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TRS Standard pair #516961515
details
property
value
status
complete
benchmark
ExIntrod_GM01_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n007.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
9.30869221687 seconds
cpu usage
22.463476728
max memory
9.55404288E8
stage attributes
key
value
output-size
12177
starexec-result
NO
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 86 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 19 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) QDP (11) MRRProof [EQUIVALENT, 20 ms] (12) QDP (13) QDPOrderProof [EQUIVALENT, 30 ms] (14) QDP (15) TransformationProof [EQUIVALENT, 0 ms] (16) QDP (17) NonTerminationLoopProof [COMPLETE, 29 ms] (18) NO ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: incr(nil) -> nil incr(cons(X, L)) -> cons(s(X), n__incr(activate(L))) adx(nil) -> nil adx(cons(X, L)) -> incr(cons(X, n__adx(activate(L)))) nats -> adx(zeros) zeros -> cons(0, n__zeros) head(cons(X, L)) -> X tail(cons(X, L)) -> activate(L) incr(X) -> n__incr(X) adx(X) -> n__adx(X) zeros -> n__zeros activate(n__incr(X)) -> incr(X) activate(n__adx(X)) -> adx(X) activate(n__zeros) -> zeros activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(activate(x_1)) = x_1 POL(adx(x_1)) = x_1 POL(cons(x_1, x_2)) = x_1 + x_2 POL(head(x_1)) = 2*x_1 POL(incr(x_1)) = x_1 POL(n__adx(x_1)) = x_1 POL(n__incr(x_1)) = x_1 POL(n__zeros) = 0 POL(nats) = 2 POL(nil) = 0 POL(s(x_1)) = x_1 POL(tail(x_1)) = 2 + 2*x_1 POL(zeros) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: nats -> adx(zeros) tail(cons(X, L)) -> activate(L) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: incr(nil) -> nil incr(cons(X, L)) -> cons(s(X), n__incr(activate(L))) adx(nil) -> nil adx(cons(X, L)) -> incr(cons(X, n__adx(activate(L)))) zeros -> cons(0, n__zeros) head(cons(X, L)) -> X
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