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TRS Standard pair #487071544
details
property
value
status
complete
benchmark
PEANO_nokinds_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n187.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
1.49928 seconds
cpu usage
1.41046
user time
1.05257
system time
0.357898
max virtual memory
707728.0
max residence set size
10936.0
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,N:S) -> mark(N:S) a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) a__U21(tt,M:S,N:S) -> s(a__plus(mark(N:S),mark(M:S))) a__U21(X1:S,X2:S,X3:S) -> U21(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__and(a__isNat(V1:S),isNat(V2:S)) a__isNat(s(V1:S)) -> a__isNat(V1:S) a__isNat(X:S) -> isNat(X:S) a__plus(N:S,0) -> a__U11(a__isNat(N:S),N:S) a__plus(N:S,s(M:S)) -> a__U21(a__and(a__isNat(M:S),isNat(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)) -> a__U11(mark(X1:S),X2:S) mark(U21(X1:S,X2:S,X3:S)) -> a__U21(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(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,N:S) -> MARK(N:S) A__U21(tt,M:S,N:S) -> A__PLUS(mark(N:S),mark(M:S)) A__U21(tt,M:S,N:S) -> MARK(M:S) A__U21(tt,M:S,N:S) -> MARK(N:S) A__AND(tt,X:S) -> MARK(X:S) A__ISNAT(plus(V1:S,V2:S)) -> A__AND(a__isNat(V1:S),isNat(V2:S)) A__ISNAT(plus(V1:S,V2:S)) -> A__ISNAT(V1:S) A__ISNAT(s(V1:S)) -> A__ISNAT(V1:S) A__PLUS(N:S,0) -> A__U11(a__isNat(N:S),N:S) A__PLUS(N:S,0) -> A__ISNAT(N:S) A__PLUS(N:S,s(M:S)) -> A__U21(a__and(a__isNat(M:S),isNat(N:S)),M:S,N:S) A__PLUS(N:S,s(M:S)) -> A__AND(a__isNat(M:S),isNat(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(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S) MARK(U21(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(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,N:S) -> mark(N:S) a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) a__U21(tt,M:S,N:S) -> s(a__plus(mark(N:S),mark(M:S))) a__U21(X1:S,X2:S,X3:S) -> U21(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__and(a__isNat(V1:S),isNat(V2:S)) a__isNat(s(V1:S)) -> a__isNat(V1:S) a__isNat(X:S) -> isNat(X:S) a__plus(N:S,0) -> a__U11(a__isNat(N:S),N:S) a__plus(N:S,s(M:S)) -> a__U21(a__and(a__isNat(M:S),isNat(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)) -> a__U11(mark(X1:S),X2:S) mark(U21(X1:S,X2:S,X3:S)) -> a__U21(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(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: SCC Processor: -> Pairs: A__U11(tt,N:S) -> MARK(N:S) A__U21(tt,M:S,N:S) -> A__PLUS(mark(N:S),mark(M:S)) A__U21(tt,M:S,N:S) -> MARK(M:S) A__U21(tt,M:S,N:S) -> MARK(N:S) A__AND(tt,X:S) -> MARK(X:S) A__ISNAT(plus(V1:S,V2:S)) -> A__AND(a__isNat(V1:S),isNat(V2:S)) A__ISNAT(plus(V1:S,V2:S)) -> A__ISNAT(V1:S) A__ISNAT(s(V1:S)) -> A__ISNAT(V1:S) A__PLUS(N:S,0) -> A__U11(a__isNat(N:S),N:S) A__PLUS(N:S,0) -> A__ISNAT(N:S) A__PLUS(N:S,s(M:S)) -> A__U21(a__and(a__isNat(M:S),isNat(N:S)),M:S,N:S) A__PLUS(N:S,s(M:S)) -> A__AND(a__isNat(M:S),isNat(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(U21(X1:S,X2:S,X3:S)) -> A__U21(mark(X1:S),X2:S,X3:S)
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