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TRS_Equational 2019-03-21 05.09 pair #429997138
details
property
value
status
complete
benchmark
PEANO-NAT_nosorts-noand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n113.star.cs.uiowa.edu
space
Mixed_C
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
5.64016 seconds
cpu usage
10.7363
user time
10.1029
system time
0.633376
max virtual memory
1.827956E7
max residence set size
2095768.0
stage attributes
key
value
starexec-result
MAYBE
output
10.49/5.50 MAYBE 10.49/5.52 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 10.49/5.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.49/5.52 10.49/5.52 10.49/5.52 Termination of the given ETRS could not be shown: 10.49/5.52 10.49/5.52 (0) ETRS 10.49/5.52 (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] 10.49/5.52 (2) EDP 10.49/5.52 (3) EDependencyGraphProof [EQUIVALENT, 0 ms] 10.49/5.52 (4) AND 10.49/5.52 (5) EDP 10.49/5.52 (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] 10.49/5.52 (7) EDP 10.49/5.52 (8) EUsableRulesReductionPairsProof [EQUIVALENT, 42 ms] 10.49/5.52 (9) EDP 10.49/5.52 (10) PisEmptyProof [EQUIVALENT, 0 ms] 10.49/5.52 (11) YES 10.49/5.52 (12) EDP 10.49/5.52 (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] 10.49/5.52 (14) EDP 10.49/5.52 (15) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] 10.49/5.52 (16) EDP 10.49/5.52 (17) EDependencyGraphProof [EQUIVALENT, 0 ms] 10.49/5.52 (18) TRUE 10.49/5.52 (19) EDP 10.49/5.52 (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] 10.49/5.52 (21) EDP 10.49/5.52 (22) EUsableRulesProof [EQUIVALENT, 0 ms] 10.49/5.52 (23) EDP 10.49/5.52 (24) EDP 10.49/5.52 (25) EDP 10.49/5.52 (26) EDP 10.49/5.52 10.49/5.52 10.49/5.52 ---------------------------------------- 10.49/5.52 10.49/5.52 (0) 10.49/5.52 Obligation: 10.49/5.52 Equational rewrite system: 10.49/5.52 The TRS R consists of the following rules: 10.49/5.52 10.49/5.52 1 -> s_(0) 10.49/5.52 2 -> s_(s_(0)) 10.49/5.52 3 -> s_(s_(s_(0))) 10.49/5.52 4 -> s_(s_(s_(s_(0)))) 10.49/5.52 5 -> s_(s_(s_(s_(s_(0))))) 10.49/5.52 6 -> s_(s_(s_(s_(s_(s_(0)))))) 10.49/5.52 7 -> s_(s_(s_(s_(s_(s_(s_(0))))))) 10.49/5.52 U11(tt, M, N) -> U12(tt, M, N) 10.49/5.52 U12(tt, M, N) -> s_(_+_(N, _+_(M, _*_(N, M)))) 10.49/5.52 U21(tt, M, N) -> U22(tt, M, N) 10.49/5.52 U22(tt, M, N) -> s_(s_(_+_(N, M))) 10.49/5.52 U31(tt, M, N) -> U32(tt, M, N) 10.49/5.52 U32(tt, M, N) -> _>_(M, N) 10.49/5.52 U41(tt, M, N) -> U42(tt, M, N) 10.49/5.52 U42(tt, M, N) -> _>_(N, M) 10.49/5.52 U51(tt, M, N) -> U52(tt, M, N) 10.49/5.52 U52(tt, M, N) -> d(N, M) 10.49/5.52 U61(tt, M', N') -> U62(tt, M', N') 10.49/5.52 U62(tt, M', N') -> U63(equal(_>_(N', M'), true), M', N') 10.49/5.52 U63(tt, M', N') -> gcd(d(N', M'), M') 10.49/5.52 U71(tt, M', N) -> U72(tt, M', N) 10.49/5.52 U72(tt, M', N) -> U73(equal(_>_(M', N), true)) 10.49/5.52 U73(tt) -> 0 10.49/5.52 U81(tt, M', N) -> U82(tt, M', N) 10.49/5.52 U82(tt, M', N) -> U83(equal(_>_(N, M'), true), M', N) 10.49/5.52 U83(tt, M', N) -> s_(quot(d(N, M'), M')) 10.49/5.52 _*_(N, 0) -> 0 10.49/5.52 _*_(s_(N), s_(M)) -> U11(tt, M, N) 10.49/5.52 _+_(N, 0) -> N 10.49/5.52 _+_(s_(N), s_(M)) -> U21(tt, M, N) 10.49/5.52 _<_(N, M) -> U31(tt, M, N) 10.49/5.52 _>_(0, M) -> false 10.49/5.52 _>_(N', 0) -> true 10.49/5.52 _>_(s_(N), s_(M)) -> U41(tt, M, N) 10.49/5.52 d(0, N) -> N 10.49/5.52 d(s_(N), s_(M)) -> U51(tt, M, N) 10.49/5.52 equal(X, X) -> tt 10.49/5.52 gcd(0, N) -> 0 10.49/5.52 gcd(N', M') -> U61(tt, M', N') 10.49/5.52 gcd(N', N') -> N' 10.49/5.52 p_(s_(N)) -> N 10.49/5.52 quot(M', M') -> s_(0) 10.49/5.52 quot(N, M') -> U71(tt, M', N) 10.49/5.52 quot(N, M') -> U81(tt, M', N) 10.49/5.52 10.49/5.52 The set E consists of the following equations: 10.49/5.52 10.49/5.52 _*_(x, y) == _*_(y, x) 10.49/5.52 _+_(x, y) == _+_(y, x) 10.49/5.52 d(x, y) == d(y, x) 10.49/5.52 gcd(x, y) == gcd(y, x) 10.49/5.52 10.49/5.52 10.49/5.52 ---------------------------------------- 10.49/5.52 10.49/5.52 (1) EquationalDependencyPairsProof (EQUIVALENT) 10.49/5.52 Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem:
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