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TRS Standard pair #487070209
details
property
value
status
complete
benchmark
Ex9_BLR02_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n178.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.355508 seconds
cpu usage
0.344535
user time
0.270926
system time
0.073609
max virtual memory
113188.0
max residence set size
11504.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S M:S N:S X:S X1:S X2:S X3:S Y:S) (RULES active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) active(filter(cons(X:S,Y:S),s(N:S),M:S)) -> mark(cons(X:S,filter(Y:S,N:S,M:S))) active(filter(cons(X:S,Y:S),0,M:S)) -> mark(cons(0,filter(Y:S,M:S,M:S))) active(filter(X1:S,X2:S,X3:S)) -> filter(active(X1:S),X2:S,X3:S) active(filter(X1:S,X2:S,X3:S)) -> filter(X1:S,active(X2:S),X3:S) active(filter(X1:S,X2:S,X3:S)) -> filter(X1:S,X2:S,active(X3:S)) active(nats(N:S)) -> mark(cons(N:S,nats(s(N:S)))) active(nats(X:S)) -> nats(active(X:S)) active(s(X:S)) -> s(active(X:S)) active(sieve(cons(s(N:S),Y:S))) -> mark(cons(s(N:S),sieve(filter(Y:S,N:S,N:S)))) active(sieve(cons(0,Y:S))) -> mark(cons(0,sieve(Y:S))) active(sieve(X:S)) -> sieve(active(X:S)) active(zprimes) -> mark(sieve(nats(s(s(0))))) cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) filter(mark(X1:S),X2:S,X3:S) -> mark(filter(X1:S,X2:S,X3:S)) filter(ok(X1:S),ok(X2:S),ok(X3:S)) -> ok(filter(X1:S,X2:S,X3:S)) filter(X1:S,mark(X2:S),X3:S) -> mark(filter(X1:S,X2:S,X3:S)) filter(X1:S,X2:S,mark(X3:S)) -> mark(filter(X1:S,X2:S,X3:S)) nats(mark(X:S)) -> mark(nats(X:S)) nats(ok(X:S)) -> ok(nats(X:S)) proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) proper(filter(X1:S,X2:S,X3:S)) -> filter(proper(X1:S),proper(X2:S),proper(X3:S)) proper(nats(X:S)) -> nats(proper(X:S)) proper(s(X:S)) -> s(proper(X:S)) proper(sieve(X:S)) -> sieve(proper(X:S)) proper(0) -> ok(0) proper(zprimes) -> ok(zprimes) s(mark(X:S)) -> mark(s(X:S)) s(ok(X:S)) -> ok(s(X:S)) sieve(mark(X:S)) -> mark(sieve(X:S)) sieve(ok(X:S)) -> ok(sieve(X:S)) top(mark(X:S)) -> top(proper(X:S)) top(ok(X:S)) -> top(active(X:S)) ) Problem 1: Dependency Pairs Processor: -> Pairs: ACTIVE(cons(X1:S,X2:S)) -> ACTIVE(X1:S) ACTIVE(cons(X1:S,X2:S)) -> CONS(active(X1:S),X2:S) ACTIVE(filter(cons(X:S,Y:S),s(N:S),M:S)) -> CONS(X:S,filter(Y:S,N:S,M:S)) ACTIVE(filter(cons(X:S,Y:S),s(N:S),M:S)) -> FILTER(Y:S,N:S,M:S) ACTIVE(filter(cons(X:S,Y:S),0,M:S)) -> CONS(0,filter(Y:S,M:S,M:S)) ACTIVE(filter(cons(X:S,Y:S),0,M:S)) -> FILTER(Y:S,M:S,M:S) ACTIVE(filter(X1:S,X2:S,X3:S)) -> ACTIVE(X1:S) ACTIVE(filter(X1:S,X2:S,X3:S)) -> ACTIVE(X2:S) ACTIVE(filter(X1:S,X2:S,X3:S)) -> ACTIVE(X3:S) ACTIVE(filter(X1:S,X2:S,X3:S)) -> FILTER(active(X1:S),X2:S,X3:S) ACTIVE(filter(X1:S,X2:S,X3:S)) -> FILTER(X1:S,active(X2:S),X3:S) ACTIVE(filter(X1:S,X2:S,X3:S)) -> FILTER(X1:S,X2:S,active(X3:S)) ACTIVE(nats(N:S)) -> CONS(N:S,nats(s(N:S))) ACTIVE(nats(N:S)) -> NATS(s(N:S)) ACTIVE(nats(N:S)) -> S(N:S) ACTIVE(nats(X:S)) -> ACTIVE(X:S) ACTIVE(nats(X:S)) -> NATS(active(X:S)) ACTIVE(s(X:S)) -> ACTIVE(X:S) ACTIVE(s(X:S)) -> S(active(X:S)) ACTIVE(sieve(cons(s(N:S),Y:S))) -> CONS(s(N:S),sieve(filter(Y:S,N:S,N:S))) ACTIVE(sieve(cons(s(N:S),Y:S))) -> FILTER(Y:S,N:S,N:S) ACTIVE(sieve(cons(s(N:S),Y:S))) -> SIEVE(filter(Y:S,N:S,N:S)) ACTIVE(sieve(cons(0,Y:S))) -> CONS(0,sieve(Y:S)) ACTIVE(sieve(cons(0,Y:S))) -> SIEVE(Y:S) ACTIVE(sieve(X:S)) -> ACTIVE(X:S) ACTIVE(sieve(X:S)) -> SIEVE(active(X:S)) CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) CONS(ok(X1:S),ok(X2:S)) -> CONS(X1:S,X2:S) FILTER(mark(X1:S),X2:S,X3:S) -> FILTER(X1:S,X2:S,X3:S) FILTER(ok(X1:S),ok(X2:S),ok(X3:S)) -> FILTER(X1:S,X2:S,X3:S) FILTER(X1:S,mark(X2:S),X3:S) -> FILTER(X1:S,X2:S,X3:S) FILTER(X1:S,X2:S,mark(X3:S)) -> FILTER(X1:S,X2:S,X3:S) NATS(mark(X:S)) -> NATS(X:S) NATS(ok(X:S)) -> NATS(X:S) PROPER(cons(X1:S,X2:S)) -> CONS(proper(X1:S),proper(X2:S)) PROPER(cons(X1:S,X2:S)) -> PROPER(X1:S) PROPER(cons(X1:S,X2:S)) -> PROPER(X2:S) PROPER(filter(X1:S,X2:S,X3:S)) -> FILTER(proper(X1:S),proper(X2:S),proper(X3:S)) PROPER(filter(X1:S,X2:S,X3:S)) -> PROPER(X1:S) PROPER(filter(X1:S,X2:S,X3:S)) -> PROPER(X2:S) PROPER(filter(X1:S,X2:S,X3:S)) -> PROPER(X3:S) PROPER(nats(X:S)) -> NATS(proper(X:S)) PROPER(nats(X:S)) -> PROPER(X:S) PROPER(s(X:S)) -> PROPER(X:S) PROPER(s(X:S)) -> S(proper(X:S)) PROPER(sieve(X:S)) -> PROPER(X:S) PROPER(sieve(X:S)) -> SIEVE(proper(X:S)) S(mark(X:S)) -> S(X:S) S(ok(X:S)) -> S(X:S) SIEVE(mark(X:S)) -> SIEVE(X:S) SIEVE(ok(X:S)) -> SIEVE(X:S) TOP(mark(X:S)) -> PROPER(X:S) TOP(mark(X:S)) -> TOP(proper(X:S)) TOP(ok(X:S)) -> ACTIVE(X:S)
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