details

property	value
status	complete
benchmark	Ex4_Zan97_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n116.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.30287790298 seconds
cpu usage	5.785802105
max memory	4.80587776E8

stage attributes

key	value
output-size	2222
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 99 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(X) -> cons(X, n__f(n__g(X))) g(0) -> s(0) g(s(X)) -> s(s(g(X))) sel(0, cons(X, Y)) -> X sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) f(X) -> n__f(X) g(X) -> n__g(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: sel_2 > activate_1 > f_1 > cons_2 > n__f_1 sel_2 > activate_1 > f_1 > n__g_1 > n__f_1 sel_2 > activate_1 > g_1 > n__g_1 > n__f_1 sel_2 > activate_1 > g_1 > 0 > n__f_1 sel_2 > activate_1 > g_1 > s_1 > n__f_1 Status: f_1: multiset status cons_2: multiset status n__f_1: multiset status n__g_1: multiset status g_1: multiset status 0: multiset status s_1: multiset status sel_2: [1,2] activate_1: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(X) -> cons(X, n__f(n__g(X))) g(0) -> s(0) g(s(X)) -> s(s(g(X))) sel(0, cons(X, Y)) -> X sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) f(X) -> n__f(X) g(X) -> n__g(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) activate(X) -> X ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES popout

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all output return to TRS Standard