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TRS Standard pair #487069359
details
property
value
status
complete
benchmark
PEANO_complete_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n182.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
15.7308 seconds
cpu usage
14.2763
user time
11.6703
system time
2.60598
max virtual memory
712132.0
max residence set size
21820.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S M:S N:S V1:S V2:S X:S X1:S X2:S X3:S) (RULES a__U11(tt,V1:S,V2:S) -> a__U12(a__isNat(V1:S),V2:S) a__U11(X1:S,X2:S,X3:S) -> U11(X1:S,X2:S,X3:S) a__U12(tt,V2:S) -> a__U13(a__isNat(V2:S)) a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) a__U13(tt) -> tt a__U13(X:S) -> U13(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,N:S) -> mark(N:S) a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) a__U41(tt,M:S,N:S) -> s(a__plus(mark(N:S),mark(M:S))) a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3: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(plus(V1:S,V2:S)) -> a__U11(a__and(a__isNatKind(V1:S),isNatKind(V2:S)),V1:S,V2:S) a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) a__isNat(X:S) -> isNat(X:S) a__isNatKind(0) -> tt a__isNatKind(plus(V1:S,V2:S)) -> a__and(a__isNatKind(V1:S),isNatKind(V2:S)) a__isNatKind(s(V1:S)) -> a__isNatKind(V1:S) a__isNatKind(X:S) -> isNatKind(X:S) a__plus(N:S,0) -> a__U31(a__and(a__isNat(N:S),isNatKind(N:S)),N:S) a__plus(N:S,s(M:S)) -> a__U41(a__and(a__and(a__isNat(M:S),isNatKind(M:S)),and(isNat(N:S),isNatKind(N:S))),M:S,N:S) a__plus(X1:S,X2:S) -> plus(X1:S,X2:S) mark(0) -> 0 mark(U11(X1:S,X2:S,X3:S)) -> a__U11(mark(X1:S),X2:S,X3:S) mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) mark(U13(X:S)) -> a__U13(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(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S) mark(isNat(X:S)) -> a__isNat(X:S) mark(isNatKind(X:S)) -> a__isNatKind(X:S) mark(plus(X1:S,X2:S)) -> a__plus(mark(X1:S),mark(X2:S)) mark(s(X:S)) -> s(mark(X:S)) mark(tt) -> tt ) Problem 1: Dependency Pairs Processor: -> Pairs: A__U11(tt,V1:S,V2:S) -> A__U12(a__isNat(V1:S),V2:S) A__U11(tt,V1:S,V2:S) -> A__ISNAT(V1:S) A__U12(tt,V2:S) -> A__U13(a__isNat(V2:S)) A__U12(tt,V2:S) -> A__ISNAT(V2:S) A__U21(tt,V1:S) -> A__U22(a__isNat(V1:S)) A__U21(tt,V1:S) -> A__ISNAT(V1:S) A__U31(tt,N:S) -> MARK(N:S) A__U41(tt,M:S,N:S) -> A__PLUS(mark(N:S),mark(M:S)) A__U41(tt,M:S,N:S) -> MARK(M:S) A__U41(tt,M:S,N:S) -> MARK(N:S) A__AND(tt,X:S) -> MARK(X:S) A__ISNAT(plus(V1:S,V2:S)) -> A__U11(a__and(a__isNatKind(V1:S),isNatKind(V2:S)),V1:S,V2:S) A__ISNAT(plus(V1:S,V2:S)) -> A__AND(a__isNatKind(V1:S),isNatKind(V2:S)) A__ISNAT(plus(V1:S,V2:S)) -> A__ISNATKIND(V1:S) A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S) A__ISNAT(s(V1:S)) -> A__ISNATKIND(V1:S) A__ISNATKIND(plus(V1:S,V2:S)) -> A__AND(a__isNatKind(V1:S),isNatKind(V2:S)) A__ISNATKIND(plus(V1:S,V2:S)) -> A__ISNATKIND(V1:S) A__ISNATKIND(s(V1:S)) -> A__ISNATKIND(V1:S) A__PLUS(N:S,0) -> A__U31(a__and(a__isNat(N:S),isNatKind(N:S)),N:S) A__PLUS(N:S,0) -> A__AND(a__isNat(N:S),isNatKind(N:S)) A__PLUS(N:S,0) -> A__ISNAT(N:S) A__PLUS(N:S,s(M:S)) -> A__U41(a__and(a__and(a__isNat(M:S),isNatKind(M:S)),and(isNat(N:S),isNatKind(N:S))),M:S,N:S) A__PLUS(N:S,s(M:S)) -> A__AND(a__and(a__isNat(M:S),isNatKind(M:S)),and(isNat(N:S),isNatKind(N:S))) A__PLUS(N:S,s(M:S)) -> A__AND(a__isNat(M:S),isNatKind(M:S)) A__PLUS(N:S,s(M:S)) -> A__ISNAT(M:S) MARK(U11(X1:S,X2:S,X3:S)) -> A__U11(mark(X1:S),X2:S,X3:S) MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S) MARK(U12(X1:S,X2:S)) -> A__U12(mark(X1:S),X2:S) MARK(U12(X1:S,X2:S)) -> MARK(X1:S) MARK(U13(X:S)) -> A__U13(mark(X:S)) MARK(U13(X:S)) -> MARK(X:S) MARK(U21(X1:S,X2:S)) -> A__U21(mark(X1:S),X2:S) MARK(U21(X1:S,X2:S)) -> MARK(X1:S) MARK(U22(X:S)) -> A__U22(mark(X:S)) MARK(U22(X:S)) -> MARK(X:S) MARK(U31(X1:S,X2:S)) -> A__U31(mark(X1:S),X2:S) MARK(U31(X1:S,X2:S)) -> MARK(X1:S) MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) MARK(U41(X1:S,X2:S,X3: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(isNat(X:S)) -> A__ISNAT(X:S) MARK(isNatKind(X:S)) -> A__ISNATKIND(X:S) MARK(plus(X1:S,X2:S)) -> A__PLUS(mark(X1:S),mark(X2:S)) MARK(plus(X1:S,X2:S)) -> MARK(X1:S) MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
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