details

property	value
status	complete
benchmark	z04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n089.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.62503385544 seconds
cpu usage	3.632328749
max memory	2.23555584E8

stage attributes

key	value
output-size	2425
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPSizeChangeProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(f, a(f, x)) -> a(x, x) a(h, x) -> a(f, a(g, a(f, x))) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: A(f, a(f, x)) -> A(x, x) A(h, x) -> A(f, a(g, a(f, x))) A(h, x) -> A(g, a(f, x)) A(h, x) -> A(f, x) The TRS R consists of the following rules: a(f, a(f, x)) -> a(x, x) a(h, x) -> a(f, a(g, a(f, x))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: A(h, x) -> A(f, x) A(f, a(f, x)) -> A(x, x) The TRS R consists of the following rules: a(f, a(f, x)) -> a(x, x) a(h, x) -> a(f, a(g, a(f, x))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *A(f, a(f, x)) -> A(x, x) The graph contains the following edges 2 > 1, 2 > 2 *A(h, x) -> A(f, x) The graph contains the following edges 2 >= 2 ---------------------------------------- (6) YES popout

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