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


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YES

Problem 1: 

(VAR X X1 X2 Y Z)
(RULES
2nd(active(X)) -> 2nd(X)
2nd(mark(X)) -> 2nd(X)
active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
active(from(X)) -> mark(cons(X,from(s(X))))
cons(active(X1),X2) -> cons(X1,X2)
cons(mark(X1),X2) -> cons(X1,X2)
cons(X1,active(X2)) -> cons(X1,X2)
cons(X1,mark(X2)) -> cons(X1,X2)
cons1(active(X1),X2) -> cons1(X1,X2)
cons1(mark(X1),X2) -> cons1(X1,X2)
cons1(X1,active(X2)) -> cons1(X1,X2)
cons1(X1,mark(X2)) -> cons1(X1,X2)
from(active(X)) -> from(X)
from(mark(X)) -> from(X)
mark(2nd(X)) -> active(2nd(mark(X)))
mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
mark(from(X)) -> active(from(mark(X)))
mark(s(X)) -> active(s(mark(X)))
s(active(X)) -> s(X)
s(mark(X)) -> s(X)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 2ND(active(X)) -> 2ND(X)
 2ND(mark(X)) -> 2ND(X)
 ACTIVE(2nd(cons(X,X1))) -> 2ND(cons1(X,X1))
 ACTIVE(2nd(cons(X,X1))) -> CONS1(X,X1)
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> CONS(X,from(s(X)))
 ACTIVE(from(X)) -> FROM(s(X))
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 ACTIVE(from(X)) -> S(X)
 CONS(active(X1),X2) -> CONS(X1,X2)
 CONS(mark(X1),X2) -> CONS(X1,X2)
 CONS(X1,active(X2)) -> CONS(X1,X2)
 CONS(X1,mark(X2)) -> CONS(X1,X2)
 CONS1(active(X1),X2) -> CONS1(X1,X2)
 CONS1(mark(X1),X2) -> CONS1(X1,X2)
 CONS1(X1,active(X2)) -> CONS1(X1,X2)
 CONS1(X1,mark(X2)) -> CONS1(X1,X2)
 FROM(active(X)) -> FROM(X)
 FROM(mark(X)) -> FROM(X)
 MARK(2nd(X)) -> 2ND(mark(X))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> ACTIVE(cons(mark(X1),X2))
 MARK(cons(X1,X2)) -> CONS(mark(X1),X2)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> ACTIVE(cons1(mark(X1),mark(X2)))
 MARK(cons1(X1,X2)) -> CONS1(mark(X1),mark(X2))
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> FROM(mark(X))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> ACTIVE(s(mark(X)))
 MARK(s(X)) -> MARK(X)
 MARK(s(X)) -> S(mark(X))
 S(active(X)) -> S(X)
 S(mark(X)) -> S(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)

Problem 1: 

SCC Processor:
-> Pairs:
 2ND(active(X)) -> 2ND(X)
 2ND(mark(X)) -> 2ND(X)
 ACTIVE(2nd(cons(X,X1))) -> 2ND(cons1(X,X1))
 ACTIVE(2nd(cons(X,X1))) -> CONS1(X,X1)
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> CONS(X,from(s(X)))
 ACTIVE(from(X)) -> FROM(s(X))
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 ACTIVE(from(X)) -> S(X)
 CONS(active(X1),X2) -> CONS(X1,X2)
 CONS(mark(X1),X2) -> CONS(X1,X2)
 CONS(X1,active(X2)) -> CONS(X1,X2)
 CONS(X1,mark(X2)) -> CONS(X1,X2)
 CONS1(active(X1),X2) -> CONS1(X1,X2)
 CONS1(mark(X1),X2) -> CONS1(X1,X2)
 CONS1(X1,active(X2)) -> CONS1(X1,X2)
 CONS1(X1,mark(X2)) -> CONS1(X1,X2)
 FROM(active(X)) -> FROM(X)
 FROM(mark(X)) -> FROM(X)
 MARK(2nd(X)) -> 2ND(mark(X))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> ACTIVE(cons(mark(X1),X2))
 MARK(cons(X1,X2)) -> CONS(mark(X1),X2)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> ACTIVE(cons1(mark(X1),mark(X2)))
 MARK(cons1(X1,X2)) -> CONS1(mark(X1),mark(X2))
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> FROM(mark(X))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> ACTIVE(s(mark(X)))
 MARK(s(X)) -> MARK(X)
 MARK(s(X)) -> S(mark(X))
 S(active(X)) -> S(X)
 S(mark(X)) -> S(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 S(active(X)) -> S(X)
 S(mark(X)) -> S(X)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->->Cycle:
->->-> Pairs:
 FROM(active(X)) -> FROM(X)
 FROM(mark(X)) -> FROM(X)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->->Cycle:
->->-> Pairs:
 CONS1(active(X1),X2) -> CONS1(X1,X2)
 CONS1(mark(X1),X2) -> CONS1(X1,X2)
 CONS1(X1,active(X2)) -> CONS1(X1,X2)
 CONS1(X1,mark(X2)) -> CONS1(X1,X2)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->->Cycle:
->->-> Pairs:
 CONS(active(X1),X2) -> CONS(X1,X2)
 CONS(mark(X1),X2) -> CONS(X1,X2)
 CONS(X1,active(X2)) -> CONS(X1,X2)
 CONS(X1,mark(X2)) -> CONS(X1,X2)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->->Cycle:
->->-> Pairs:
 2ND(active(X)) -> 2ND(X)
 2ND(mark(X)) -> 2ND(X)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->->Cycle:
->->-> Pairs:
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> ACTIVE(cons(mark(X1),X2))
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> ACTIVE(cons1(mark(X1),mark(X2)))
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> ACTIVE(s(mark(X)))
 MARK(s(X)) -> MARK(X)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)


