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TRS Inner 89993 pair #381733445
details
property
value
status
complete
benchmark
appendAll.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.53510594368 seconds
cpu usage
3.387428308
max memory
2.1921792E8
stage attributes
key
value
output-size
3258
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 43 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) 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 appendAll(@l) -> appendAll#1(@l) appendAll#1(::(@l1, @ls)) -> append(@l1, appendAll(@ls)) appendAll#1(nil) -> nil appendAll2(@l) -> appendAll2#1(@l) appendAll2#1(::(@l1, @ls)) -> append(appendAll(@l1), appendAll2(@ls)) appendAll2#1(nil) -> nil appendAll3(@l) -> appendAll3#1(@l) appendAll3#1(::(@l1, @ls)) -> append(appendAll2(@l1), appendAll3(@ls)) appendAll3#1(nil) -> nil The set Q consists of the following terms: append(x0, x1) append#1(::(x0, x1), x2) append#1(nil, x0) appendAll(x0) appendAll#1(::(x0, x1)) appendAll#1(nil) appendAll2(x0) appendAll2#1(::(x0, x1)) appendAll2#1(nil) appendAll3(x0) appendAll3#1(::(x0, x1)) appendAll3#1(nil) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:appendAll3#1_1 > appendAll3_1 > appendAll2#1_1 > append_2 > append#1_2 > appendAll2_1 > ::_2 > appendAll_1 > appendAll#1_1 > nil and weight map: nil=1 appendAll_1=2 appendAll#1_1=2 appendAll2_1=2 appendAll2#1_1=1 appendAll3_1=1 appendAll3#1_1=0 append_2=0 append#1_2=0 ::_2=3 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: append(@l1, @l2) -> append#1(@l1, @l2) append#1(::(@x, @xs), @l2) -> ::(@x, append(@xs, @l2)) append#1(nil, @l2) -> @l2 appendAll(@l) -> appendAll#1(@l) appendAll#1(::(@l1, @ls)) -> append(@l1, appendAll(@ls)) appendAll#1(nil) -> nil appendAll2(@l) -> appendAll2#1(@l) appendAll2#1(::(@l1, @ls)) -> append(appendAll(@l1), appendAll2(@ls)) appendAll2#1(nil) -> nil appendAll3(@l) -> appendAll3#1(@l) appendAll3#1(::(@l1, @ls)) -> append(appendAll2(@l1), appendAll3(@ls)) appendAll3#1(nil) -> nil ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. The set Q consists of the following terms:
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