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TRS Standard pair #487070403
details
property
value
status
complete
benchmark
Ex5_DLMMU04_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.21862 seconds
cpu usage
8.68647
user time
8.28053
system time
0.405935
max virtual memory
1.8545532E7
max residence set size
574568.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 129 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 38 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 28 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 24 ms] (8) QTRS (9) DependencyPairsProof [EQUIVALENT, 0 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) QDP (13) MRRProof [EQUIVALENT, 28 ms] (14) QDP (15) DependencyGraphProof [EQUIVALENT, 0 ms] (16) QDP (17) MRRProof [EQUIVALENT, 34 ms] (18) QDP (19) DependencyGraphProof [EQUIVALENT, 0 ms] (20) QDP (21) MRRProof [EQUIVALENT, 42 ms] (22) QDP (23) MRRProof [EQUIVALENT, 26 ms] (24) QDP (25) DependencyGraphProof [EQUIVALENT, 0 ms] (26) QDP (27) MRRProof [EQUIVALENT, 0 ms] (28) QDP (29) DependencyGraphProof [EQUIVALENT, 0 ms] (30) QDP (31) QDPOrderProof [EQUIVALENT, 70 ms] (32) QDP (33) DependencyGraphProof [EQUIVALENT, 0 ms] (34) QDP (35) UsableRulesProof [EQUIVALENT, 0 ms] (36) QDP (37) QDPSizeChangeProof [EQUIVALENT, 0 ms] (38) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__pairNs -> cons(0, incr(oddNs)) a__oddNs -> a__incr(a__pairNs) a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) a__take(0, XS) -> nil a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) a__zip(nil, XS) -> nil a__zip(X, nil) -> nil a__zip(cons(X, XS), cons(Y, YS)) -> cons(pair(mark(X), mark(Y)), zip(XS, YS)) a__tail(cons(X, XS)) -> mark(XS) a__repItems(nil) -> nil a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS))) mark(pairNs) -> a__pairNs mark(incr(X)) -> a__incr(mark(X)) mark(oddNs) -> a__oddNs mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2)) mark(tail(X)) -> a__tail(mark(X)) mark(repItems(X)) -> a__repItems(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(s(X)) -> s(mark(X)) mark(nil) -> nil mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) a__pairNs -> pairNs a__incr(X) -> incr(X) a__oddNs -> oddNs a__take(X1, X2) -> take(X1, X2) a__zip(X1, X2) -> zip(X1, X2) a__tail(X) -> tail(X) a__repItems(X) -> repItems(X) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(a__incr(x_1)) = 2*x_1 POL(a__oddNs) = 0 POL(a__pairNs) = 0 POL(a__repItems(x_1)) = 1 + 2*x_1 POL(a__tail(x_1)) = 2*x_1
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