details

property	value
status	complete
benchmark	size-12-alpha-3-num-64.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.1467 seconds
cpu usage	5.76208
user time	5.51197
system time	0.250116
max virtual memory	1.927652E7
max residence set size	631652.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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(x1) -> x1 a(a(x1)) -> a(b(c(a(x1)))) c(b(x1)) -> a(b(a(x1))) 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(a(x1)) -> A(b(c(a(x1)))) A(a(x1)) -> C(a(x1)) C(b(x1)) -> A(b(a(x1))) C(b(x1)) -> A(x1) The TRS R consists of the following rules: a(x1) -> x1 a(a(x1)) -> a(b(c(a(x1)))) c(b(x1)) -> a(b(a(x1))) 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(a(x1)) -> C(a(x1)) C(b(x1)) -> A(x1) The TRS R consists of the following rules: a(x1) -> x1 a(a(x1)) -> a(b(c(a(x1)))) c(b(x1)) -> a(b(a(x1))) 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: *C(b(x1)) -> A(x1) The graph contains the following edges 1 > 1 *A(a(x1)) -> C(a(x1)) The graph contains the following edges 1 >= 1 ---------------------------------------- (6) YES popout

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all output return to SRS Standard