/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO

Problem 1: 

(VAR v_NonEmpty:S N:S X:S XS:S Y:S)
(RULES
add(0,X:S) -> X:S
add(s(X:S),Y:S) -> s(add(X:S,Y:S))
fib(N:S) -> sel(N:S,fib1(s(0),s(0)))
fib1(X:S,Y:S) -> cons(X:S,fib1(Y:S,add(X:S,Y:S)))
sel(0,cons(X:S,XS:S)) -> X:S
sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ADD(s(X:S),Y:S) -> ADD(X:S,Y:S)
 FIB(N:S) -> FIB1(s(0),s(0))
 FIB(N:S) -> SEL(N:S,fib1(s(0),s(0)))
 FIB1(X:S,Y:S) -> ADD(X:S,Y:S)
 FIB1(X:S,Y:S) -> FIB1(Y:S,add(X:S,Y:S))
 SEL(s(N:S),cons(X:S,XS:S)) -> SEL(N:S,XS:S)
-> Rules:
 add(0,X:S) -> X:S
 add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 fib(N:S) -> sel(N:S,fib1(s(0),s(0)))
 fib1(X:S,Y:S) -> cons(X:S,fib1(Y:S,add(X:S,Y:S)))
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S)

Problem 1: 

Infinite Processor:
-> Pairs:
 ADD(s(X:S),Y:S) -> ADD(X:S,Y:S)
 FIB(N:S) -> FIB1(s(0),s(0))
 FIB(N:S) -> SEL(N:S,fib1(s(0),s(0)))
 FIB1(X:S,Y:S) -> ADD(X:S,Y:S)
 FIB1(X:S,Y:S) -> FIB1(Y:S,add(X:S,Y:S))
 SEL(s(N:S),cons(X:S,XS:S)) -> SEL(N:S,XS:S)
-> Rules:
 add(0,X:S) -> X:S
 add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 fib(N:S) -> sel(N:S,fib1(s(0),s(0)))
 fib1(X:S,Y:S) -> cons(X:S,fib1(Y:S,add(X:S,Y:S)))
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S)
-> Pairs in cycle:
 FIB1(X:S,Y:S) -> FIB1(Y:S,add(X:S,Y:S))

The problem is infinite.