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TRS Contextsensitive pair #487092592
details
property
value
status
complete
benchmark
MYNAT_complete-peanoSimple.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
Maude_06
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.259137 seconds
cpu usage
0.270173
user time
0.207793
system time
0.06238
max virtual memory
113188.0
max residence set size
8200.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR M N V1 V2 X) (STRATEGY CONTEXTSENSITIVE (U11 1) (U12 1) (U13 1) (U21 1) (U22 1) (U31 1) (U41 1) (and 1) (isNat) (isNatKind) (plus 1 2) (0) (s 1) (tt) ) (RULES U11(tt,V1,V2) -> U12(isNat(V1),V2) U12(tt,V2) -> U13(isNat(V2)) U13(tt) -> tt U21(tt,V1) -> U22(isNat(V1)) U22(tt) -> tt U31(tt,N) -> N U41(tt,M,N) -> s(plus(N,M)) and(tt,X) -> X isNat(plus(V1,V2)) -> U11(and(isNatKind(V1),isNatKind(V2)),V1,V2) isNat(0) -> tt isNat(s(V1)) -> U21(isNatKind(V1),V1) isNatKind(plus(V1,V2)) -> and(isNatKind(V1),isNatKind(V2)) isNatKind(0) -> tt isNatKind(s(V1)) -> isNatKind(V1) plus(N,0) -> U31(and(isNat(N),isNatKind(N)),N) plus(N,s(M)) -> U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) ) Problem 1: Dependency Pairs Processor: -> Pairs: U11#(tt,V1,V2) -> U12#(isNat(V1),V2) U11#(tt,V1,V2) -> ISNAT(V1) U12#(tt,V2) -> U13#(isNat(V2)) U12#(tt,V2) -> ISNAT(V2) U21#(tt,V1) -> U22#(isNat(V1)) U21#(tt,V1) -> ISNAT(V1) U31#(tt,N) -> N U41#(tt,M,N) -> PLUS(N,M) U41#(tt,M,N) -> M U41#(tt,M,N) -> N AND(tt,X) -> X ISNAT(plus(V1,V2)) -> U11#(and(isNatKind(V1),isNatKind(V2)),V1,V2) ISNAT(plus(V1,V2)) -> AND(isNatKind(V1),isNatKind(V2)) ISNAT(plus(V1,V2)) -> ISNATKIND(V1) ISNAT(s(V1)) -> U21#(isNatKind(V1),V1) ISNAT(s(V1)) -> ISNATKIND(V1) ISNATKIND(plus(V1,V2)) -> AND(isNatKind(V1),isNatKind(V2)) ISNATKIND(plus(V1,V2)) -> ISNATKIND(V1) ISNATKIND(s(V1)) -> ISNATKIND(V1) PLUS(N,0) -> U31#(and(isNat(N),isNatKind(N)),N) PLUS(N,0) -> AND(isNat(N),isNatKind(N)) PLUS(N,0) -> ISNAT(N) PLUS(N,s(M)) -> U41#(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) PLUS(N,s(M)) -> AND(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))) PLUS(N,s(M)) -> AND(isNat(M),isNatKind(M)) PLUS(N,s(M)) -> ISNAT(M) -> Rules: U11(tt,V1,V2) -> U12(isNat(V1),V2) U12(tt,V2) -> U13(isNat(V2)) U13(tt) -> tt U21(tt,V1) -> U22(isNat(V1)) U22(tt) -> tt U31(tt,N) -> N U41(tt,M,N) -> s(plus(N,M)) and(tt,X) -> X isNat(plus(V1,V2)) -> U11(and(isNatKind(V1),isNatKind(V2)),V1,V2) isNat(0) -> tt isNat(s(V1)) -> U21(isNatKind(V1),V1) isNatKind(plus(V1,V2)) -> and(isNatKind(V1),isNatKind(V2)) isNatKind(0) -> tt isNatKind(s(V1)) -> isNatKind(V1) plus(N,0) -> U31(and(isNat(N),isNatKind(N)),N) plus(N,s(M)) -> U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) -> Unhiding Rules: and(isNat(N),isNatKind(N)) -> AND(isNat(N),isNatKind(N)) and(isNat(N),isNatKind(N)) -> ISNAT(N) isNatKind(M) -> ISNATKIND(M) isNatKind(N) -> ISNATKIND(N) isNatKind(V2) -> ISNATKIND(V2) Problem 1: SCC Processor: -> Pairs: U11#(tt,V1,V2) -> U12#(isNat(V1),V2) U11#(tt,V1,V2) -> ISNAT(V1)
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