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TRS Standard pair #487069749
details
property
value
status
complete
benchmark
Ex26_Luc03b_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.209857 seconds
cpu usage
0.215581
user time
0.169389
system time
0.046192
max virtual memory
113188.0
max residence set size
12308.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S N:S X:S X1:S X2:S Y:S Z:S) (RULES active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S))) active(add(0,X:S)) -> mark(X:S) active(add(X1:S,X2:S)) -> add(active(X1:S),X2:S) active(add(X1:S,X2:S)) -> add(X1:S,active(X2:S)) active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) active(dbl(s(X:S))) -> mark(s(s(dbl(X:S)))) active(dbl(0)) -> mark(0) active(dbl(X:S)) -> dbl(active(X:S)) active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S))) active(first(0,X:S)) -> mark(nil) active(first(X1:S,X2:S)) -> first(active(X1:S),X2:S) active(first(X1:S,X2:S)) -> first(X1:S,active(X2:S)) active(recip(X:S)) -> recip(active(X:S)) active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S)))) active(sqr(0)) -> mark(0) active(sqr(X:S)) -> sqr(active(X:S)) active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S)))) active(terms(X:S)) -> terms(active(X:S)) add(mark(X1:S),X2:S) -> mark(add(X1:S,X2:S)) add(ok(X1:S),ok(X2:S)) -> ok(add(X1:S,X2:S)) add(X1:S,mark(X2:S)) -> mark(add(X1:S,X2:S)) 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)) dbl(mark(X:S)) -> mark(dbl(X:S)) dbl(ok(X:S)) -> ok(dbl(X:S)) first(mark(X1:S),X2:S) -> mark(first(X1:S,X2:S)) first(ok(X1:S),ok(X2:S)) -> ok(first(X1:S,X2:S)) first(X1:S,mark(X2:S)) -> mark(first(X1:S,X2:S)) proper(add(X1:S,X2:S)) -> add(proper(X1:S),proper(X2:S)) proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) proper(dbl(X:S)) -> dbl(proper(X:S)) proper(first(X1:S,X2:S)) -> first(proper(X1:S),proper(X2:S)) proper(recip(X:S)) -> recip(proper(X:S)) proper(s(X:S)) -> s(proper(X:S)) proper(sqr(X:S)) -> sqr(proper(X:S)) proper(terms(X:S)) -> terms(proper(X:S)) proper(0) -> ok(0) proper(nil) -> ok(nil) recip(mark(X:S)) -> mark(recip(X:S)) recip(ok(X:S)) -> ok(recip(X:S)) s(ok(X:S)) -> ok(s(X:S)) sqr(mark(X:S)) -> mark(sqr(X:S)) sqr(ok(X:S)) -> ok(sqr(X:S)) terms(mark(X:S)) -> mark(terms(X:S)) terms(ok(X:S)) -> ok(terms(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(add(s(X:S),Y:S)) -> ADD(X:S,Y:S) ACTIVE(add(s(X:S),Y:S)) -> S(add(X:S,Y:S)) ACTIVE(add(X1:S,X2:S)) -> ACTIVE(X1:S) ACTIVE(add(X1:S,X2:S)) -> ACTIVE(X2:S) ACTIVE(add(X1:S,X2:S)) -> ADD(active(X1:S),X2:S) ACTIVE(add(X1:S,X2:S)) -> ADD(X1:S,active(X2:S)) ACTIVE(cons(X1:S,X2:S)) -> ACTIVE(X1:S) ACTIVE(cons(X1:S,X2:S)) -> CONS(active(X1:S),X2:S) ACTIVE(dbl(s(X:S))) -> DBL(X:S) ACTIVE(dbl(s(X:S))) -> S(dbl(X:S)) ACTIVE(dbl(s(X:S))) -> S(s(dbl(X:S))) ACTIVE(dbl(X:S)) -> ACTIVE(X:S) ACTIVE(dbl(X:S)) -> DBL(active(X:S)) ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> CONS(Y:S,first(X:S,Z:S)) ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> FIRST(X:S,Z:S) ACTIVE(first(X1:S,X2:S)) -> ACTIVE(X1:S) ACTIVE(first(X1:S,X2:S)) -> ACTIVE(X2:S) ACTIVE(first(X1:S,X2:S)) -> FIRST(active(X1:S),X2:S) ACTIVE(first(X1:S,X2:S)) -> FIRST(X1:S,active(X2:S)) ACTIVE(recip(X:S)) -> ACTIVE(X:S) ACTIVE(recip(X:S)) -> RECIP(active(X:S)) ACTIVE(sqr(s(X:S))) -> ADD(sqr(X:S),dbl(X:S)) ACTIVE(sqr(s(X:S))) -> DBL(X:S) ACTIVE(sqr(s(X:S))) -> S(add(sqr(X:S),dbl(X:S))) ACTIVE(sqr(s(X:S))) -> SQR(X:S) ACTIVE(sqr(X:S)) -> ACTIVE(X:S) ACTIVE(sqr(X:S)) -> SQR(active(X:S)) ACTIVE(terms(N:S)) -> CONS(recip(sqr(N:S)),terms(s(N:S))) ACTIVE(terms(N:S)) -> RECIP(sqr(N:S)) ACTIVE(terms(N:S)) -> S(N:S) ACTIVE(terms(N:S)) -> SQR(N:S) ACTIVE(terms(N:S)) -> TERMS(s(N:S)) ACTIVE(terms(X:S)) -> ACTIVE(X:S) ACTIVE(terms(X:S)) -> TERMS(active(X:S)) ADD(mark(X1:S),X2:S) -> ADD(X1:S,X2:S) ADD(ok(X1:S),ok(X2:S)) -> ADD(X1:S,X2:S) ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S) CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) CONS(ok(X1:S),ok(X2:S)) -> CONS(X1:S,X2:S) DBL(mark(X:S)) -> DBL(X:S) DBL(ok(X:S)) -> DBL(X:S)
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