details

property	value
status	complete
benchmark	linear1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n024.star.cs.uiowa.edu
space	Endrullis_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.08430790901 seconds
cpu usage	4.91046342
max memory	3.334144E8

stage attributes

key	value
output-size	4368
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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) MRRProof [EQUIVALENT, 7 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 32 ms] (8) QDP (9) PisEmptyProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(f(b, a(x)))) -> f(a(a(a(x))), b) a(a(x)) -> f(b, a(f(a(x), b))) f(a(x), b) -> f(b, a(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(a(f(b, a(x)))) -> F(a(a(a(x))), b) A(a(f(b, a(x)))) -> A(a(a(x))) A(a(f(b, a(x)))) -> A(a(x)) A(a(x)) -> F(b, a(f(a(x), b))) A(a(x)) -> A(f(a(x), b)) A(a(x)) -> F(a(x), b) F(a(x), b) -> F(b, a(x)) The TRS R consists of the following rules: a(a(f(b, a(x)))) -> f(a(a(a(x))), b) a(a(x)) -> f(b, a(f(a(x), b))) f(a(x), b) -> f(b, a(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 5 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: A(a(f(b, a(x)))) -> A(a(x)) A(a(f(b, a(x)))) -> A(a(a(x))) The TRS R consists of the following rules: a(a(f(b, a(x)))) -> f(a(a(a(x))), b) a(a(x)) -> f(b, a(f(a(x), b))) f(a(x), b) -> f(b, a(x)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: A(a(f(b, a(x)))) -> A(a(x)) Used ordering: Polynomial interpretation [POLO]: popout

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

job log

popout

actions

all output return to TRS Stand 20472