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TRS Innermost pair #487093496
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
n147.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
1.5971 seconds
cpu usage
1.40957
user time
1.08051
system time
0.329065
max virtual memory
707760.0
max residence set size
11272.0
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 ) (STRATEGY INNERMOST) 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)
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