details

property	value
status	complete
benchmark	ExAppendixB_AEL03.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n051.star.cs.uiowa.edu
space	Strategy_removed_CSR_05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.59169793129 seconds
cpu usage	3.2609326
max memory	2.12426752E8

stage attributes

key	value
output-size	5355
starexec-result	WORST_CASE(NON_POLY, ?)

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection (9) InfiniteLowerBoundProof [FINISHED, 0 ms] (10) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: from(X) -> cons(X, from(s(X))) 2ndspos(0, Z) -> rnil 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, Z)) 2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, Z)) 2ndsneg(0, Z) -> rnil 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, Z)) 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, 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) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: from(X) -> cons(X, from(s(X))) 2ndspos(0, Z) -> rnil 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, Z)) 2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, Z)) 2ndsneg(0, Z) -> rnil 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, Z)) 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, 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) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence plus(s(X), Y) ->^+ s(plus(X, Y)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. The pumping substitution is [X / s(X)]. The result substitution is [ ]. popout

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actions

all output return to Runti Compl Inner Rewri 22807