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	n189.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.61922 seconds
cpu usage	3.4955
user time	3.31455
system time	0.180946
max virtual memory	1.8408912E7
max residence set size	225228.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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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all output return to TRS Standard