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Runti Compl Inner Rewri 22807 pair #381904909
details
property
value
status
complete
benchmark
thiemann07.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n041.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.423512936 seconds
cpu usage
1140.17335892
max memory
1.528877056E10
stage attributes
key
value
output-size
19864
starexec-result
WORST_CASE(Omega(n^2), ?)
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), ?) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 286 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 89 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^2, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 16 ms] (20) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: car(cons(x, l)) -> x cddr(nil) -> nil cddr(cons(x, nil)) -> nil cddr(cons(x, cons(y, l))) -> l cadr(cons(x, cons(y, l))) -> y isZero(0) -> true isZero(s(x)) -> false plus(x, y) -> ifplus(isZero(x), x, y) ifplus(true, x, y) -> y ifplus(false, x, y) -> s(plus(p(x), y)) times(x, y) -> iftimes(isZero(x), x, y) iftimes(true, x, y) -> 0 iftimes(false, x, y) -> plus(y, times(p(x), y)) p(s(x)) -> x p(0) -> 0 shorter(nil, y) -> true shorter(cons(x, l), 0) -> false shorter(cons(x, l), s(y)) -> shorter(l, y) prod(l) -> if(shorter(l, 0), shorter(l, s(0)), l) if(true, b, l) -> s(0) if(false, b, l) -> if2(b, l) if2(true, l) -> car(l) if2(false, l) -> prod(cons(times(car(l), cadr(l)), cddr(l))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: car(cons(x, l)) -> x cddr(nil) -> nil cddr(cons(x, nil)) -> nil cddr(cons(x, cons(y, l))) -> l cadr(cons(x, cons(y, l))) -> y isZero(0') -> true isZero(s(x)) -> false plus(x, y) -> ifplus(isZero(x), x, y) ifplus(true, x, y) -> y ifplus(false, x, y) -> s(plus(p(x), y)) times(x, y) -> iftimes(isZero(x), x, y) iftimes(true, x, y) -> 0' iftimes(false, x, y) -> plus(y, times(p(x), y)) p(s(x)) -> x p(0') -> 0' shorter(nil, y) -> true
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