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TRS Innermost pair #516978949
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
n142.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
3.13585615158 seconds
cpu usage
8.919606427
max memory
5.93801216E8
stage attributes
key
value
output-size
23533
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 88 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 10 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 17 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 17 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 15 ms] (10) QTRS (11) QTRSRRRProof [EQUIVALENT, 0 ms] (12) QTRS (13) QTRSRRRProof [EQUIVALENT, 8 ms] (14) QTRS (15) DependencyPairsProof [EQUIVALENT, 0 ms] (16) QDP (17) DependencyGraphProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) MRRProof [EQUIVALENT, 13 ms] (22) QDP (23) DependencyGraphProof [EQUIVALENT, 0 ms] (24) QDP (25) QDPQMonotonicMRRProof [EQUIVALENT, 31 ms] (26) QDP (27) UsableRulesProof [EQUIVALENT, 0 ms] (28) QDP (29) QReductionProof [EQUIVALENT, 0 ms] (30) QDP (31) QDPSizeChangeProof [EQUIVALENT, 0 ms] (32) 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) The set Q consists of the following terms: a__nats a__pairs a__odds mark(nats) mark(incr(x0)) mark(pairs) mark(odds) mark(head(x0)) mark(tail(x0)) mark(cons(x0, x1)) mark(0) mark(s(x0)) a__incr(x0) a__head(x0) a__tail(x0) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering:
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