0.00/0.29	YES
0.00/0.29	
0.00/0.29	Problem 1: 
0.00/0.29	
0.00/0.29	(VAR v_NonEmpty:S M:S N:S X:S X1:S X2:S X3:S)
0.00/0.29	(RULES
0.00/0.29	U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	mark(0) -> active(0)
0.00/0.29	mark(tt) -> active(tt)
0.00/0.29	plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	s(active(X:S)) -> s(X:S)
0.00/0.29	s(mark(X:S)) -> s(X:S)
0.00/0.29	) 
0.00/0.29	(STRATEGY INNERMOST)
0.00/0.29	
0.00/0.29	Problem 1: 
0.00/0.29	
0.00/0.29	Dependency Pairs Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U11#(active(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(mark(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(active(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(mark(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 ACTIVE(U11(tt,M:S,N:S)) -> U12#(tt,M:S,N:S)
0.00/0.29	 ACTIVE(U11(tt,M:S,N:S)) -> MARK(U12(tt,M:S,N:S))
0.00/0.29	 ACTIVE(U12(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S)))
0.00/0.29	 ACTIVE(U12(tt,M:S,N:S)) -> PLUS(N:S,M:S)
0.00/0.29	 ACTIVE(U12(tt,M:S,N:S)) -> S(plus(N:S,M:S))
0.00/0.29	 ACTIVE(plus(N:S,s(M:S))) -> U11#(tt,M:S,N:S)
0.00/0.29	 ACTIVE(plus(N:S,s(M:S))) -> MARK(U11(tt,M:S,N:S))
0.00/0.29	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.29	 MARK(U11(X1:S,X2:S,X3:S)) -> U11#(mark(X1:S),X2:S,X3:S)
0.00/0.29	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.29	 MARK(U12(X1:S,X2:S,X3:S)) -> U12#(mark(X1:S),X2:S,X3:S)
0.00/0.29	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.29	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.29	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.29	 MARK(plus(X1:S,X2:S)) -> PLUS(mark(X1:S),mark(X2:S))
0.00/0.29	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.29	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.29	 MARK(s(X:S)) -> S(mark(X:S))
0.00/0.29	 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	 S(active(X:S)) -> S(X:S)
0.00/0.29	 S(mark(X:S)) -> S(X:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	
0.00/0.29	Problem 1: 
0.00/0.29	
0.00/0.29	SCC Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U11#(active(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(mark(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(active(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(mark(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 ACTIVE(U11(tt,M:S,N:S)) -> U12#(tt,M:S,N:S)
0.00/0.29	 ACTIVE(U11(tt,M:S,N:S)) -> MARK(U12(tt,M:S,N:S))
0.00/0.29	 ACTIVE(U12(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S)))
0.00/0.29	 ACTIVE(U12(tt,M:S,N:S)) -> PLUS(N:S,M:S)
0.00/0.29	 ACTIVE(U12(tt,M:S,N:S)) -> S(plus(N:S,M:S))
0.00/0.29	 ACTIVE(plus(N:S,s(M:S))) -> U11#(tt,M:S,N:S)
0.00/0.29	 ACTIVE(plus(N:S,s(M:S))) -> MARK(U11(tt,M:S,N:S))
0.00/0.29	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.29	 MARK(U11(X1:S,X2:S,X3:S)) -> U11#(mark(X1:S),X2:S,X3:S)
0.00/0.29	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.29	 MARK(U12(X1:S,X2:S,X3:S)) -> U12#(mark(X1:S),X2:S,X3:S)
0.00/0.29	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.29	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.29	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.29	 MARK(plus(X1:S,X2:S)) -> PLUS(mark(X1:S),mark(X2:S))
0.00/0.29	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.29	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.29	 MARK(s(X:S)) -> S(mark(X:S))
0.00/0.29	 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	 S(active(X:S)) -> S(X:S)
0.00/0.29	 S(mark(X:S)) -> S(X:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Strongly Connected Components:
0.00/0.29	->->Cycle:
0.00/0.29	->->-> Pairs:
0.00/0.29	 S(active(X:S)) -> S(X:S)
0.00/0.29	 S(mark(X:S)) -> S(X:S)
0.00/0.29	->->-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->->Cycle:
0.00/0.29	->->-> Pairs:
0.00/0.29	 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	->->-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->->Cycle:
0.00/0.29	->->-> Pairs:
0.00/0.29	 U12#(active(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(mark(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	->->-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->->Cycle:
0.00/0.29	->->-> Pairs:
0.00/0.29	 U11#(active(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(mark(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	->->-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->->Cycle:
0.00/0.29	->->-> Pairs:
0.00/0.29	 ACTIVE(U11(tt,M:S,N:S)) -> MARK(U12(tt,M:S,N:S))
0.00/0.29	 ACTIVE(U12(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S)))
0.00/0.29	 ACTIVE(plus(N:S,s(M:S))) -> MARK(U11(tt,M:S,N:S))
0.00/0.29	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.29	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.29	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.29	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.29	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.29	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.29	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.29	->->-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	
0.00/0.29	
0.00/0.29	The problem is decomposed in 5 subproblems.
