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TRS Innermost pair #487093192
details
property
value
status
complete
benchmark
LengthOfFiniteLists_complete_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
21.5592 seconds
cpu usage
20.7748
user time
18.3949
system time
2.37991
max virtual memory
716588.0
max residence set size
38124.0
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 X3:S) (RULES a__U11(tt,V1:S) -> a__U12(a__isNatList(V1:S)) a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) a__U12(tt) -> tt a__U12(X:S) -> U12(X:S) a__U21(tt,V1:S) -> a__U22(a__isNat(V1:S)) a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) a__U22(tt) -> tt a__U22(X:S) -> U22(X:S) a__U31(tt,V:S) -> a__U32(a__isNatList(V:S)) a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) a__U32(tt) -> tt a__U32(X:S) -> U32(X:S) a__U41(tt,V1:S,V2:S) -> a__U42(a__isNat(V1:S),V2:S) a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) a__U42(tt,V2:S) -> a__U43(a__isNatIList(V2:S)) a__U42(X1:S,X2:S) -> U42(X1:S,X2:S) a__U43(tt) -> tt a__U43(X:S) -> U43(X:S) a__U51(tt,V1:S,V2:S) -> a__U52(a__isNat(V1:S),V2:S) a__U51(X1:S,X2:S,X3:S) -> U51(X1:S,X2:S,X3:S) a__U52(tt,V2:S) -> a__U53(a__isNatList(V2:S)) a__U52(X1:S,X2:S) -> U52(X1:S,X2:S) a__U53(tt) -> tt a__U53(X:S) -> U53(X:S) a__U61(tt,L:S) -> s(a__length(mark(L:S))) a__U61(X1:S,X2:S) -> U61(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__U11(a__isNatIListKind(V1:S),V1:S) a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) a__isNat(X:S) -> isNat(X:S) a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__and(a__isNatKind(V1:S),isNatIListKind(V2:S)),V1:S,V2:S) a__isNatIList(zeros) -> tt a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) a__isNatIList(X:S) -> isNatIList(X:S) a__isNatIListKind(cons(V1:S,V2:S)) -> a__and(a__isNatKind(V1:S),isNatIListKind(V2:S)) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(X:S) -> isNatIListKind(X:S) a__isNatKind(0) -> tt a__isNatKind(length(V1:S)) -> a__isNatIListKind(V1:S) a__isNatKind(s(V1:S)) -> a__isNatKind(V1:S) a__isNatKind(X:S) -> isNatKind(X:S) a__isNatList(cons(V1:S,V2:S)) -> a__U51(a__and(a__isNatKind(V1:S),isNatIListKind(V2:S)),V1:S,V2:S) a__isNatList(nil) -> tt a__isNatList(X:S) -> isNatList(X:S) a__length(cons(N:S,L:S)) -> a__U61(a__and(a__and(a__isNatList(L:S),isNatIListKind(L:S)),and(isNat(N:S),isNatKind(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(U12(X:S)) -> a__U12(mark(X:S)) mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) mark(U22(X:S)) -> a__U22(mark(X:S)) mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) mark(U32(X:S)) -> a__U32(mark(X:S)) mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) mark(U42(X1:S,X2:S)) -> a__U42(mark(X1:S),X2:S) mark(U43(X:S)) -> a__U43(mark(X:S)) mark(U51(X1:S,X2:S,X3:S)) -> a__U51(mark(X1:S),X2:S,X3:S) mark(U52(X1:S,X2:S)) -> a__U52(mark(X1:S),X2:S) mark(U53(X:S)) -> a__U53(mark(X:S)) mark(U61(X1:S,X2:S)) -> a__U61(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(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) mark(isNatKind(X:S)) -> a__isNatKind(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,V1:S) -> A__U12(a__isNatList(V1:S)) A__U11(tt,V1:S) -> A__ISNATLIST(V1:S) A__U21(tt,V1:S) -> A__U22(a__isNat(V1:S)) A__U21(tt,V1:S) -> A__ISNAT(V1:S) A__U31(tt,V:S) -> A__U32(a__isNatList(V:S)) A__U31(tt,V:S) -> A__ISNATLIST(V:S) A__U41(tt,V1:S,V2:S) -> A__U42(a__isNat(V1:S),V2:S) A__U41(tt,V1:S,V2:S) -> A__ISNAT(V1:S) A__U42(tt,V2:S) -> A__U43(a__isNatIList(V2:S))
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