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	n051.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.63714003563 seconds
cpu usage	3.62180817
max memory	2.31370752E8

stage attributes

key	value
output-size	2932
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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) QDPSizeChangeProof [EQUIVALENT, 2 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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