Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Innermost pair #487093359
details
property
value
status
complete
benchmark
Ex26_Luc03b_GM.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
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.50738 seconds
cpu usage
6.23974
user time
5.9505
system time
0.289241
max virtual memory
1.8477752E7
max residence set size
421380.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 35 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPQMonotonicMRRProof [EQUIVALENT, 113 ms] (6) QDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) QDP (9) QReductionProof [EQUIVALENT, 0 ms] (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) a__sqr(0) -> 0 a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) a__dbl(0) -> 0 a__dbl(s(X)) -> s(s(dbl(X))) a__add(0, X) -> mark(X) a__add(s(X), Y) -> s(add(X, Y)) a__first(0, X) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) mark(terms(X)) -> a__terms(mark(X)) mark(sqr(X)) -> a__sqr(mark(X)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(dbl(X)) -> a__dbl(mark(X)) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(recip(X)) -> recip(mark(X)) mark(s(X)) -> s(X) mark(0) -> 0 mark(nil) -> nil a__terms(X) -> terms(X) a__sqr(X) -> sqr(X) a__add(X1, X2) -> add(X1, X2) a__dbl(X) -> dbl(X) a__first(X1, X2) -> first(X1, X2) The set Q consists of the following terms: a__terms(x0) mark(terms(x0)) mark(sqr(x0)) mark(add(x0, x1)) mark(dbl(x0)) mark(first(x0, x1)) mark(cons(x0, x1)) mark(recip(x0)) mark(s(x0)) mark(0) mark(nil) a__sqr(x0) a__add(x0, x1) a__dbl(x0) a__first(x0, x1) ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: A__TERMS(N) -> A__SQR(mark(N)) A__TERMS(N) -> MARK(N) A__ADD(0, X) -> MARK(X) A__FIRST(s(X), cons(Y, Z)) -> MARK(Y) MARK(terms(X)) -> A__TERMS(mark(X)) MARK(terms(X)) -> MARK(X) MARK(sqr(X)) -> A__SQR(mark(X)) MARK(sqr(X)) -> MARK(X) MARK(add(X1, X2)) -> A__ADD(mark(X1), mark(X2)) MARK(add(X1, X2)) -> MARK(X1) MARK(add(X1, X2)) -> MARK(X2) MARK(dbl(X)) -> A__DBL(mark(X)) MARK(dbl(X)) -> MARK(X) MARK(first(X1, X2)) -> A__FIRST(mark(X1), mark(X2)) MARK(first(X1, X2)) -> MARK(X1) MARK(first(X1, X2)) -> MARK(X2)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Innermost