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TRS Innermost pair #487093456
details
property
value
status
complete
benchmark
PEANO_nokinds_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.274057 seconds
cpu usage
0.282497
user time
0.232665
system time
0.049832
max virtual memory
113188.0
max residence set size
9904.0
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,V2:S) -> a__U12(a__isNat(V2: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) -> tt a__U21(X:S) -> U21(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) -> a__U42(a__isNat(N:S),M:S,N:S) a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) a__U42(tt,M:S,N:S) -> s(a__plus(mark(N:S),mark(M:S))) a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) a__isNat(0) -> tt a__isNat(plus(V1:S,V2:S)) -> a__U11(a__isNat(V1:S),V2:S) a__isNat(s(V1:S)) -> a__U21(a__isNat(V1:S)) a__isNat(X:S) -> isNat(X:S) a__plus(N:S,0) -> a__U31(a__isNat(N:S),N:S) a__plus(N:S,s(M:S)) -> a__U41(a__isNat(M: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)) -> a__U11(mark(X1:S),X2:S) mark(U12(X:S)) -> a__U12(mark(X:S)) mark(U21(X:S)) -> a__U21(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(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) mark(isNat(X:S)) -> a__isNat(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 ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: A__U11(tt,V2:S) -> A__U12(a__isNat(V2:S)) A__U11(tt,V2:S) -> A__ISNAT(V2:S) A__U31(tt,N:S) -> MARK(N:S) A__U41(tt,M:S,N:S) -> A__U42(a__isNat(N:S),M:S,N:S) A__U41(tt,M:S,N:S) -> A__ISNAT(N:S) A__U42(tt,M:S,N:S) -> A__PLUS(mark(N:S),mark(M:S)) A__U42(tt,M:S,N:S) -> MARK(M:S) A__U42(tt,M:S,N:S) -> MARK(N:S) A__ISNAT(plus(V1:S,V2:S)) -> A__U11(a__isNat(V1:S),V2:S) A__ISNAT(plus(V1:S,V2:S)) -> A__ISNAT(V1:S) A__ISNAT(s(V1:S)) -> A__U21(a__isNat(V1:S)) A__ISNAT(s(V1:S)) -> A__ISNAT(V1:S) A__PLUS(N:S,0) -> A__U31(a__isNat(N:S),N:S) A__PLUS(N:S,0) -> A__ISNAT(N:S) A__PLUS(N:S,s(M:S)) -> A__U41(a__isNat(M:S),M:S,N:S) A__PLUS(N:S,s(M:S)) -> A__ISNAT(M:S) MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S) MARK(U11(X1:S,X2:S)) -> MARK(X1:S) MARK(U12(X:S)) -> A__U12(mark(X:S)) MARK(U12(X:S)) -> MARK(X:S) MARK(U21(X:S)) -> A__U21(mark(X:S)) MARK(U21(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(U42(X1:S,X2:S,X3:S)) -> A__U42(mark(X1:S),X2:S,X3:S) MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S) MARK(isNat(X:S)) -> A__ISNAT(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) MARK(s(X:S)) -> MARK(X:S) -> Rules: a__U11(tt,V2:S) -> a__U12(a__isNat(V2: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) -> tt a__U21(X:S) -> U21(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) -> a__U42(a__isNat(N:S),M:S,N:S) a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) a__U42(tt,M:S,N:S) -> s(a__plus(mark(N:S),mark(M:S))) a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) a__isNat(0) -> tt a__isNat(plus(V1:S,V2:S)) -> a__U11(a__isNat(V1:S),V2:S) a__isNat(s(V1:S)) -> a__U21(a__isNat(V1:S)) a__isNat(X:S) -> isNat(X:S) a__plus(N:S,0) -> a__U31(a__isNat(N:S),N:S) a__plus(N:S,s(M:S)) -> a__U41(a__isNat(M: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)) -> a__U11(mark(X1:S),X2:S) mark(U12(X:S)) -> a__U12(mark(X:S)) mark(U21(X:S)) -> a__U21(mark(X:S))
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