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TRS Standard pair #487068213
details
property
value
status
complete
benchmark
4.27.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.88323 seconds
cpu usage
4.05313
user time
3.85602
system time
0.197104
max virtual memory
1.84124E7
max residence set size
261168.0
stage attributes
key
value
starexec-result
YES
output
YES 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 54 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 14 ms] (4) QTRS (5) Overlay + Local Confluence [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) AND (11) QDP (12) UsableRulesProof [EQUIVALENT, 0 ms] (13) QDP (14) QReductionProof [EQUIVALENT, 0 ms] (15) QDP (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: int(0, 0) -> .(0, nil) int(0, s(y)) -> .(0, int(s(0), s(y))) int(s(x), 0) -> nil int(s(x), s(y)) -> int_list(int(x, y)) int_list(nil) -> nil int_list(.(x, y)) -> .(s(x), int_list(y)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(.(x_1, x_2)) = 2*x_1 + x_2 POL(0) = 0 POL(int(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 POL(int_list(x_1)) = x_1 POL(nil) = 0 POL(s(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: int(0, 0) -> .(0, nil) int(s(x), 0) -> nil ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: int(0, s(y)) -> .(0, int(s(0), s(y))) int(s(x), s(y)) -> int_list(int(x, y)) int_list(nil) -> nil int_list(.(x, y)) -> .(s(x), int_list(y)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(.(x_1, x_2)) = x_1 + x_2 POL(0) = 0 POL(int(x_1, x_2)) = 2*x_1 + 2*x_2 POL(int_list(x_1)) = 2*x_1 POL(nil) = 1 POL(s(x_1)) = 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: int_list(nil) -> nil
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