details

property	value
status	complete
benchmark	AC44.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Mixed_C

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.1613 seconds
cpu usage	4.8231
user time	4.61901
system time	0.204091
max virtual memory	1.827784E7
max residence set size	264188.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof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, 1 ms] (14) EDP (15) EDPPoloProof [EQUIVALENT, 10 ms] (16) EDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES (19) EDP (20) EDPPoloProof [EQUIVALENT, 18 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(0, y) -> 0 minus(s(x), y) -> if_minus(le(s(x), y), s(x), y) if_minus(true, s(x), y) -> 0 if_minus(false, s(x), y) -> s(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), y) -> IF_MINUS(le(s(x), y), s(x), y) MINUS(s(x), y) -> LE(s(x), y) IF_MINUS(false, s(x), 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(0, y) -> 0 minus(s(x), y) -> if_minus(le(s(x), y), s(x), y) if_minus(true, s(x), y) -> 0 if_minus(false, s(x), y) -> s(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