details

property	value
status	complete
benchmark	Ex4_4_Luc96b_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n119.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.3018488884 seconds
cpu usage	6.043512601
max memory	4.7941632E8

stage attributes

key	value
output-size	3998
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 96 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 13 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(g(X), Y)) -> mark(f(X, f(g(X), Y))) active(f(X1, X2)) -> f(active(X1), X2) active(g(X)) -> g(active(X)) f(mark(X1), X2) -> mark(f(X1, X2)) g(mark(X)) -> mark(g(X)) proper(f(X1, X2)) -> f(proper(X1), proper(X2)) proper(g(X)) -> g(proper(X)) f(ok(X1), ok(X2)) -> ok(f(X1, X2)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(active(x_1)) = 1 + 2*x_1 POL(f(x_1, x_2)) = x_1 + x_2 POL(g(x_1)) = x_1 POL(mark(x_1)) = x_1 POL(ok(x_1)) = 1 + 2*x_1 POL(proper(x_1)) = x_1 POL(top(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: active(f(g(X), Y)) -> mark(f(X, f(g(X), Y))) f(ok(X1), ok(X2)) -> ok(f(X1, X2)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(X1, X2)) -> f(active(X1), X2) active(g(X)) -> g(active(X)) f(mark(X1), X2) -> mark(f(X1, X2)) g(mark(X)) -> mark(g(X)) proper(f(X1, X2)) -> f(proper(X1), proper(X2)) proper(g(X)) -> g(proper(X)) g(ok(X)) -> ok(g(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(active(x_1)) = x_1 POL(f(x_1, x_2)) = 2*x_1 + x_2 POL(g(x_1)) = 2*x_1 POL(mark(x_1)) = 1 + x_1 POL(ok(x_1)) = x_1 POL(proper(x_1)) = x_1 POL(top(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: popout

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

job log

popout

actions

all output return to TRS Standard