details

property	value
status	complete
benchmark	#3.53b.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n007.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.11326479912 seconds
cpu usage	5.376398581
max memory	4.72395776E8

stage attributes

key	value
output-size	1883
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 5 ms] (2) QDP (3) QDPSizeChangeProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(x, y) -> x g(x, y) -> y f(0, 1, x) -> f(s(x), x, x) f(x, y, s(z)) -> s(f(0, 1, z)) 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: F(0, 1, x) -> F(s(x), x, x) F(x, y, s(z)) -> F(0, 1, z) The TRS R consists of the following rules: g(x, y) -> x g(x, y) -> y f(0, 1, x) -> f(s(x), x, x) f(x, y, s(z)) -> s(f(0, 1, z)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) 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: *F(x, y, s(z)) -> F(0, 1, z) The graph contains the following edges 3 > 3 *F(0, 1, x) -> F(s(x), x, x) The graph contains the following edges 3 >= 2, 3 >= 3 ---------------------------------------- (4) YES popout

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job log

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actions

all output return to TRS Standard