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TRS Innermost pair #487093461
details
property
value
status
complete
benchmark
LengthOfFiniteLists_nokinds_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.38111 seconds
cpu usage
5.86017
user time
5.57569
system time
0.284482
max virtual memory
1.8418344E7
max residence set size
386136.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 124 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 33 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 6 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 13 ms] (10) QTRS (11) QTRSRRRProof [EQUIVALENT, 15 ms] (12) QTRS (13) QTRSRRRProof [EQUIVALENT, 0 ms] (14) QTRS (15) RisEmptyProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__U11(tt, L) -> s(a__length(mark(L))) a__and(tt, X) -> mark(X) a__isNat(0) -> tt a__isNat(length(V1)) -> a__isNatList(V1) a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(V) -> a__isNatList(V) a__isNatIList(zeros) -> tt a__isNatIList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatIList(V2)) a__isNatList(nil) -> tt a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2)) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U11(a__and(a__isNatList(L), isNat(N)), L) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(X) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__length(X) -> length(X) a__and(X1, X2) -> and(X1, X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) The set Q consists of the following terms: a__zeros a__isNatIList(x0) mark(zeros) mark(U11(x0, x1)) mark(length(x0)) mark(and(x0, x1)) mark(isNat(x0)) mark(isNatList(x0)) mark(isNatIList(x0)) mark(cons(x0, x1)) mark(0) mark(tt) mark(s(x0)) mark(nil) a__U11(x0, x1) a__length(x0) a__and(x0, x1) a__isNat(x0) a__isNatList(x0) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(U11(x_1, x_2)) = 2*x_1 + 2*x_2 POL(a__U11(x_1, x_2)) = 2*x_1 + 2*x_2 POL(a__and(x_1, x_2)) = x_1 + 2*x_2 POL(a__isNat(x_1)) = x_1
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