details

property	value
status	complete
benchmark	31.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n083.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	6.56573104858 seconds
cpu usage	5.519048265
max memory	4.68557824E8

stage attributes

key	value
output-size	2925
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0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: :(:(x, y), z) -> :(x, :(y, z)) :(+(x, y), z) -> +(:(x, z), :(y, z)) :(z, +(x, f(y))) -> :(g(z, y), +(x, a)) 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: :^1(:(x, y), z) -> :^1(x, :(y, z)) :^1(:(x, y), z) -> :^1(y, z) :^1(+(x, y), z) -> :^1(x, z) :^1(+(x, y), z) -> :^1(y, z) :^1(z, +(x, f(y))) -> :^1(g(z, y), +(x, a)) The TRS R consists of the following rules: :(:(x, y), z) -> :(x, :(y, z)) :(+(x, y), z) -> +(:(x, z), :(y, z)) :(z, +(x, f(y))) -> :(g(z, y), +(x, a)) 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 1 less node. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: :^1(:(x, y), z) -> :^1(y, z) :^1(:(x, y), z) -> :^1(x, :(y, z)) :^1(+(x, y), z) -> :^1(x, z) :^1(+(x, y), z) -> :^1(y, z) The TRS R consists of the following rules: :(:(x, y), z) -> :(x, :(y, z)) :(+(x, y), z) -> +(:(x, z), :(y, z)) :(z, +(x, f(y))) -> :(g(z, y), +(x, a)) 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: *:^1(:(x, y), z) -> :^1(y, z) The graph contains the following edges 1 > 1, 2 >= 2 *:^1(:(x, y), z) -> :^1(x, :(y, z)) The graph contains the following edges 1 > 1 *:^1(+(x, y), z) -> :^1(x, z) The graph contains the following edges 1 > 1, 2 >= 2 popout

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job log

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actions

all output return to TRS Standard