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TRS Standard pair #487069548
details
property
value
status
complete
benchmark
MYNAT_nosorts-noand_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n182.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.81288 seconds
cpu usage
3.9676
user time
3.79882
system time
0.168786
max virtual memory
1.8408912E7
max residence set size
248924.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 96 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: U11(tt, M, N) -> U12(tt, activate(M), activate(N)) U12(tt, M, N) -> s(plus(activate(N), activate(M))) U21(tt, M, N) -> U22(tt, activate(M), activate(N)) U22(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) plus(N, 0) -> N plus(N, s(M)) -> U11(tt, M, N) x(N, 0) -> 0 x(N, s(M)) -> U21(tt, M, N) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: U11/3(YES,YES,YES) tt/0) U12/3(YES,YES,YES) activate/1)YES( s/1(YES) plus/2(YES,YES) U21/3(YES,YES,YES) U22/3(YES,YES,YES) x/2(YES,YES) 0/0) Quasi precedence: [U21_3, U22_3, x_2] > [U11_3, U12_3, plus_2] > s_1 > [tt, 0] Status: U11_3: multiset status tt: multiset status U12_3: multiset status s_1: multiset status plus_2: multiset status U21_3: multiset status U22_3: multiset status x_2: multiset status 0: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: U12(tt, M, N) -> s(plus(activate(N), activate(M))) U22(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) plus(N, 0) -> N plus(N, s(M)) -> U11(tt, M, N) x(N, 0) -> 0 x(N, s(M)) -> U21(tt, M, N) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: U11(tt, M, N) -> U12(tt, activate(M), activate(N)) U21(tt, M, N) -> U22(tt, activate(M), activate(N)) activate(X) -> X Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:U21_3 > U22_3 > activate_1 > U11_3 > U12_3 > tt and weight map: tt=1 activate_1=1
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