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TRS Equational pair #487092878
details
property
value
status
complete
benchmark
PEANO-NAT_nokinds.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Mixed_C
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
8.00167 seconds
cpu usage
16.2185
user time
15.4022
system time
0.816299
max virtual memory
1.8322376E7
max residence set size
2397376.0
stage attributes
key
value
starexec-result
MAYBE
output
MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could not be shown: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) EDP (6) ESharpUsableEquationsProof [EQUIVALENT, 10 ms] (7) EDP (8) EUsableRulesReductionPairsProof [EQUIVALENT, 80 ms] (9) EDP (10) EDependencyGraphProof [EQUIVALENT, 0 ms] (11) TRUE (12) EDP (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (14) EDP (15) EUsableRulesReductionPairsProof [EQUIVALENT, 52 ms] (16) EDP (17) EDependencyGraphProof [EQUIVALENT, 0 ms] (18) TRUE (19) EDP (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (21) EDP (22) EUsableRulesReductionPairsProof [EQUIVALENT, 46 ms] (23) EDP (24) EDependencyGraphProof [EQUIVALENT, 0 ms] (25) TRUE (26) EDP (27) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (28) EDP (29) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (30) EDP (31) PisEmptyProof [EQUIVALENT, 0 ms] (32) YES (33) EDP (34) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (35) EDP (36) EUsableRulesReductionPairsProof [EQUIVALENT, 15 ms] (37) EDP (38) PisEmptyProof [EQUIVALENT, 0 ms] (39) YES (40) EDP (41) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (42) EDP (43) EUsableRulesProof [EQUIVALENT, 4 ms] (44) EDP (45) EDP ---------------------------------------- (0) Obligation: Equational rewrite system: The TRS R consists of the following rules: 1 -> s_(0) 2 -> s_(s_(0)) 3 -> s_(s_(s_(0))) 4 -> s_(s_(s_(s_(0)))) 5 -> s_(s_(s_(s_(s_(0))))) 6 -> s_(s_(s_(s_(s_(s_(0)))))) 7 -> s_(s_(s_(s_(s_(s_(s_(0))))))) U101(tt, M, N) -> d(N, M) U11(tt) -> 0 U111(tt) -> 0 U121(tt, M', N') -> U122(equal(_>_(N', M'), true), M', N') U122(tt, M', N') -> gcd(d(N', M'), M') U131(tt, N') -> N' U141(tt, N) -> N U151(tt) -> s_(0) U161(tt, M', N) -> U162(equal(_>_(M', N), true)) U162(tt) -> 0 U171(tt, M', N) -> U172(equal(_>_(N, M'), true), M', N) U172(tt, M', N) -> s_(quot(d(N, M'), M')) U21(tt, M, N) -> s_(_+_(N, _+_(M, _*_(N, M)))) U31(tt, N) -> N U41(tt, M, N) -> s_(s_(_+_(N, M))) U51(tt, M, N) -> _>_(M, N) U61(tt) -> false U71(tt) -> true U81(tt, M, N) -> _>_(N, M) U91(tt, N) -> N _*_(N, 0) -> U11(isNat(N)) _*_(s_(N), s_(M)) -> U21(and(isNat(M), isNat(N)), M, N) _+_(N, 0) -> U31(isNat(N), N) _+_(s_(N), s_(M)) -> U41(and(isNat(M), isNat(N)), M, N) _<_(N, M) -> U51(and(isNat(M), isNat(N)), M, N) _>_(0, M) -> U61(isNat(M)) _>_(N', 0) -> U71(isNzNat(N')) _>_(s_(N), s_(M)) -> U81(and(isNat(M), isNat(N)), M, N) and(tt, X) -> X d(0, N) -> U91(isNat(N), N) d(s_(N), s_(M)) -> U101(and(isNat(M), isNat(N)), M, N)
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