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TRS Equational pair #487092854
details
property
value
status
complete
benchmark
AC42.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
Mixed_C
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.93045 seconds
cpu usage
4.36452
user time
4.17902
system time
0.185501
max virtual memory
1.8283044E7
max residence set size
249500.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof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, 6 ms] (9) EDP (10) PisEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) EDP (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (14) EDP (15) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (16) EDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES (19) EDP (20) EDPPoloProof [EQUIVALENT, 0 ms] (21) EDP (22) PisEmptyProof [EQUIVALENT, 0 ms] (23) YES ---------------------------------------- (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) pred(s(x)) -> x minus(x, 0) -> x minus(x, s(y)) -> pred(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(x, s(y)) -> PRED(minus(x, y)) MINUS(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) pred(s(x)) -> x minus(x, 0) -> x minus(x, s(y)) -> pred(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 ---------------------------------------- (2)
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