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TRS Standard pair #487072083
details
property
value
status
complete
benchmark
ExIntrod_GM01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Strategy_removed_CSR_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.35564 seconds
cpu usage
5.73038
user time
5.4695
system time
0.260871
max virtual memory
1.8543288E7
max residence set size
449568.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 52 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 11 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) Overlay + Local Confluence [EQUIVALENT, 0 ms] (10) QTRS (11) DependencyPairsProof [EQUIVALENT, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) AND (15) QDP (16) UsableRulesProof [EQUIVALENT, 0 ms] (17) QDP (18) QReductionProof [EQUIVALENT, 0 ms] (19) QDP (20) NonTerminationLoopProof [COMPLETE, 0 ms] (21) NO (22) QDP (23) UsableRulesProof [EQUIVALENT, 0 ms] (24) QDP (25) QReductionProof [EQUIVALENT, 0 ms] (26) QDP (27) QDPSizeChangeProof [EQUIVALENT, 0 ms] (28) YES (29) QDP (30) UsableRulesProof [EQUIVALENT, 0 ms] (31) QDP (32) QReductionProof [EQUIVALENT, 0 ms] (33) QDP (34) QDPSizeChangeProof [EQUIVALENT, 0 ms] (35) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: incr(nil) -> nil incr(cons(X, L)) -> cons(s(X), incr(L)) adx(nil) -> nil adx(cons(X, L)) -> incr(cons(X, adx(L))) nats -> adx(zeros) zeros -> cons(0, zeros) head(cons(X, L)) -> X tail(cons(X, L)) -> L Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 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(nats) = 2 POL(nil) = 0 POL(s(x_1)) = x_1 POL(tail(x_1)) = 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) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: incr(nil) -> nil incr(cons(X, L)) -> cons(s(X), incr(L)) adx(nil) -> nil adx(cons(X, L)) -> incr(cons(X, adx(L))) zeros -> cons(0, zeros) head(cons(X, L)) -> X tail(cons(X, L)) -> L
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