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TRS Standard pair #487071923
details
property
value
status
complete
benchmark
ExSec4_2_DLMMU04_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.78678 seconds
cpu usage
4.0959
user time
3.9171
system time
0.178803
max virtual memory
1.8408912E7
max residence set size
248048.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 151 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: natsFrom(N) -> cons(N, n__natsFrom(n__s(N))) fst(pair(XS, YS)) -> XS snd(pair(XS, YS)) -> YS splitAt(0, XS) -> pair(nil, XS) splitAt(s(N), cons(X, XS)) -> u(splitAt(N, activate(XS)), N, X, activate(XS)) u(pair(YS, ZS), N, X, XS) -> pair(cons(activate(X), YS), ZS) head(cons(N, XS)) -> N tail(cons(N, XS)) -> activate(XS) sel(N, XS) -> head(afterNth(N, XS)) take(N, XS) -> fst(splitAt(N, XS)) afterNth(N, XS) -> snd(splitAt(N, XS)) natsFrom(X) -> n__natsFrom(X) s(X) -> n__s(X) activate(n__natsFrom(X)) -> natsFrom(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: natsFrom/1(YES) cons/2(YES,YES) n__natsFrom/1(YES) n__s/1(YES) fst/1)YES( pair/2(YES,YES) snd/1)YES( splitAt/2(YES,YES) 0/0) nil/0) s/1(YES) u/4(YES,YES,YES,YES) activate/1(YES) head/1)YES( tail/1(YES) sel/2(YES,YES) afterNth/2(YES,YES) take/2(YES,YES) Quasi precedence: [splitAt_2, sel_2, afterNth_2, take_2] > nil > [cons_2, n__s_1] [splitAt_2, sel_2, afterNth_2, take_2] > [u_4, activate_1, tail_1] > natsFrom_1 > n__natsFrom_1 > [cons_2, n__s_1] [splitAt_2, sel_2, afterNth_2, take_2] > [u_4, activate_1, tail_1] > pair_2 > [cons_2, n__s_1] [splitAt_2, sel_2, afterNth_2, take_2] > [u_4, activate_1, tail_1] > s_1 > [cons_2, n__s_1] 0 > pair_2 > [cons_2, n__s_1] Status: natsFrom_1: multiset status cons_2: multiset status n__natsFrom_1: multiset status n__s_1: multiset status pair_2: multiset status splitAt_2: [1,2] 0: multiset status nil: multiset status s_1: multiset status u_4: multiset status activate_1: multiset status tail_1: multiset status sel_2: [1,2] afterNth_2: [1,2] take_2: [1,2] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: natsFrom(N) -> cons(N, n__natsFrom(n__s(N))) fst(pair(XS, YS)) -> XS snd(pair(XS, YS)) -> YS splitAt(0, XS) -> pair(nil, XS) splitAt(s(N), cons(X, XS)) -> u(splitAt(N, activate(XS)), N, X, activate(XS)) u(pair(YS, ZS), N, X, XS) -> pair(cons(activate(X), YS), ZS) head(cons(N, XS)) -> N tail(cons(N, XS)) -> activate(XS)
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