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TRS Innermost pair #487092891
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
n149.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.59074 seconds
cpu usage
3.97403
user time
3.80385
system time
0.170182
max virtual memory
1.8343148E7
max residence set size
252968.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 111 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: append(@l1, @l2) -> append#1(@l1, @l2) append#1(::(@x, @xs), @l2) -> ::(@x, append(@xs, @l2)) append#1(nil, @l2) -> @l2 subtrees(@t) -> subtrees#1(@t) subtrees#1(leaf) -> nil subtrees#1(node(@x, @t1, @t2)) -> subtrees#2(subtrees(@t1), @t1, @t2, @x) subtrees#2(@l1, @t1, @t2, @x) -> subtrees#3(subtrees(@t2), @l1, @t1, @t2, @x) subtrees#3(@l2, @l1, @t1, @t2, @x) -> ::(node(@x, @t1, @t2), append(@l1, @l2)) The set Q consists of the following terms: append(x0, x1) append#1(::(x0, x1), x2) append#1(nil, x0) subtrees(x0) subtrees#1(leaf) subtrees#1(node(x0, x1, x2)) subtrees#2(x0, x1, x2, x3) subtrees#3(x0, x1, x2, x3, x4) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: [nil, subtrees_1, subtrees#1_1, subtrees#2_4] > [node_3, subtrees#3_5] > [append_2, append#1_2] > ::_2 Status: append_2: multiset status append#1_2: multiset status ::_2: multiset status nil: multiset status subtrees_1: [1] subtrees#1_1: [1] leaf: multiset status node_3: multiset status subtrees#2_4: [3,1,2,4] subtrees#3_5: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: append#1(::(@x, @xs), @l2) -> ::(@x, append(@xs, @l2)) append#1(nil, @l2) -> @l2 subtrees#1(leaf) -> nil subtrees#1(node(@x, @t1, @t2)) -> subtrees#2(subtrees(@t1), @t1, @t2, @x) subtrees#2(@l1, @t1, @t2, @x) -> subtrees#3(subtrees(@t2), @l1, @t1, @t2, @x) subtrees#3(@l2, @l1, @t1, @t2, @x) -> ::(node(@x, @t1, @t2), append(@l1, @l2)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: append(@l1, @l2) -> append#1(@l1, @l2) subtrees(@t) -> subtrees#1(@t) The set Q consists of the following terms: append(x0, x1) append#1(::(x0, x1), x2) append#1(nil, x0) subtrees(x0) subtrees#1(leaf) subtrees#1(node(x0, x1, x2)) subtrees#2(x0, x1, x2, x3) subtrees#3(x0, x1, x2, x3, x4)
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