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TRS Innermost pair #487093460
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
n146.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.305046 seconds
cpu usage
0.309184
user time
0.261792
system time
0.047392
max virtual memory
113188.0
max residence set size
9360.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S L:S N:S V:S V1:S V2:S X:S X1:S X2:S) (RULES a__U11(tt,L:S) -> s(a__length(mark(L:S))) a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) a__and(tt,X:S) -> mark(X:S) a__and(X1:S,X2:S) -> and(X1:S,X2:S) a__isNat(0) -> tt a__isNat(length(V1:S)) -> a__isNatList(V1:S) a__isNat(s(V1:S)) -> a__isNat(V1:S) a__isNat(X:S) -> isNat(X:S) a__isNatIList(cons(V1:S,V2:S)) -> a__and(a__isNat(V1:S),isNatIList(V2:S)) a__isNatIList(zeros) -> tt a__isNatIList(V:S) -> a__isNatList(V:S) a__isNatIList(X:S) -> isNatIList(X:S) a__isNatList(cons(V1:S,V2:S)) -> a__and(a__isNat(V1:S),isNatList(V2:S)) a__isNatList(nil) -> tt a__isNatList(X:S) -> isNatList(X:S) a__length(cons(N:S,L:S)) -> a__U11(a__and(a__isNatList(L:S),isNat(N:S)),L:S) a__length(nil) -> 0 a__length(X:S) -> length(X:S) a__zeros -> cons(0,zeros) a__zeros -> zeros mark(0) -> 0 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) mark(isNat(X:S)) -> a__isNat(X:S) mark(isNatIList(X:S)) -> a__isNatIList(X:S) mark(isNatList(X:S)) -> a__isNatList(X:S) mark(length(X:S)) -> a__length(mark(X:S)) mark(nil) -> nil mark(s(X:S)) -> s(mark(X:S)) mark(tt) -> tt mark(zeros) -> a__zeros ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: A__U11(tt,L:S) -> A__LENGTH(mark(L:S)) A__U11(tt,L:S) -> MARK(L:S) A__AND(tt,X:S) -> MARK(X:S) A__ISNAT(length(V1:S)) -> A__ISNATLIST(V1:S) A__ISNAT(s(V1:S)) -> A__ISNAT(V1:S) A__ISNATILIST(cons(V1:S,V2:S)) -> A__AND(a__isNat(V1:S),isNatIList(V2:S)) A__ISNATILIST(cons(V1:S,V2:S)) -> A__ISNAT(V1:S) A__ISNATILIST(V:S) -> A__ISNATLIST(V:S) A__ISNATLIST(cons(V1:S,V2:S)) -> A__AND(a__isNat(V1:S),isNatList(V2:S)) A__ISNATLIST(cons(V1:S,V2:S)) -> A__ISNAT(V1:S) A__LENGTH(cons(N:S,L:S)) -> A__U11(a__and(a__isNatList(L:S),isNat(N:S)),L:S) A__LENGTH(cons(N:S,L:S)) -> A__AND(a__isNatList(L:S),isNat(N:S)) A__LENGTH(cons(N:S,L:S)) -> A__ISNATLIST(L:S) MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S) MARK(U11(X1:S,X2:S)) -> MARK(X1:S) MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S) MARK(and(X1:S,X2:S)) -> MARK(X1:S) MARK(cons(X1:S,X2:S)) -> MARK(X1:S) MARK(isNat(X:S)) -> A__ISNAT(X:S) MARK(isNatIList(X:S)) -> A__ISNATILIST(X:S) MARK(isNatList(X:S)) -> A__ISNATLIST(X:S) MARK(length(X:S)) -> A__LENGTH(mark(X:S)) MARK(length(X:S)) -> MARK(X:S) MARK(s(X:S)) -> MARK(X:S) MARK(zeros) -> A__ZEROS -> Rules: a__U11(tt,L:S) -> s(a__length(mark(L:S))) a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) a__and(tt,X:S) -> mark(X:S) a__and(X1:S,X2:S) -> and(X1:S,X2:S) a__isNat(0) -> tt a__isNat(length(V1:S)) -> a__isNatList(V1:S) a__isNat(s(V1:S)) -> a__isNat(V1:S) a__isNat(X:S) -> isNat(X:S) a__isNatIList(cons(V1:S,V2:S)) -> a__and(a__isNat(V1:S),isNatIList(V2:S)) a__isNatIList(zeros) -> tt a__isNatIList(V:S) -> a__isNatList(V:S) a__isNatIList(X:S) -> isNatIList(X:S) a__isNatList(cons(V1:S,V2:S)) -> a__and(a__isNat(V1:S),isNatList(V2:S)) a__isNatList(nil) -> tt a__isNatList(X:S) -> isNatList(X:S) a__length(cons(N:S,L:S)) -> a__U11(a__and(a__isNatList(L:S),isNat(N:S)),L:S) a__length(nil) -> 0 a__length(X:S) -> length(X:S) a__zeros -> cons(0,zeros) a__zeros -> zeros mark(0) -> 0 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) mark(isNat(X:S)) -> a__isNat(X:S) mark(isNatIList(X:S)) -> a__isNatIList(X:S) mark(isNatList(X:S)) -> a__isNatList(X:S) mark(length(X:S)) -> a__length(mark(X:S)) mark(nil) -> nil
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