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TRS Standard pair #487072954
details
property
value
status
complete
benchmark
ExSec11_1_Luc02a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n191.star.cs.uiowa.edu
space
Strategy_removed_mixed_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.018345 seconds
cpu usage
0.018923
user time
0.008476
system time
0.010447
max virtual memory
113188.0
max residence set size
5200.0
stage attributes
key
value
starexec-result
NO
output
NO Problem 1: (VAR v_NonEmpty:S N:S X:S Y:S Z:S) (RULES add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S)) half(dbl(X:S)) -> X:S half(0) -> 0 half(s(0)) -> 0 half(s(s(X:S))) -> s(half(X:S)) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S)),terms(s(N:S))) ) Problem 1: Dependency Pairs Processor: -> Pairs: ADD(s(X:S),Y:S) -> ADD(X:S,Y:S) DBL(s(X:S)) -> DBL(X:S) FIRST(s(X:S),cons(Y:S,Z:S)) -> FIRST(X:S,Z:S) HALF(s(s(X: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)) -> SQR(X:S) TERMS(N:S) -> SQR(N:S) TERMS(N:S) -> TERMS(s(N:S)) -> Rules: add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S)) half(dbl(X:S)) -> X:S half(0) -> 0 half(s(0)) -> 0 half(s(s(X:S))) -> s(half(X:S)) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S)),terms(s(N:S))) Problem 1: Infinite Processor: -> Pairs: ADD(s(X:S),Y:S) -> ADD(X:S,Y:S) DBL(s(X:S)) -> DBL(X:S) FIRST(s(X:S),cons(Y:S,Z:S)) -> FIRST(X:S,Z:S) HALF(s(s(X: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)) -> SQR(X:S) TERMS(N:S) -> SQR(N:S) TERMS(N:S) -> TERMS(s(N:S)) -> Rules: add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,first(X:S,Z:S)) half(dbl(X:S)) -> X:S half(0) -> 0 half(s(0)) -> 0 half(s(s(X:S))) -> s(half(X:S)) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S)),terms(s(N:S))) -> Pairs in cycle: TERMS(N:S) -> TERMS(s(N:S)) The problem is infinite.
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