details

property	value
status	complete
benchmark	AC43.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n171.star.cs.uiowa.edu
space	Mixed_C

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.60693192482 seconds
cpu usage	6.598879531
max memory	4.80477184E8

stage attributes

key	value
output-size	13385
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 3 ms] (2) EDP (3) EDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) EDP (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (7) EDP (8) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (9) EDP (10) PisEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) EDP (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (14) EDP (15) EUsableRulesReductionPairsProof [EQUIVALENT, 5 ms] (16) EDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES (19) EDP (20) EDPPoloProof [EQUIVALENT, 0 ms] (21) EDP (22) EDependencyGraphProof [EQUIVALENT, 0 ms] (23) TRUE ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) gcd(0, y) -> y gcd(s(x), 0) -> s(x) gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) The set E consists of the following equations: gcd(x, y) == gcd(y, x) ---------------------------------------- (1) EquationalDependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem: The TRS P consists of the following rules: LE(s(x), s(y)) -> LE(x, y) MINUS(s(x), s(y)) -> MINUS(x, y) GCD(s(x), s(y)) -> IF_GCD(le(y, x), s(x), s(y)) GCD(s(x), s(y)) -> LE(y, x) IF_GCD(true, s(x), s(y)) -> GCD(minus(x, y), s(y)) IF_GCD(true, s(x), s(y)) -> MINUS(x, y) IF_GCD(false, s(x), s(y)) -> GCD(minus(y, x), s(x)) IF_GCD(false, s(x), s(y)) -> MINUS(y, x) The TRS R consists of the following rules: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) gcd(0, y) -> y gcd(s(x), 0) -> s(x) gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) The set E consists of the following equations: gcd(x, y) == gcd(y, x) The set E# consists of the following equations: GCD(x, y) == GCD(y, x) We have to consider all minimal (P,E#,R,E)-chains popout

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job log

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actions

all output return to TRS Equational