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TRS Standard pair #516964510
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
n175.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.95064091682 seconds
cpu usage
8.404282923
max memory
5.73038592E8
stage attributes
key
value
output-size
16758
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 97 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 21 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 4 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 12 ms] (10) QTRS (11) DependencyPairsProof [EQUIVALENT, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) QDP (15) MRRProof [EQUIVALENT, 15 ms] (16) QDP (17) DependencyGraphProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPOrderProof [EQUIVALENT, 9 ms] (20) QDP (21) DependencyGraphProof [EQUIVALENT, 0 ms] (22) QDP (23) UsableRulesProof [EQUIVALENT, 0 ms] (24) QDP (25) QDPSizeChangeProof [EQUIVALENT, 0 ms] (26) 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(pairs) -> a__pairs mark(odds) -> a__odds mark(incr(X)) -> a__incr(mark(X)) mark(head(X)) -> a__head(mark(X)) mark(tail(X)) -> a__tail(mark(X)) mark(0) -> 0 mark(s(X)) -> s(mark(X)) mark(nil) -> nil mark(cons(X1, X2)) -> cons(mark(X1), X2) a__nats -> nats a__pairs -> pairs a__odds -> odds a__incr(X) -> incr(X) 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)) = 1 + 2*x_1 POL(cons(x_1, x_2)) = 2*x_1 + 2*x_2 POL(head(x_1)) = 1 + x_1 POL(incr(x_1)) = 2*x_1 POL(mark(x_1)) = 2*x_1 POL(nats) = 0 POL(nil) = 0 POL(odds) = 0 POL(pairs) = 0 POL(s(x_1)) = x_1 POL(tail(x_1)) = 1 + 2*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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