5.37 zeros -> n__zeros 17.60/5.37 s(X) -> n__s(X) 17.60/5.37 incr(X) -> n__incr(X) 17.60/5.37 adx(X) -> n__adx(X) 17.60/5.37 activate(n__0) -> 0 17.60/5.37 activate(n__zeros) -> zeros 17.60/5.37 activate(n__s(X)) -> s(X) 17.60/5.37 activate(n__incr(X)) -> incr(activate(X)) 17.60/5.37 activate(n__adx(X)) -> adx(activate(X)) 17.60/5.37 activate(X) -> X 17.60/5.37 17.60/5.37 S is empty. 17.60/5.37 Rewrite Strategy: INNERMOST 17.60/5.37 ---------------------------------------- 17.60/5.37 17.60/5.37 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 17.60/5.37 Transformed a relative TRS into a decreasing-loop problem. 17.60/5.37 ---------------------------------------- 17.60/5.37 17.60/5.37 (2) 17.60/5.37 Obligation: 17.60/5.37 Analyzing the following TRS for decreasing loops: 17.60/5.37 17.60/5.37 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 17.60/5.37 17.60/5.37 17.60/5.37 The TRS R consists of the following rules: 17.60/5.37 17.60/5.37 nats -> adx(zeros) 17.60/5.37 zeros -> cons(n__0, n__zeros) 17.60/5.37 incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) 17.60/5.37 adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) 17.60/5.37 hd(cons(X, Y)) -> activate(X) 17.60/5.37 tl(cons(X, Y)) -> activate(Y) 17.60/5.37 0 -> n__0 17.60/5.37 zeros -> n__zeros 17.60/5.37 s(X) -> n__s(X) 17.60/5.37 incr(X) -> n__incr(X) 17.60/5.37 adx(X) -> n__adx(X) 17.60/5.37 activate(n__0) -> 0 17.60/5.37 activate(n__zeros) -> zeros 17.60/5.37 activate(n__s(X)) -> s(X) 17.60/5.37 activate(n__incr(X)) -> incr(activate(X)) 17.60/5.37 activate(n__adx(X)) -> adx(activate(X)) 17.60/5.37 activate(X) -> X 17.60/5.37 17.60/5.37 S is empty. 17.60/5.37 Rewrite Strategy: INNERMOST 17.60/5.37 ---------------------------------------- 17.60/5.37 17.60/5.37 (3) DecreasingLoopProof (LOWER BOUND(ID)) 17.60/5.37 The following loop(s) give(s) rise to the lower bound Omega(n^1): 17.60/5.37 17.60/5.37 The rewrite sequence 17.60/5.37 17.60/5.37 activate(n__adx(X)) ->^+ adx(activate(X)) 17.60/5.37 17.60/5.37 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 17.60/5.37 17.60/5.37 The pumping substitution is [X / n__adx(X)]. 17.60/5.37 17.60/5.37 The result substitution is [ ]. 17.60/5.37 17.60/5.37
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