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


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YES

Problem 1: 

(VAR X X1 X2 Y Z)
(RULES
activate(n__add(X1,X2)) -> add(X1,X2)
activate(n__from(X)) -> from(X)
activate(n__fst(X1,X2)) -> fst(X1,X2)
activate(n__len(X)) -> len(X)
activate(X) -> X
add(0,X) -> X
add(s(X),Y) -> s(n__add(activate(X),Y))
add(X1,X2) -> n__add(X1,X2)
from(X) -> cons(X,n__from(s(X)))
from(X) -> n__from(X)
fst(0,Z) -> nil
fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
fst(X1,X2) -> n__fst(X1,X2)
len(cons(X,Z)) -> s(n__len(activate(Z)))
len(nil) -> 0
len(X) -> n__len(X)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__add(X1,X2)) -> ADD(X1,X2)
 ACTIVATE(n__from(X)) -> FROM(X)
 ACTIVATE(n__fst(X1,X2)) -> FST(X1,X2)
 ACTIVATE(n__len(X)) -> LEN(X)
 ADD(s(X),Y) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(Z)
 LEN(cons(X,Z)) -> ACTIVATE(Z)
-> Rules:
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 add(X1,X2) -> n__add(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 fst(0,Z) -> nil
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 len(nil) -> 0
 len(X) -> n__len(X)

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__add(X1,X2)) -> ADD(X1,X2)
 ACTIVATE(n__from(X)) -> FROM(X)
 ACTIVATE(n__fst(X1,X2)) -> FST(X1,X2)
 ACTIVATE(n__len(X)) -> LEN(X)
 ADD(s(X),Y) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(Z)
 LEN(cons(X,Z)) -> ACTIVATE(Z)
-> Rules:
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 add(X1,X2) -> n__add(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 fst(0,Z) -> nil
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 len(nil) -> 0
 len(X) -> n__len(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__add(X1,X2)) -> ADD(X1,X2)
 ACTIVATE(n__fst(X1,X2)) -> FST(X1,X2)
 ACTIVATE(n__len(X)) -> LEN(X)
 ADD(s(X),Y) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(Z)
 LEN(cons(X,Z)) -> ACTIVATE(Z)
->->-> Rules:
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 add(X1,X2) -> n__add(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 fst(0,Z) -> nil
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 len(nil) -> 0
 len(X) -> n__len(X)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ACTIVATE(n__add(X1,X2)) -> ADD(X1,X2)
 ACTIVATE(n__fst(X1,X2)) -> FST(X1,X2)
 ACTIVATE(n__len(X)) -> LEN(X)
 ADD(s(X),Y) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(Z)
 LEN(cons(X,Z)) -> ACTIVATE(Z)
-> Rules:
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 add(X1,X2) -> n__add(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 fst(0,Z) -> nil
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 len(nil) -> 0
 len(X) -> n__len(X)
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[cons](X1,X2) = 2.X2 + 2
[n__add](X1,X2) = 2.X1 + 2.X2 + 2
[n__fst](X1,X2) = 2.X1 + 2.X2
[n__len](X) = X + 2
[s](X) = 2.X + 2
[ACTIVATE](X) = 2.X + 2
[ADD](X1,X2) = 2.X1 + 2
[FST](X1,X2) = 2.X1 + X2
[LEN](X) = X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__fst(X1,X2)) -> FST(X1,X2)
 ACTIVATE(n__len(X)) -> LEN(X)
 ADD(s(X),Y) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(Z)
 LEN(cons(X,Z)) -> ACTIVATE(Z)
-> Rules:
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 add(X1,X2) -> n__add(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 fst(0,Z) -> nil
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 len(nil) -> 0
 len(X) -> n__len(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__fst(X1,X2)) -> FST(X1,X2)
 ACTIVATE(n__len(X)) -> LEN(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(Z)
 LEN(cons(X,Z)) -> ACTIVATE(Z)
->->-> Rules:
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 add(X1,X2) -> n__add(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 fst(0,Z) -> nil
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 len(nil) -> 0
 len(X) -> n__len(X)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 ACTIVATE(n__fst(X1,X2)) -> FST(X1,X2)
 ACTIVATE(n__len(X)) -> LEN(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(Z)
 LEN(cons(X,Z)) -> ACTIVATE(Z)
-> Rules:
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 add(X1,X2) -> n__add(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 fst(0,Z) -> nil
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 len(nil) -> 0
 len(X) -> n__len(X)
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[cons](X1,X2) = 2.X2 + 2
[n__fst](X1,X2) = X1 + 2.X2 + 1
[n__len](X) = 2.X + 2
[s](X) = 2.X + 2
[ACTIVATE](X) = 2.X + 2
[FST](X1,X2) = 2.X1 + 2.X2 + 2
[LEN](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__len(X)) -> LEN(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(X)
 FST(s(X),cons(Y,Z)) -> ACTIVATE(Z)
 LEN(cons(X,Z)) -> ACTIVATE(Z)
-> Rules:
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 add(X1,X2) -> n__add(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 fst(0,Z) -> nil
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 len(nil) -> 0
 len(X) -> n__len(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__len(X)) -> LEN(X)
 LEN(cons(X,Z)) -> ACTIVATE(Z)
->->-> Rules:
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 add(X1,X2) -> n__add(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 fst(0,Z) -> nil
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 len(nil) -> 0
 len(X) -> n__len(X)

Problem 1: 

Subterm Processor:
-> Pairs:
 ACTIVATE(n__len(X)) -> LEN(X)
 LEN(cons(X,Z)) -> ACTIVATE(Z)
-> Rules:
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 add(X1,X2) -> n__add(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 fst(0,Z) -> nil
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 len(nil) -> 0
 len(X) -> n__len(X)
->Projection:
 pi(ACTIVATE) = 1
 pi(LEN) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(n__add(X1,X2)) -> add(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__fst(X1,X2)) -> fst(X1,X2)
 activate(n__len(X)) -> len(X)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(n__add(activate(X),Y))
 add(X1,X2) -> n__add(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
 fst(0,Z) -> nil
 fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z)))
 fst(X1,X2) -> n__fst(X1,X2)
 len(cons(X,Z)) -> s(n__len(activate(Z)))
 len(nil) -> 0
 len(X) -> n__len(X)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.