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TRS_Innermost 2019-03-28 22.12 pair #432270728
details
property
value
status
complete
benchmark
subtrees.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.80737 seconds
cpu usage
3.70439
user time
3.53639
system time
0.167995
max virtual memory
1.8347308E7
max residence set size
245172.0
stage attributes
key
value
starexec-result
YES
output
3.64/1.78 YES 3.64/1.79 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.64/1.79 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.64/1.79 3.64/1.79 3.64/1.79 Termination w.r.t. Q of the given QTRS could be proven: 3.64/1.79 3.64/1.79 (0) QTRS 3.64/1.79 (1) QTRSRRRProof [EQUIVALENT, 118 ms] 3.64/1.79 (2) QTRS 3.64/1.79 (3) QTRSRRRProof [EQUIVALENT, 0 ms] 3.64/1.79 (4) QTRS 3.64/1.79 (5) RisEmptyProof [EQUIVALENT, 0 ms] 3.64/1.79 (6) YES 3.64/1.79 3.64/1.79 3.64/1.79 ---------------------------------------- 3.64/1.79 3.64/1.79 (0) 3.64/1.79 Obligation: 3.64/1.79 Q restricted rewrite system: 3.64/1.79 The TRS R consists of the following rules: 3.64/1.79 3.64/1.79 append(@l1, @l2) -> append#1(@l1, @l2) 3.64/1.79 append#1(::(@x, @xs), @l2) -> ::(@x, append(@xs, @l2)) 3.64/1.79 append#1(nil, @l2) -> @l2 3.64/1.79 subtrees(@t) -> subtrees#1(@t) 3.64/1.79 subtrees#1(leaf) -> nil 3.64/1.79 subtrees#1(node(@x, @t1, @t2)) -> subtrees#2(subtrees(@t1), @t1, @t2, @x) 3.64/1.79 subtrees#2(@l1, @t1, @t2, @x) -> subtrees#3(subtrees(@t2), @l1, @t1, @t2, @x) 3.64/1.79 subtrees#3(@l2, @l1, @t1, @t2, @x) -> ::(node(@x, @t1, @t2), append(@l1, @l2)) 3.64/1.79 3.64/1.79 The set Q consists of the following terms: 3.64/1.79 3.64/1.79 append(x0, x1) 3.64/1.79 append#1(::(x0, x1), x2) 3.64/1.79 append#1(nil, x0) 3.64/1.79 subtrees(x0) 3.64/1.79 subtrees#1(leaf) 3.64/1.79 subtrees#1(node(x0, x1, x2)) 3.64/1.79 subtrees#2(x0, x1, x2, x3) 3.64/1.79 subtrees#3(x0, x1, x2, x3, x4) 3.64/1.79 3.64/1.79 3.64/1.79 ---------------------------------------- 3.64/1.79 3.64/1.79 (1) QTRSRRRProof (EQUIVALENT) 3.64/1.79 Used ordering: 3.64/1.79 Quasi precedence: 3.64/1.79 [nil, subtrees_1, subtrees#1_1, subtrees#2_4] > [node_3, subtrees#3_5] > [append_2, append#1_2] > ::_2 3.64/1.79 3.64/1.79 3.64/1.79 Status: 3.64/1.79 append_2: multiset status 3.64/1.79 append#1_2: multiset status 3.64/1.79 ::_2: multiset status 3.64/1.79 nil: multiset status 3.64/1.79 subtrees_1: [1] 3.64/1.79 subtrees#1_1: [1] 3.64/1.79 leaf: multiset status 3.64/1.79 node_3: multiset status 3.64/1.79 subtrees#2_4: [3,1,2,4] 3.64/1.79 subtrees#3_5: multiset status 3.64/1.79 3.64/1.79 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 3.64/1.79 3.64/1.79 append#1(::(@x, @xs), @l2) -> ::(@x, append(@xs, @l2)) 3.64/1.79 append#1(nil, @l2) -> @l2 3.64/1.79 subtrees#1(leaf) -> nil 3.64/1.79 subtrees#1(node(@x, @t1, @t2)) -> subtrees#2(subtrees(@t1), @t1, @t2, @x) 3.64/1.79 subtrees#2(@l1, @t1, @t2, @x) -> subtrees#3(subtrees(@t2), @l1, @t1, @t2, @x) 3.64/1.79 subtrees#3(@l2, @l1, @t1, @t2, @x) -> ::(node(@x, @t1, @t2), append(@l1, @l2)) 3.64/1.79 3.64/1.79 3.64/1.79 3.64/1.79 3.64/1.79 ---------------------------------------- 3.64/1.79 3.64/1.79 (2) 3.64/1.79 Obligation: 3.64/1.79 Q restricted rewrite system: 3.64/1.79 The TRS R consists of the following rules: 3.64/1.79 3.64/1.79 append(@l1, @l2) -> append#1(@l1, @l2) 3.64/1.79 subtrees(@t) -> subtrees#1(@t) 3.64/1.79 3.64/1.79 The set Q consists of the following terms: 3.64/1.79 3.64/1.79 append(x0, x1) 3.64/1.79 append#1(::(x0, x1), x2) 3.64/1.79 append#1(nil, x0) 3.64/1.79 subtrees(x0) 3.64/1.79 subtrees#1(leaf) 3.64/1.79 subtrees#1(node(x0, x1, x2)) 3.64/1.79 subtrees#2(x0, x1, x2, x3) 3.64/1.79 subtrees#3(x0, x1, x2, x3, x4) 3.64/1.79 3.64/1.79 3.64/1.79 ---------------------------------------- 3.64/1.79
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