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TRS Standard pair #487069648
details
property
value
status
complete
benchmark
Ex1_Luc04b_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.83697 seconds
cpu usage
11.4211
user time
10.9924
system time
0.428757
max virtual memory
1.855026E7
max residence set size
794576.0
stage attributes
key
value
starexec-result
NO
output
NO 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 60 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) TransformationProof [EQUIVALENT, 0 ms] (10) QDP (11) TransformationProof [EQUIVALENT, 0 ms] (12) QDP (13) TransformationProof [EQUIVALENT, 0 ms] (14) QDP (15) DependencyGraphProof [EQUIVALENT, 0 ms] (16) QDP (17) NonTerminationLoopProof [COMPLETE, 0 ms] (18) NO ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: nats -> cons(0, n__incr(n__nats)) pairs -> cons(0, n__incr(n__odds)) odds -> incr(pairs) incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS))) head(cons(X, XS)) -> X tail(cons(X, XS)) -> activate(XS) incr(X) -> n__incr(X) nats -> n__nats odds -> n__odds activate(n__incr(X)) -> incr(activate(X)) activate(n__nats) -> nats activate(n__odds) -> odds activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(activate(x_1)) = x_1 POL(cons(x_1, x_2)) = 2*x_1 + x_2 POL(head(x_1)) = 2*x_1 POL(incr(x_1)) = 2*x_1 POL(n__incr(x_1)) = 2*x_1 POL(n__nats) = 0 POL(n__odds) = 0 POL(nats) = 0 POL(odds) = 0 POL(pairs) = 0 POL(s(x_1)) = 2*x_1 POL(tail(x_1)) = 2 + 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: tail(cons(X, XS)) -> activate(XS) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: nats -> cons(0, n__incr(n__nats)) pairs -> cons(0, n__incr(n__odds)) odds -> incr(pairs) incr(cons(X, XS)) -> cons(s(X), n__incr(activate(XS))) head(cons(X, XS)) -> X incr(X) -> n__incr(X) nats -> n__nats odds -> n__odds activate(n__incr(X)) -> incr(activate(X)) activate(n__nats) -> nats activate(n__odds) -> odds activate(X) -> X Q is empty. ----------------------------------------
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