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TRS Innermost pair #516979507
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
n170.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.2589468956 seconds
cpu usage
5.838366303
max memory
4.81509376E8
stage attributes
key
value
output-size
3824
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 140 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) 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))
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