details

property	value
status	complete
benchmark	ExAppendixB_AEL03_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.569 seconds
cpu usage	314.846
user time	312.921
system time	1.92488
max virtual memory	1.8281244E7
max residence set size	5391216.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^2), ?)

output

WORST_CASE(Omega(n^2), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) SlicingProof [LOWER BOUND(ID), 0 ms] (4) CpxTRS (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) typed CpxTrs (7) OrderProof [LOWER BOUND(ID), 0 ms] (8) typed CpxTrs (9) RewriteLemmaProof [LOWER BOUND(ID), 251 ms] (10) BEST (11) proven lower bound (12) LowerBoundPropagationProof [FINISHED, 0 ms] (13) BOUNDS(n^1, INF) (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 56 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^2, INF) (20) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: from(X) -> cons(X, n__from(s(X))) 2ndspos(0, Z) -> rnil 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z))) 2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, activate(Z))) 2ndsneg(0, Z) -> rnil 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z))) 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, activate(Z))) pi(X) -> 2ndspos(X, from(0)) plus(0, Y) -> Y plus(s(X), Y) -> s(plus(X, Y)) times(0, Y) -> 0 times(s(X), Y) -> plus(Y, times(X, Y)) square(X) -> times(X, X) from(X) -> n__from(X) activate(n__from(X)) -> from(X) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: from(X) -> cons(X, n__from(s(X))) 2ndspos(0', Z) -> rnil 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z))) 2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, activate(Z))) 2ndsneg(0', Z) -> rnil 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z))) 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, activate(Z))) pi(X) -> 2ndspos(X, from(0')) plus(0', Y) -> Y plus(s(X), Y) -> s(plus(X, Y)) times(0', Y) -> 0' times(s(X), Y) -> plus(Y, times(X, Y)) square(X) -> times(X, X) from(X) -> n__from(X) activate(n__from(X)) -> from(X) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) SlicingProof (LOWER BOUND(ID)) Sliced the following arguments: from/0 cons/0 n__from/0 cons2/0 rcons/0 posrecip/0 popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runtime Complexity: TRS