details

property	value
status	complete
benchmark	#3.17.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n173.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.9823 seconds
cpu usage	4.65246
user time	4.42729
system time	0.225167
max virtual memory	1.8408912E7
max residence set size	300604.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 70 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 15 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 15 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)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 2 POL(app(x_1, x_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(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 ---------------------------------------- (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 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: app(nil, k) -> k app(l, nil) -> l ---------------------------------------- popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard