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TRS Standard pair #487070524
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
n070.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
14.1538 seconds
cpu usage
13.8838
user time
12.2392
system time
1.64459
max virtual memory
716784.0
max residence set size
35576.0
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 ) 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)) A__U42(tt,V2:S) -> A__ISNATILIST(V2:S)
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