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TRS Innermost pair #487523935
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
n141.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.68077802658 seconds
cpu usage
3.518979838
max memory
2.22826496E8
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 27 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4)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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