0.00/0.29	
0.00/0.29	Problem 1.1: 
0.00/0.29	
0.00/0.29	Subterm Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 S(active(X:S)) -> S(X:S)
0.00/0.29	 S(mark(X:S)) -> S(X:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Projection:
0.00/0.29	 pi(S) = 1
0.00/0.29	
0.00/0.29	Problem 1.1: 
0.00/0.29	
0.00/0.29	SCC Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 Empty
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Strongly Connected Components:
0.00/0.29	 There is no strongly connected component
0.00/0.29	
0.00/0.29	The problem is finite.
0.00/0.29	
0.00/0.29	Problem 1.2: 
0.00/0.29	
0.00/0.29	Subterm Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Projection:
0.00/0.29	 pi(PLUS) = 1
0.00/0.29	
0.00/0.29	Problem 1.2: 
0.00/0.29	
0.00/0.29	SCC Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Strongly Connected Components:
0.00/0.29	->->Cycle:
0.00/0.29	->->-> Pairs:
0.00/0.29	 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	->->-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	
0.00/0.29	Problem 1.2: 
0.00/0.29	
0.00/0.29	Subterm Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Projection:
0.00/0.29	 pi(PLUS) = 2
0.00/0.29	
0.00/0.29	Problem 1.2: 
0.00/0.29	
0.00/0.29	SCC Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 Empty
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Strongly Connected Components:
0.00/0.29	 There is no strongly connected component
0.00/0.29	
0.00/0.29	The problem is finite.
0.00/0.29	
0.00/0.29	Problem 1.3: 
0.00/0.29	
0.00/0.29	Subterm Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U12#(active(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(mark(X1:S),X2:S,X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Projection:
0.00/0.29	 pi(U12#) = 1
0.00/0.29	
0.00/0.29	Problem 1.3: 
0.00/0.29	
0.00/0.29	SCC Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Strongly Connected Components:
0.00/0.29	->->Cycle:
0.00/0.29	->->-> Pairs:
0.00/0.29	 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	->->-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	
0.00/0.29	Problem 1.3: 
0.00/0.29	
0.00/0.29	Subterm Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U12#(X1:S,active(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,mark(X2:S),X3:S) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Projection:
0.00/0.29	 pi(U12#) = 2
0.00/0.29	
0.00/0.29	Problem 1.3: 
0.00/0.29	
0.00/0.29	SCC Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Strongly Connected Components:
0.00/0.29	->->Cycle:
0.00/0.29	->->-> Pairs:
0.00/0.29	 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	->->-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	
0.00/0.29	Problem 1.3: 
0.00/0.29	
0.00/0.29	Subterm Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U12#(X1:S,X2:S,active(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	 U12#(X1:S,X2:S,mark(X3:S)) -> U12#(X1:S,X2:S,X3:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Projection:
0.00/0.29	 pi(U12#) = 3
0.00/0.29	
0.00/0.29	Problem 1.3: 
0.00/0.29	
0.00/0.29	SCC Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 Empty
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Strongly Connected Components:
0.00/0.29	 There is no strongly connected component
0.00/0.29	
0.00/0.29	The problem is finite.
