details

property	value
status	complete
benchmark	#3.17a.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n072.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.50862002373 seconds
cpu usage	6.99603407
max memory	5.20134656E8

stage attributes

key	value
output-size	6313
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 145 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 1 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) Overlay + Local Confluence [EQUIVALENT, 0 ms] (10) QTRS (11) DependencyPairsProof [EQUIVALENT, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, nil)) -> cons(x, nil) sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) sum(plus(cons(0, x), cons(y, l))) -> pred(sum(cons(s(x), cons(y, l)))) pred(cons(s(x), nil)) -> cons(x, nil) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 2 POL(app(x_1, x_2)) = 2*x_1 + x_2 POL(cons(x_1, x_2)) = x_1 + x_2 POL(nil) = 0 POL(plus(x_1, x_2)) = x_1 + x_2 POL(pred(x_1)) = 1 + x_1 POL(s(x_1)) = x_1 POL(sum(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: plus(0, y) -> y sum(plus(cons(0, x), cons(y, l))) -> pred(sum(cons(s(x), cons(y, l)))) pred(cons(s(x), nil)) -> cons(x, nil) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(nil, k) -> k app(l, nil) -> l app(cons(x, l), k) -> cons(x, app(l, k)) sum(cons(x, nil)) -> cons(x, nil) sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))) plus(s(x), y) -> s(plus(x, y)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(app(x_1, x_2)) = 2*x_1 + 2*x_2 POL(cons(x_1, x_2)) = x_1 + x_2 POL(nil) = 1 POL(plus(x_1, x_2)) = x_1 + x_2 popout

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job log

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actions

all output return to TRS Standard