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TRS Standard pair #516963481
details
property
value
status
complete
benchmark
ExSec11_1_Luc02a_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n032.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.196168899536 seconds
cpu usage
0.156637484
max memory
5640192.0
stage attributes
key
value
output-size
27308
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S N:S X:S X1:S X2:S Y:S Z:S) (RULES activate(n__first(X1:S,X2:S)) -> first(activate(X1:S),activate(X2:S)) activate(n__s(X:S)) -> s(activate(X:S)) activate(n__terms(X:S)) -> terms(activate(X:S)) activate(X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) add(0,X:S) -> X:S dbl(s(X:S)) -> s(s(dbl(X:S))) dbl(0) -> 0 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S))) first(0,X:S) -> nil first(X1:S,X2:S) -> n__first(X1:S,X2:S) half(dbl(X:S)) -> X:S half(s(s(X:S))) -> s(half(X:S)) half(s(0)) -> 0 half(0) -> 0 s(X:S) -> n__s(X:S) sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) sqr(0) -> 0 terms(N:S) -> cons(recip(sqr(N:S)),n__terms(n__s(N:S))) terms(X:S) -> n__terms(X:S) ) Problem 1: Dependency Pairs Processor: -> Pairs: ACTIVATE(n__first(X1:S,X2:S)) -> ACTIVATE(X1:S) ACTIVATE(n__first(X1:S,X2:S)) -> ACTIVATE(X2:S) ACTIVATE(n__first(X1:S,X2:S)) -> FIRST(activate(X1:S),activate(X2:S)) ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S) ACTIVATE(n__s(X:S)) -> S(activate(X:S)) ACTIVATE(n__terms(X:S)) -> ACTIVATE(X:S) ACTIVATE(n__terms(X:S)) -> TERMS(activate(X:S)) ADD(s(X:S),Y:S) -> ADD(X:S,Y:S) ADD(s(X:S),Y:S) -> S(add(X:S,Y:S)) DBL(s(X:S)) -> DBL(X:S) DBL(s(X:S)) -> S(dbl(X:S)) DBL(s(X:S)) -> S(s(dbl(X:S))) FIRST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S) HALF(s(s(X:S))) -> HALF(X:S) HALF(s(s(X:S))) -> S(half(X:S)) SQR(s(X:S)) -> ADD(sqr(X:S),dbl(X:S)) SQR(s(X:S)) -> DBL(X:S) SQR(s(X:S)) -> S(add(sqr(X:S),dbl(X:S))) SQR(s(X:S)) -> SQR(X:S) TERMS(N:S) -> SQR(N:S) -> Rules: activate(n__first(X1:S,X2:S)) -> first(activate(X1:S),activate(X2:S)) activate(n__s(X:S)) -> s(activate(X:S)) activate(n__terms(X:S)) -> terms(activate(X:S)) activate(X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) add(0,X:S) -> X:S dbl(s(X:S)) -> s(s(dbl(X:S))) dbl(0) -> 0 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S))) first(0,X:S) -> nil first(X1:S,X2:S) -> n__first(X1:S,X2:S) half(dbl(X:S)) -> X:S half(s(s(X:S))) -> s(half(X:S)) half(s(0)) -> 0 half(0) -> 0 s(X:S) -> n__s(X:S) sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) sqr(0) -> 0 terms(N:S) -> cons(recip(sqr(N:S)),n__terms(n__s(N:S))) terms(X:S) -> n__terms(X:S) Problem 1: SCC Processor: -> Pairs: ACTIVATE(n__first(X1:S,X2:S)) -> ACTIVATE(X1:S) ACTIVATE(n__first(X1:S,X2:S)) -> ACTIVATE(X2:S) ACTIVATE(n__first(X1:S,X2:S)) -> FIRST(activate(X1:S),activate(X2:S)) ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S) ACTIVATE(n__s(X:S)) -> S(activate(X:S)) ACTIVATE(n__terms(X:S)) -> ACTIVATE(X:S) ACTIVATE(n__terms(X:S)) -> TERMS(activate(X:S)) ADD(s(X:S),Y:S) -> ADD(X:S,Y:S) ADD(s(X:S),Y:S) -> S(add(X:S,Y:S)) DBL(s(X:S)) -> DBL(X:S) DBL(s(X:S)) -> S(dbl(X:S)) DBL(s(X:S)) -> S(s(dbl(X:S))) FIRST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S) HALF(s(s(X:S))) -> HALF(X:S) HALF(s(s(X:S))) -> S(half(X:S)) SQR(s(X:S)) -> ADD(sqr(X:S),dbl(X:S))
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