/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 I P X X1 X2 Y Z)
(RULES
__(active(X1),X2) -> __(X1,X2)
__(mark(X1),X2) -> __(X1,X2)
__(X1,active(X2)) -> __(X1,X2)
__(X1,mark(X2)) -> __(X1,X2)
active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
active(__(nil,X)) -> mark(X)
active(__(X,nil)) -> mark(X)
active(and(tt,X)) -> mark(X)
active(isNePal(__(I,__(P,I)))) -> mark(tt)
and(active(X1),X2) -> and(X1,X2)
and(mark(X1),X2) -> and(X1,X2)
and(X1,active(X2)) -> and(X1,X2)
and(X1,mark(X2)) -> and(X1,X2)
isNePal(active(X)) -> isNePal(X)
isNePal(mark(X)) -> isNePal(X)
mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
mark(and(X1,X2)) -> active(and(mark(X1),X2))
mark(isNePal(X)) -> active(isNePal(mark(X)))
mark(nil) -> active(nil)
mark(tt) -> active(tt)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 __#(active(X1),X2) -> __#(X1,X2)
 __#(mark(X1),X2) -> __#(X1,X2)
 __#(X1,active(X2)) -> __#(X1,X2)
 __#(X1,mark(X2)) -> __#(X1,X2)
 ACTIVE(__(__(X,Y),Z)) -> __#(X,__(Y,Z))
 ACTIVE(__(__(X,Y),Z)) -> __#(Y,Z)
 ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z)))
 ACTIVE(__(nil,X)) -> MARK(X)
 ACTIVE(__(X,nil)) -> MARK(X)
 ACTIVE(and(tt,X)) -> MARK(X)
 ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(tt)
 AND(active(X1),X2) -> AND(X1,X2)
 AND(mark(X1),X2) -> AND(X1,X2)
 AND(X1,active(X2)) -> AND(X1,X2)
 AND(X1,mark(X2)) -> AND(X1,X2)
 ISNEPAL(active(X)) -> ISNEPAL(X)
 ISNEPAL(mark(X)) -> ISNEPAL(X)
 MARK(__(X1,X2)) -> __#(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> ISNEPAL(mark(X))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1: 

SCC Processor:
-> Pairs:
 __#(active(X1),X2) -> __#(X1,X2)
 __#(mark(X1),X2) -> __#(X1,X2)
 __#(X1,active(X2)) -> __#(X1,X2)
 __#(X1,mark(X2)) -> __#(X1,X2)
 ACTIVE(__(__(X,Y),Z)) -> __#(X,__(Y,Z))
 ACTIVE(__(__(X,Y),Z)) -> __#(Y,Z)
 ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z)))
 ACTIVE(__(nil,X)) -> MARK(X)
 ACTIVE(__(X,nil)) -> MARK(X)
 ACTIVE(and(tt,X)) -> MARK(X)
 ACTIVE(isNePal(__(I,__(P,I)))) -> MARK(tt)
 AND(active(X1),X2) -> AND(X1,X2)
 AND(mark(X1),X2) -> AND(X1,X2)
 AND(X1,active(X2)) -> AND(X1,X2)
 AND(X1,mark(X2)) -> AND(X1,X2)
 ISNEPAL(active(X)) -> ISNEPAL(X)
 ISNEPAL(mark(X)) -> ISNEPAL(X)
 MARK(__(X1,X2)) -> __#(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> ISNEPAL(mark(X))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ISNEPAL(active(X)) -> ISNEPAL(X)
 ISNEPAL(mark(X)) -> ISNEPAL(X)
->->-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->->Cycle:
->->-> Pairs:
 AND(active(X1),X2) -> AND(X1,X2)
 AND(mark(X1),X2) -> AND(X1,X2)
 AND(X1,active(X2)) -> AND(X1,X2)
 AND(X1,mark(X2)) -> AND(X1,X2)
->->-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->->Cycle:
->->-> Pairs:
 __#(active(X1),X2) -> __#(X1,X2)
 __#(mark(X1),X2) -> __#(X1,X2)
 __#(X1,active(X2)) -> __#(X1,X2)
 __#(X1,mark(X2)) -> __#(X1,X2)
->->-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->->Cycle:
->->-> Pairs:
 ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z)))
 ACTIVE(__(nil,X)) -> MARK(X)
 ACTIVE(__(X,nil)) -> MARK(X)
 ACTIVE(and(tt,X)) -> MARK(X)
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)


The problem is decomposed in 4 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ISNEPAL(active(X)) -> ISNEPAL(X)
 ISNEPAL(mark(X)) -> ISNEPAL(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(ISNEPAL) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 AND(active(X1),X2) -> AND(X1,X2)
 AND(mark(X1),X2) -> AND(X1,X2)
 AND(X1,active(X2)) -> AND(X1,X2)
 AND(X1,mark(X2)) -> AND(X1,X2)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(AND) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 AND(X1,active(X2)) -> AND(X1,X2)
 AND(X1,mark(X2)) -> AND(X1,X2)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 AND(X1,active(X2)) -> AND(X1,X2)
 AND(X1,mark(X2)) -> AND(X1,X2)
->->-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.2: 

