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TRS Stand 20472 pair #381717017
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
n056.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.24388408661 seconds
cpu usage
6.015034167
max memory
3.82398464E8
stage attributes
key
value
output-size
14697
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 109 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 33 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 25 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 19 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 0 ms] (10) QTRS (11) QTRSRRRProof [EQUIVALENT, 0 ms] (12) QTRS (13) QTRSRRRProof [EQUIVALENT, 11 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) Q is empty. ---------------------------------------- (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 POL(a__isNatIList(x_1)) = 2*x_1 POL(a__isNatList(x_1)) = x_1 POL(a__length(x_1)) = 2*x_1 POL(a__zeros) = 0 POL(and(x_1, x_2)) = x_1 + 2*x_2 POL(cons(x_1, x_2)) = 2*x_1 + 2*x_2 POL(isNat(x_1)) = x_1 POL(isNatIList(x_1)) = 2*x_1 POL(isNatList(x_1)) = x_1 POL(length(x_1)) = 2*x_1 POL(mark(x_1)) = x_1 POL(nil) = 1 POL(s(x_1)) = x_1 POL(tt) = 0 POL(zeros) = 0
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