details

property	value
status	complete
benchmark	AC23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.79616212845 seconds
cpu usage	3.994946068
max memory	2.32599552E8

stage attributes

key	value
output-size	5183
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) RRRPoloETRSProof [EQUIVALENT, 155 ms] (2) ETRS (3) RRRPoloETRSProof [EQUIVALENT, 24 ms] (4) ETRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: zero(S) -> S plus(x, S) -> x plus(zero(x), zero(y)) -> zero(plus(x, y)) plus(zero(x), un(y)) -> un(plus(x, y)) plus(un(x), un(y)) -> zero(plus(x, plus(y, un(S)))) times(x, S) -> S times(x, times(S, z)) -> times(S, z) times(x, zero(y)) -> zero(times(x, y)) times(x, times(zero(y), z)) -> times(zero(times(x, y)), z) times(x, un(y)) -> plus(x, zero(times(x, y))) times(x, times(un(y), z)) -> times(plus(x, zero(times(x, y))), z) The set E consists of the following equations: plus(x, y) == plus(y, x) times(x, y) == times(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) times(times(x, y), z) == times(x, times(y, z)) ---------------------------------------- (1) RRRPoloETRSProof (EQUIVALENT) The following E TRS is given: Equational rewrite system: The TRS R consists of the following rules: zero(S) -> S plus(x, S) -> x plus(zero(x), zero(y)) -> zero(plus(x, y)) plus(zero(x), un(y)) -> un(plus(x, y)) plus(un(x), un(y)) -> zero(plus(x, plus(y, un(S)))) times(x, S) -> S times(x, times(S, z)) -> times(S, z) times(x, zero(y)) -> zero(times(x, y)) times(x, times(zero(y), z)) -> times(zero(times(x, y)), z) times(x, un(y)) -> plus(x, zero(times(x, y))) times(x, times(un(y), z)) -> times(plus(x, zero(times(x, y))), z) The set E consists of the following equations: plus(x, y) == plus(y, x) times(x, y) == times(y, x) plus(plus(x, y), z) == plus(x, plus(y, z)) times(times(x, y), z) == times(x, times(y, z)) The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering: plus(un(x), un(y)) -> zero(plus(x, plus(y, un(S)))) times(x, un(y)) -> plus(x, zero(times(x, y))) times(x, times(un(y), z)) -> times(plus(x, zero(times(x, y))), z) Used ordering: Polynomial interpretation [POLO]: POL(S) = 0 POL(plus(x_1, x_2)) = x_1 + x_2 POL(times(x_1, x_2)) = x_1 + x_1*x_2 + x_2 POL(un(x_1)) = 2 + x_1 POL(zero(x_1)) = x_1 ---------------------------------------- (2) Obligation: Equational rewrite system: The TRS R consists of the following rules: zero(S) -> S plus(x, S) -> x popout

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job log

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actions

all output return to TRS Equational