details

property	value
status	complete
benchmark	4.28.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n102.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.73185610771 seconds
cpu usage	3.947576451
max memory	2.4567808E8

stage attributes

key	value
output-size	3278
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 153 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4)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: f(x, nil) -> g(nil, x) f(x, g(y, z)) -> g(f(x, y), z) ++(x, nil) -> x ++(x, g(y, z)) -> g(++(x, y), z) null(nil) -> true null(g(x, y)) -> false mem(nil, y) -> false mem(g(x, y), z) -> or(=(y, z), mem(x, z)) mem(x, max(x)) -> not(null(x)) max(g(g(nil, x), y)) -> max'(x, y) max(g(g(g(x, y), z), u)) -> max'(max(g(g(x, y), z)), u) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: f/2(YES,YES) nil/0) g/2(YES,YES) ++/2(YES,YES) null/1(YES) true/0) false/0) mem/2(YES,YES) or/2(YES,YES) =/2(YES,YES) max/1)YES( not/1(YES) max'/2(YES,YES) u/0) Quasi precedence: f_2 > nil f_2 > [g_2, max'_2] > false f_2 > [g_2, max'_2] > or_2 ++_2 > [g_2, max'_2] > false ++_2 > [g_2, max'_2] > or_2 [mem_2, =_2] > [null_1, true] > false [mem_2, =_2] > or_2 [mem_2, =_2] > not_1 u > [g_2, max'_2] > false u > [g_2, max'_2] > or_2 Status: f_2: multiset status nil: multiset status g_2: multiset status ++_2: [1,2] null_1: multiset status true: multiset status false: multiset status mem_2: multiset status or_2: [1,2] =_2: multiset status not_1: multiset status max'_2: multiset status u: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(x, nil) -> g(nil, x) f(x, g(y, z)) -> g(f(x, y), z) ++(x, nil) -> x ++(x, g(y, z)) -> g(++(x, y), z) null(nil) -> true null(g(x, y)) -> false mem(nil, y) -> false mem(g(x, y), z) -> or(=(y, z), mem(x, z)) popout

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job log

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actions

all output return to TRS Stand 20472