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TRS Standard pair #487069463
details
property
value
status
complete
benchmark
MYNAT_nosorts_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.89321 seconds
cpu usage
4.62084
user time
4.41063
system time
0.210204
max virtual memory
1.8408912E7
max residence set size
278144.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 229 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4)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: a__U11(tt, M, N) -> a__U12(tt, M, N) a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__U21(tt, M, N) -> a__U22(tt, M, N) a__U22(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) a__plus(N, 0) -> mark(N) a__plus(N, s(M)) -> a__U11(tt, M, N) a__x(N, 0) -> 0 a__x(N, s(M)) -> a__U21(tt, M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2, X3) -> U12(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__U21(X1, X2, X3) -> U21(X1, X2, X3) a__U22(X1, X2, X3) -> U22(X1, X2, X3) a__x(X1, X2) -> x(X1, X2) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: a__U11/3(YES,YES,YES) tt/0) a__U12/3(YES,YES,YES) s/1(YES) a__plus/2(YES,YES) mark/1)YES( a__U21/3(YES,YES,YES) a__U22/3(YES,YES,YES) a__x/2(YES,YES) 0/0) U11/3(YES,YES,YES) U12/3(YES,YES,YES) plus/2(YES,YES) U21/3(YES,YES,YES) U22/3(YES,YES,YES) x/2(YES,YES) Quasi precedence: [a__U21_3, a__U22_3, a__x_2, U21_3, U22_3, x_2] > [a__U11_3, a__U12_3, a__plus_2, U11_3, U12_3, plus_2] > [tt, s_1] 0 > [tt, s_1] Status: a__U11_3: multiset status tt: multiset status a__U12_3: multiset status s_1: multiset status a__plus_2: multiset status a__U21_3: [3,2,1] a__U22_3: [3,2,1] a__x_2: [1,2] 0: multiset status U11_3: multiset status U12_3: multiset status plus_2: multiset status U21_3: [3,2,1] U22_3: [3,2,1] x_2: [1,2] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__U22(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) a__plus(N, 0) -> mark(N) a__plus(N, s(M)) -> a__U11(tt, M, N) a__x(N, 0) -> 0 a__x(N, s(M)) -> a__U21(tt, M, N)
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