0.00/0.29	
0.00/0.29	Problem 1.4: 
0.00/0.29	
0.00/0.29	Subterm Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U11#(active(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(mark(X1:S),X2:S,X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Projection:
0.00/0.29	 pi(U11#) = 1
0.00/0.29	
0.00/0.29	Problem 1.4: 
0.00/0.29	
0.00/0.29	SCC Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Strongly Connected Components:
0.00/0.29	->->Cycle:
0.00/0.29	->->-> Pairs:
0.00/0.29	 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	->->-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	
0.00/0.29	Problem 1.4: 
0.00/0.29	
0.00/0.29	Subterm Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U11#(X1:S,active(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,mark(X2:S),X3:S) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Projection:
0.00/0.29	 pi(U11#) = 2
0.00/0.29	
0.00/0.29	Problem 1.4: 
0.00/0.29	
0.00/0.29	SCC Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Strongly Connected Components:
0.00/0.29	->->Cycle:
0.00/0.29	->->-> Pairs:
0.00/0.29	 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	->->-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	
0.00/0.29	Problem 1.4: 
0.00/0.29	
0.00/0.29	Subterm Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 U11#(X1:S,X2:S,active(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	 U11#(X1:S,X2:S,mark(X3:S)) -> U11#(X1:S,X2:S,X3:S)
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.29	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.29	 mark(0) -> active(0)
0.00/0.29	 mark(tt) -> active(tt)
0.00/0.29	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.29	 s(active(X:S)) -> s(X:S)
0.00/0.29	 s(mark(X:S)) -> s(X:S)
0.00/0.29	->Projection:
0.00/0.29	 pi(U11#) = 3
0.00/0.29	
0.00/0.29	Problem 1.4: 
0.00/0.29	
0.00/0.29	SCC Processor:
0.00/0.29	-> Pairs:
0.00/0.29	 Empty
0.00/0.29	-> Rules:
0.00/0.29	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.29	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.29	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.29	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.29	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.29	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.29	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.29	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	->Strongly Connected Components:
0.00/0.30	 There is no strongly connected component
0.00/0.30	
0.00/0.30	The problem is finite.
0.00/0.30	
0.00/0.30	Problem 1.5: 
0.00/0.30	
0.00/0.30	Reduction Pairs Processor:
0.00/0.30	-> Pairs:
0.00/0.30	 ACTIVE(U11(tt,M:S,N:S)) -> MARK(U12(tt,M:S,N:S))
0.00/0.30	 ACTIVE(U12(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S)))
0.00/0.30	 ACTIVE(plus(N:S,s(M:S))) -> MARK(U11(tt,M:S,N:S))
0.00/0.30	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	-> Usable rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	->Interpretation type:
0.00/0.30	 Linear
0.00/0.30	->Coefficients:
0.00/0.30	 Natural Numbers
0.00/0.30	->Dimension:
0.00/0.30	 1
0.00/0.30	->Bound:
0.00/0.30	 2
0.00/0.30	->Interpretation:
0.00/0.30	 
0.00/0.30	[U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
0.00/0.30	[U12](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
0.00/0.30	[active](X) = X
0.00/0.30	[mark](X) = X
