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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313936
details
property
value
status
complete
benchmark
append-wrong.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.76006 seconds
cpu usage
3.43483
user time
3.29454
system time
0.140295
max virtual memory
1.8275288E7
max residence set size
220700.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
3.29/1.72 WORST_CASE(NON_POLY, ?) 3.29/1.72 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.29/1.72 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.29/1.72 3.29/1.72 3.29/1.72 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 3.29/1.72 3.29/1.72 (0) CpxTRS 3.29/1.72 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 3.29/1.72 (2) TRS for Loop Detection 3.29/1.72 (3) InfiniteLowerBoundProof [FINISHED, 0 ms] 3.29/1.72 (4) BOUNDS(INF, INF) 3.29/1.72 3.29/1.72 3.29/1.72 ---------------------------------------- 3.29/1.72 3.29/1.72 (0) 3.29/1.72 Obligation: 3.29/1.72 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 3.29/1.72 3.29/1.72 3.29/1.72 The TRS R consists of the following rules: 3.29/1.72 3.29/1.72 is_empty(nil) -> true 3.29/1.72 is_empty(cons(x, l)) -> false 3.29/1.72 hd(cons(x, l)) -> x 3.29/1.72 tl(cons(x, l)) -> cons(x, l) 3.29/1.72 append(l1, l2) -> ifappend(l1, l2, is_empty(l1)) 3.29/1.72 ifappend(l1, l2, true) -> l2 3.29/1.72 ifappend(l1, l2, false) -> cons(hd(l1), append(tl(l1), l2)) 3.29/1.72 3.29/1.72 S is empty. 3.29/1.72 Rewrite Strategy: INNERMOST 3.29/1.72 ---------------------------------------- 3.29/1.72 3.29/1.72 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 3.29/1.72 Transformed a relative TRS into a decreasing-loop problem. 3.29/1.72 ---------------------------------------- 3.29/1.72 3.29/1.72 (2) 3.29/1.72 Obligation: 3.29/1.72 Analyzing the following TRS for decreasing loops: 3.29/1.72 3.29/1.72 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). 3.29/1.72 3.29/1.72 3.29/1.72 The TRS R consists of the following rules: 3.29/1.72 3.29/1.72 is_empty(nil) -> true 3.29/1.72 is_empty(cons(x, l)) -> false 3.29/1.72 hd(cons(x, l)) -> x 3.29/1.72 tl(cons(x, l)) -> cons(x, l) 3.29/1.72 append(l1, l2) -> ifappend(l1, l2, is_empty(l1)) 3.29/1.72 ifappend(l1, l2, true) -> l2 3.29/1.72 ifappend(l1, l2, false) -> cons(hd(l1), append(tl(l1), l2)) 3.29/1.72 3.29/1.72 S is empty. 3.29/1.72 Rewrite Strategy: INNERMOST 3.29/1.72 ---------------------------------------- 3.29/1.72 3.29/1.72 (3) InfiniteLowerBoundProof (FINISHED) 3.29/1.72 The following loop proves infinite runtime complexity: 3.29/1.72 3.29/1.72 The rewrite sequence 3.29/1.72 3.29/1.72 ifappend(cons(x1_0, l2_0), l2, false) ->^+ cons(hd(cons(x1_0, l2_0)), ifappend(cons(x1_0, l2_0), l2, false)) 3.29/1.72 3.29/1.72 gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. 3.29/1.72 3.29/1.72 The pumping substitution is [ ]. 3.29/1.72 3.29/1.72 The result substitution is [ ]. 3.29/1.72 3.29/1.72 3.29/1.72 3.29/1.72 3.29/1.72 ---------------------------------------- 3.29/1.72 3.29/1.72 (4) 3.29/1.72 BOUNDS(INF, INF) 3.29/1.76 EOF
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