Subterm Processor:
-> Pairs:
 AND(X1,active(X2)) -> AND(X1,X2)
 AND(X1,mark(X2)) -> AND(X1,X2)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(AND) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 __#(active(X1),X2) -> __#(X1,X2)
 __#(mark(X1),X2) -> __#(X1,X2)
 __#(X1,active(X2)) -> __#(X1,X2)
 __#(X1,mark(X2)) -> __#(X1,X2)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(__#) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 __#(X1,active(X2)) -> __#(X1,X2)
 __#(X1,mark(X2)) -> __#(X1,X2)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 __#(X1,active(X2)) -> __#(X1,X2)
 __#(X1,mark(X2)) -> __#(X1,X2)
->->-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.3: 

Subterm Processor:
-> Pairs:
 __#(X1,active(X2)) -> __#(X1,X2)
 __#(X1,mark(X2)) -> __#(X1,X2)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(__#) = 2

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.4: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(__(__(X,Y),Z)) -> MARK(__(X,__(Y,Z)))
 ACTIVE(__(nil,X)) -> MARK(X)
 ACTIVE(__(X,nil)) -> MARK(X)
 ACTIVE(and(tt,X)) -> MARK(X)
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
-> Usable rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[and](X1,X2) = X1 + 2.X2 + 1
[isNePal](X) = 2.X + 2
[mark](X) = X
[nil] = 1
[tt] = 0
[ACTIVE](X) = 2.X + 1
[MARK](X) = 2.X + 2

Problem 1.4: 

SCC Processor:
-> Pairs:
 ACTIVE(__(nil,X)) -> MARK(X)
 ACTIVE(__(X,nil)) -> MARK(X)
 ACTIVE(and(tt,X)) -> MARK(X)
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(__(nil,X)) -> MARK(X)
 ACTIVE(__(X,nil)) -> MARK(X)
 ACTIVE(and(tt,X)) -> MARK(X)
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.4: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(__(nil,X)) -> MARK(X)
 ACTIVE(__(X,nil)) -> MARK(X)
 ACTIVE(and(tt,X)) -> MARK(X)
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
-> Usable rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[and](X1,X2) = 2.X1 + 2.X2 + 2
[isNePal](X) = 2.X + 1
[mark](X) = X
[nil] = 2
[tt] = 2
[ACTIVE](X) = 2.X + 1
[MARK](X) = 2.X + 2

Problem 1.4: 

SCC Processor:
-> Pairs:
 ACTIVE(__(X,nil)) -> MARK(X)
 ACTIVE(and(tt,X)) -> MARK(X)
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(__(X,nil)) -> MARK(X)
 ACTIVE(and(tt,X)) -> MARK(X)
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.4: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(__(X,nil)) -> MARK(X)
 ACTIVE(and(tt,X)) -> MARK(X)
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
-> Usable rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[__](X1,X2) = 2.X1 + X2 + 1
[active](X) = X
[and](X1,X2) = 2.X1 + 2.X2 + 1
[isNePal](X) = 2.X + 2
[mark](X) = X
[nil] = 1
[tt] = 1
[ACTIVE](X) = 2.X + 2
[MARK](X) = 2.X + 2

Problem 1.4: 

SCC Processor:
-> Pairs:
 ACTIVE(and(tt,X)) -> MARK(X)
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(and(tt,X)) -> MARK(X)
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.4: 

Reduction Pair Processor:
-> Pairs:
 ACTIVE(and(tt,X)) -> MARK(X)
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
-> Usable rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[and](X1,X2) = 2.X1 + 2.X2 + 2
[isNePal](X) = 2.X + 2
[mark](X) = X
[nil] = 1
[tt] = 1
[ACTIVE](X) = 2.X
[MARK](X) = 2.X + 1

Problem 1.4: 

SCC Processor:
-> Pairs:
 MARK(__(X1,X2)) -> ACTIVE(__(mark(X1),mark(X2)))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> ACTIVE(and(mark(X1),X2))
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> ACTIVE(isNePal(mark(X)))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.4: 

Subterm Processor:
-> Pairs:
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(MARK) = 1

Problem 1.4: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 __(active(X1),X2) -> __(X1,X2)
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(nil,X)) -> mark(X)
 active(__(X,nil)) -> mark(X)
 active(and(tt,X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt)
 and(active(X1),X2) -> and(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 isNePal(active(X)) -> isNePal(X)
 isNePal(mark(X)) -> isNePal(X)
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.