details

property	value
status	complete
benchmark	Ex6_Luc98_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n112.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.21662783623 seconds
cpu usage	5.882067726
max memory	4.80075776E8

stage attributes

key	value
output-size	3689
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 101 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 1 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) from(X) -> cons(X, n__from(s(X))) first(X1, X2) -> n__first(X1, X2) from(X) -> n__from(X) activate(n__first(X1, X2)) -> first(X1, X2) activate(n__from(X)) -> from(X) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(activate(x_1)) = 2*x_1 POL(cons(x_1, x_2)) = 1 + x_1 + x_2 POL(first(x_1, x_2)) = 2*x_1 + 2*x_2 POL(from(x_1)) = 2 + 2*x_1 POL(n__first(x_1, x_2)) = x_1 + x_2 POL(n__from(x_1)) = 1 + x_1 POL(nil) = 0 POL(s(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) from(X) -> n__from(X) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: first(0, X) -> nil from(X) -> cons(X, n__from(s(X))) first(X1, X2) -> n__first(X1, X2) activate(n__first(X1, X2)) -> first(X1, X2) activate(n__from(X)) -> from(X) activate(X) -> X Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(activate(x_1)) = 1 + 2*x_1 POL(cons(x_1, x_2)) = x_1 + x_2 POL(first(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 POL(from(x_1)) = 1 + 2*x_1 POL(n__first(x_1, x_2)) = 2 + 2*x_1 + x_2 POL(n__from(x_1)) = x_1 POL(nil) = 1 POL(s(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: first(0, X) -> nil from(X) -> cons(X, n__from(s(X))) popout

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job log

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actions

all output return to TRS Standard