The problem is decomposed in 6 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 S(active(X)) -> S(X)
 S(mark(X)) -> S(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Projection:
 pi(S) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 FROM(active(X)) -> FROM(X)
 FROM(mark(X)) -> FROM(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Projection:
 pi(FROM) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 CONS1(active(X1),X2) -> CONS1(X1,X2)
 CONS1(mark(X1),X2) -> CONS1(X1,X2)
 CONS1(X1,active(X2)) -> CONS1(X1,X2)
 CONS1(X1,mark(X2)) -> CONS1(X1,X2)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Projection:
 pi(CONS1) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 CONS1(X1,active(X2)) -> CONS1(X1,X2)
 CONS1(X1,mark(X2)) -> CONS1(X1,X2)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 CONS1(X1,active(X2)) -> CONS1(X1,X2)
 CONS1(X1,mark(X2)) -> CONS1(X1,X2)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)

Problem 1.3: 

Subterm Processor:
-> Pairs:
 CONS1(X1,active(X2)) -> CONS1(X1,X2)
 CONS1(X1,mark(X2)) -> CONS1(X1,X2)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Projection:
 pi(CONS1) = 2

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.4: 

Subterm Processor:
-> Pairs:
 CONS(active(X1),X2) -> CONS(X1,X2)
 CONS(mark(X1),X2) -> CONS(X1,X2)
 CONS(X1,active(X2)) -> CONS(X1,X2)
 CONS(X1,mark(X2)) -> CONS(X1,X2)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Projection:
 pi(CONS) = 1

Problem 1.4: 

SCC Processor:
-> Pairs:
 CONS(X1,active(X2)) -> CONS(X1,X2)
 CONS(X1,mark(X2)) -> CONS(X1,X2)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 CONS(X1,active(X2)) -> CONS(X1,X2)
 CONS(X1,mark(X2)) -> CONS(X1,X2)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)

Problem 1.4: 

Subterm Processor:
-> Pairs:
 CONS(X1,active(X2)) -> CONS(X1,X2)
 CONS(X1,mark(X2)) -> CONS(X1,X2)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Projection:
 pi(CONS) = 2

Problem 1.4: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.5: 

Subterm Processor:
-> Pairs:
 2ND(active(X)) -> 2ND(X)
 2ND(mark(X)) -> 2ND(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Projection:
 pi(2ND) = 1

Problem 1.5: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.6: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> ACTIVE(cons(mark(X1),X2))
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> ACTIVE(cons1(mark(X1),mark(X2)))
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> ACTIVE(s(mark(X)))
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
-> Usable rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[2nd](X) = 1
[active](X) = 2.X
[cons](X1,X2) = 0
[cons1](X1,X2) = 1
[from](X) = 1
[mark](X) = 2
[s](X) = 1
[ACTIVE](X) = 2.X
[MARK](X) = 2

Problem 1.6: 

SCC Processor:
-> Pairs:
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> ACTIVE(cons1(mark(X1),mark(X2)))
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> ACTIVE(s(mark(X)))
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> ACTIVE(cons1(mark(X1),mark(X2)))
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> ACTIVE(s(mark(X)))
 MARK(s(X)) -> MARK(X)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)

Problem 1.6: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> ACTIVE(cons1(mark(X1),mark(X2)))
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> ACTIVE(s(mark(X)))
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
-> Usable rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[2nd](X) = 1
[active](X) = 2.X
[cons](X1,X2) = 0
[cons1](X1,X2) = 0
[from](X) = 1
[mark](X) = 2
[s](X) = 1
[ACTIVE](X) = 2.X
[MARK](X) = 2

