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TRS Innermost pair #487523929
details
property
value
status
complete
benchmark
rationalPotential.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.30995607376 seconds
cpu usage
4.057335049
max memory
2.37473792E8
stage attributes
key
value
output-size
3697
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 32 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: group3(@l) -> group3#1(@l) group3#1(::(@x, @xs)) -> group3#2(@xs, @x) group3#1(nil) -> nil group3#2(::(@y, @ys), @x) -> group3#3(@ys, @x, @y) group3#2(nil, @x) -> nil group3#3(::(@z, @zs), @x, @y) -> ::(tuple#3(@x, @y, @z), group3(@zs)) group3#3(nil, @x, @y) -> nil zip3(@l1, @l2, @l3) -> zip3#1(@l1, @l2, @l3) zip3#1(::(@x, @xs), @l2, @l3) -> zip3#2(@l2, @l3, @x, @xs) zip3#1(nil, @l2, @l3) -> nil zip3#2(::(@y, @ys), @l3, @x, @xs) -> zip3#3(@l3, @x, @xs, @y, @ys) zip3#2(nil, @l3, @x, @xs) -> nil zip3#3(::(@z, @zs), @x, @xs, @y, @ys) -> ::(tuple#3(@x, @y, @z), zip3(@xs, @ys, @zs)) zip3#3(nil, @x, @xs, @y, @ys) -> nil The set Q consists of the following terms: group3(x0) group3#1(::(x0, x1)) group3#1(nil) group3#2(::(x0, x1), x2) group3#2(nil, x0) group3#3(::(x0, x1), x2, x3) group3#3(nil, x0, x1) zip3(x0, x1, x2) zip3#1(::(x0, x1), x2, x3) zip3#1(nil, x0, x1) zip3#2(::(x0, x1), x2, x3, x4) zip3#2(nil, x0, x1, x2) zip3#3(::(x0, x1), x2, x3, x4, x5) zip3#3(nil, x0, x1, x2, x3) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:zip3#2_4 > nil > group3#2_2 > zip3#1_3 > group3_1 > ::_2 > zip3#3_5 > zip3_3 > tuple#3_3 > group3#3_3 > group3#1_1 and weight map: nil=1 group3_1=2 group3#1_1=1 ::_2=2 group3#2_2=1 group3#3_3=3 tuple#3_3=0 zip3_3=1 zip3#1_3=0 zip3#2_4=1 zip3#3_5=2 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: group3(@l) -> group3#1(@l) group3#1(::(@x, @xs)) -> group3#2(@xs, @x) group3#1(nil) -> nil group3#2(::(@y, @ys), @x) -> group3#3(@ys, @x, @y) group3#2(nil, @x) -> nil group3#3(::(@z, @zs), @x, @y) -> ::(tuple#3(@x, @y, @z), group3(@zs)) group3#3(nil, @x, @y) -> nil zip3(@l1, @l2, @l3) -> zip3#1(@l1, @l2, @l3) zip3#1(::(@x, @xs), @l2, @l3) -> zip3#2(@l2, @l3, @x, @xs) zip3#1(nil, @l2, @l3) -> nil zip3#2(::(@y, @ys), @l3, @x, @xs) -> zip3#3(@l3, @x, @xs, @y, @ys) zip3#2(nil, @l3, @x, @xs) -> nil zip3#3(::(@z, @zs), @x, @xs, @y, @ys) -> ::(tuple#3(@x, @y, @z), zip3(@xs, @ys, @zs)) zip3#3(nil, @x, @xs, @y, @ys) -> nil
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