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TRS Standard pair #487069563
details
property
value
status
complete
benchmark
ExSec4_2_DLMMU04_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.93698 seconds
cpu usage
4.34404
user time
4.18028
system time
0.163766
max virtual memory
1.827784E7
max residence set size
251372.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSRInnermostProof [EQUIVALENT, 0 ms] (4) CSR (5) CSDependencyPairsProof [EQUIVALENT, 4 ms] (6) QCSDP (7) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QCSDP (10) QCSDPSubtermProof [EQUIVALENT, 0 ms] (11) QCSDP (12) PIsEmptyProof [EQUIVALENT, 0 ms] (13) YES (14) QCSDP (15) QCSDPSubtermProof [EQUIVALENT, 0 ms] (16) QCSDP (17) PIsEmptyProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N)))) active(fst(pair(XS, YS))) -> mark(XS) active(snd(pair(XS, YS))) -> mark(YS) active(splitAt(0, XS)) -> mark(pair(nil, XS)) active(splitAt(s(N), cons(X, XS))) -> mark(u(splitAt(N, XS), N, X, XS)) active(u(pair(YS, ZS), N, X, XS)) -> mark(pair(cons(X, YS), ZS)) active(head(cons(N, XS))) -> mark(N) active(tail(cons(N, XS))) -> mark(XS) active(sel(N, XS)) -> mark(head(afterNth(N, XS))) active(take(N, XS)) -> mark(fst(splitAt(N, XS))) active(afterNth(N, XS)) -> mark(snd(splitAt(N, XS))) active(natsFrom(X)) -> natsFrom(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(s(X)) -> s(active(X)) active(fst(X)) -> fst(active(X)) active(pair(X1, X2)) -> pair(active(X1), X2) active(pair(X1, X2)) -> pair(X1, active(X2)) active(snd(X)) -> snd(active(X)) active(splitAt(X1, X2)) -> splitAt(active(X1), X2) active(splitAt(X1, X2)) -> splitAt(X1, active(X2)) active(u(X1, X2, X3, X4)) -> u(active(X1), X2, X3, X4) active(head(X)) -> head(active(X)) active(tail(X)) -> tail(active(X)) active(sel(X1, X2)) -> sel(active(X1), X2) active(sel(X1, X2)) -> sel(X1, active(X2)) active(afterNth(X1, X2)) -> afterNth(active(X1), X2) active(afterNth(X1, X2)) -> afterNth(X1, active(X2)) active(take(X1, X2)) -> take(active(X1), X2) active(take(X1, X2)) -> take(X1, active(X2)) natsFrom(mark(X)) -> mark(natsFrom(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) s(mark(X)) -> mark(s(X)) fst(mark(X)) -> mark(fst(X)) pair(mark(X1), X2) -> mark(pair(X1, X2)) pair(X1, mark(X2)) -> mark(pair(X1, X2)) snd(mark(X)) -> mark(snd(X)) splitAt(mark(X1), X2) -> mark(splitAt(X1, X2)) splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2)) u(mark(X1), X2, X3, X4) -> mark(u(X1, X2, X3, X4)) head(mark(X)) -> mark(head(X)) tail(mark(X)) -> mark(tail(X)) sel(mark(X1), X2) -> mark(sel(X1, X2)) sel(X1, mark(X2)) -> mark(sel(X1, X2)) afterNth(mark(X1), X2) -> mark(afterNth(X1, X2)) afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2)) take(mark(X1), X2) -> mark(take(X1, X2)) take(X1, mark(X2)) -> mark(take(X1, X2)) proper(natsFrom(X)) -> natsFrom(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(s(X)) -> s(proper(X)) proper(fst(X)) -> fst(proper(X)) proper(pair(X1, X2)) -> pair(proper(X1), proper(X2)) proper(snd(X)) -> snd(proper(X)) proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2)) proper(0) -> ok(0) proper(nil) -> ok(nil) proper(u(X1, X2, X3, X4)) -> u(proper(X1), proper(X2), proper(X3), proper(X4)) proper(head(X)) -> head(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) proper(afterNth(X1, X2)) -> afterNth(proper(X1), proper(X2)) proper(take(X1, X2)) -> take(proper(X1), proper(X2)) natsFrom(ok(X)) -> ok(natsFrom(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) s(ok(X)) -> ok(s(X))
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