Problem 1.6: 

SCC Processor:
-> Pairs:
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> ACTIVE(s(mark(X)))
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> ACTIVE(s(mark(X)))
 MARK(s(X)) -> MARK(X)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)

Problem 1.6: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> ACTIVE(s(mark(X)))
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
-> Usable rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[2nd](X) = 2
[active](X) = 1
[cons](X1,X2) = 2
[cons1](X1,X2) = 0
[from](X) = 2
[mark](X) = 1
[s](X) = 0
[ACTIVE](X) = X
[MARK](X) = 2

Problem 1.6: 

SCC Processor:
-> Pairs:
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)

Problem 1.6: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(2nd(cons(X,X1))) -> MARK(2nd(cons1(X,X1)))
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
-> Usable rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[2nd](X) = [1 1;1 1].X + [1;1]
[active](X) = [1 0;0 1].X
[cons](X1,X2) = [1 1;0 0].X1 + [0 0;1 0].X2 + [0;1]
[cons1](X1,X2) = [1 0;0 0].X1 + [1 0;0 0].X2
[from](X) = [1 1;1 0].X + [0;1]
[mark](X) = [1 0;0 1].X
[s](X) = [1 0;0 0].X
[ACTIVE](X) = [1 0;1 0].X + [0;1]
[MARK](X) = [1 0;1 0].X + [0;1]

Problem 1.6: 

SCC Processor:
-> Pairs:
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)

Problem 1.6: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(2nd(cons1(X,cons(Y,Z)))) -> MARK(Y)
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
-> Usable rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[2nd](X) = [1 1;1 1].X + [1;1]
[active](X) = [1 0;0 1].X
[cons](X1,X2) = [0 0;1 1].X1 + [0 1;0 0].X2 + [0;1]
[cons1](X1,X2) = [1 0;0 1].X1 + [0 0;0 1].X2 + [1;0]
[from](X) = [0 1;1 1].X + [1;1]
[mark](X) = [1 0;0 1].X
[s](X) = [0 0;0 1].X
[ACTIVE](X) = [0 1;0 1].X + [1;1]
[MARK](X) = [0 1;0 1].X + [1;1]

Problem 1.6: 

SCC Processor:
-> Pairs:
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)

Problem 1.6: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> ACTIVE(2nd(mark(X)))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
-> Usable rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[2nd](X) = 0
[active](X) = 2
[cons](X1,X2) = 0
[cons1](X1,X2) = 0
[from](X) = 1
[mark](X) = 2
[s](X) = 0
[ACTIVE](X) = 2.X
[MARK](X) = 2

Problem 1.6: 

SCC Processor:
-> Pairs:
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)

Problem 1.6: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(from(X)) -> MARK(cons(X,from(s(X))))
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
-> Usable rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[2nd](X) = [1 1;1 1].X + [1;1]
[active](X) = [1 0;0 1].X
[cons](X1,X2) = [1 1;0 0].X1 + [0 0;1 0].X2
[cons1](X1,X2) = [1 1;0 0].X1 + [1 0;0 0].X2
[from](X) = [1 1;1 0].X + [1;1]
[mark](X) = [1 0;0 1].X
[s](X) = [1 0;0 0].X
[ACTIVE](X) = [1 0;1 0].X + [1;0]
[MARK](X) = [1 0;1 0].X + [1;1]

Problem 1.6: 

SCC Processor:
-> Pairs:
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> ACTIVE(from(mark(X)))
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
->->-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)

Problem 1.6: 

Subterm Processor:
-> Pairs:
 MARK(2nd(X)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X1)
 MARK(cons1(X1,X2)) -> MARK(X2)
 MARK(from(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Projection:
 pi(MARK) = 1

Problem 1.6: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 2nd(active(X)) -> 2nd(X)
 2nd(mark(X)) -> 2nd(X)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(from(X)) -> mark(cons(X,from(s(X))))
 cons(active(X1),X2) -> cons(X1,X2)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons1(active(X1),X2) -> cons1(X1,X2)
 cons1(mark(X1),X2) -> cons1(X1,X2)
 cons1(X1,active(X2)) -> cons1(X1,X2)
 cons1(X1,mark(X2)) -> cons1(X1,X2)
 from(active(X)) -> from(X)
 from(mark(X)) -> from(X)
 mark(2nd(X)) -> active(2nd(mark(X)))
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(cons1(X1,X2)) -> active(cons1(mark(X1),mark(X2)))
 mark(from(X)) -> active(from(mark(X)))
 mark(s(X)) -> active(s(mark(X)))
 s(active(X)) -> s(X)
 s(mark(X)) -> s(X)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.