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TRS Stand 20472 pair #381715522
details
property
value
status
complete
benchmark
Ex1_Luc04b_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n103.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.79881095886 seconds
cpu usage
6.373110364
max memory
4.390912E8
stage attributes
key
value
output-size
19205
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 68 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 17 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 16 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 12 ms] (10) QTRS (11) QTRSRRRProof [EQUIVALENT, 0 ms] (12) QTRS (13) QTRSRRRProof [EQUIVALENT, 10 ms] (14) QTRS (15) DependencyPairsProof [EQUIVALENT, 0 ms] (16) QDP (17) DependencyGraphProof [EQUIVALENT, 0 ms] (18) QDP (19) MRRProof [EQUIVALENT, 14 ms] (20) QDP (21) DependencyGraphProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPOrderProof [EQUIVALENT, 21 ms] (24) QDP (25) UsableRulesProof [EQUIVALENT, 0 ms] (26) QDP (27) QDPSizeChangeProof [EQUIVALENT, 0 ms] (28) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__nats -> cons(0, incr(nats)) a__pairs -> cons(0, incr(odds)) a__odds -> a__incr(a__pairs) a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) a__head(cons(X, XS)) -> mark(X) a__tail(cons(X, XS)) -> mark(XS) mark(nats) -> a__nats mark(incr(X)) -> a__incr(mark(X)) mark(pairs) -> a__pairs mark(odds) -> a__odds mark(head(X)) -> a__head(mark(X)) mark(tail(X)) -> a__tail(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__nats -> nats a__incr(X) -> incr(X) a__pairs -> pairs a__odds -> odds a__head(X) -> head(X) a__tail(X) -> tail(X) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(a__head(x_1)) = 1 + x_1 POL(a__incr(x_1)) = 2*x_1 POL(a__nats) = 0 POL(a__odds) = 0 POL(a__pairs) = 0 POL(a__tail(x_1)) = x_1 POL(cons(x_1, x_2)) = x_1 + 2*x_2 POL(head(x_1)) = 1 + x_1 POL(incr(x_1)) = 2*x_1 POL(mark(x_1)) = x_1 POL(nats) = 0 POL(odds) = 0 POL(pairs) = 0 POL(s(x_1)) = x_1 POL(tail(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a__head(cons(X, XS)) -> mark(X)
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