0.00/0.30	[plus](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.30	[s](X) = X + 2
0.00/0.30	[0] = 2
0.00/0.30	[fSNonEmpty] = 0
0.00/0.30	[tt] = 2
0.00/0.30	[U11#](X1,X2,X3) = 0
0.00/0.30	[U12#](X1,X2,X3) = 0
0.00/0.30	[ACTIVE](X) = 2.X + 2
0.00/0.30	[MARK](X) = 2.X + 2
0.00/0.30	[PLUS](X1,X2) = 0
0.00/0.30	[S](X) = 0
0.00/0.30	
0.00/0.30	Problem 1.5: 
0.00/0.30	
0.00/0.30	SCC Processor:
0.00/0.30	-> Pairs:
0.00/0.30	 ACTIVE(U12(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S)))
0.00/0.30	 ACTIVE(plus(N:S,s(M:S))) -> MARK(U11(tt,M:S,N:S))
0.00/0.30	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	->Strongly Connected Components:
0.00/0.30	->->Cycle:
0.00/0.30	->->-> Pairs:
0.00/0.30	 ACTIVE(U12(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S)))
0.00/0.30	 ACTIVE(plus(N:S,s(M:S))) -> MARK(U11(tt,M:S,N:S))
0.00/0.30	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	->->-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	
0.00/0.30	Problem 1.5: 
0.00/0.30	
0.00/0.30	Reduction Pairs Processor:
0.00/0.30	-> Pairs:
0.00/0.30	 ACTIVE(U12(tt,M:S,N:S)) -> MARK(s(plus(N:S,M:S)))
0.00/0.30	 ACTIVE(plus(N:S,s(M:S))) -> MARK(U11(tt,M:S,N:S))
0.00/0.30	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	-> Usable rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	->Interpretation type:
0.00/0.30	 Linear
0.00/0.30	->Coefficients:
0.00/0.30	 Natural Numbers
0.00/0.30	->Dimension:
0.00/0.30	 1
0.00/0.30	->Bound:
0.00/0.30	 2
0.00/0.30	->Interpretation:
0.00/0.30	 
0.00/0.30	[U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
0.00/0.30	[U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
0.00/0.30	[active](X) = X
0.00/0.30	[mark](X) = X
0.00/0.30	[plus](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.30	[s](X) = X + 2
0.00/0.30	[0] = 2
0.00/0.30	[fSNonEmpty] = 0
0.00/0.30	[tt] = 2
0.00/0.30	[U11#](X1,X2,X3) = 0
0.00/0.30	[U12#](X1,X2,X3) = 0
0.00/0.30	[ACTIVE](X) = 2.X + 1
0.00/0.30	[MARK](X) = 2.X + 1
0.00/0.30	[PLUS](X1,X2) = 0
0.00/0.30	[S](X) = 0
0.00/0.30	
0.00/0.30	Problem 1.5: 
0.00/0.30	
0.00/0.30	SCC Processor:
0.00/0.30	-> Pairs:
0.00/0.30	 ACTIVE(plus(N:S,s(M:S))) -> MARK(U11(tt,M:S,N:S))
0.00/0.30	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	->Strongly Connected Components:
0.00/0.30	->->Cycle:
0.00/0.30	->->-> Pairs:
0.00/0.30	 ACTIVE(plus(N:S,s(M:S))) -> MARK(U11(tt,M:S,N:S))
0.00/0.30	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	->->-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	
0.00/0.30	Problem 1.5: 
0.00/0.30	
0.00/0.30	Reduction Pairs Processor:
0.00/0.30	-> Pairs:
0.00/0.30	 ACTIVE(plus(N:S,s(M:S))) -> MARK(U11(tt,M:S,N:S))
0.00/0.30	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	-> Usable rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	->Interpretation type:
0.00/0.30	 Linear
0.00/0.30	->Coefficients:
0.00/0.30	 Natural Numbers
0.00/0.30	->Dimension:
0.00/0.30	 1
0.00/0.30	->Bound:
0.00/0.30	 2
0.00/0.30	->Interpretation:
0.00/0.30	 
0.00/0.30	[U11](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
0.00/0.30	[U12](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 1
0.00/0.30	[active](X) = X
0.00/0.30	[mark](X) = X
0.00/0.30	[plus](X1,X2) = 2.X1 + 2.X2 + 1
0.00/0.30	[s](X) = X + 2
0.00/0.30	[0] = 2
0.00/0.30	[fSNonEmpty] = 0
0.00/0.30	[tt] = 2
0.00/0.30	[U11#](X1,X2,X3) = 0
0.00/0.30	[U12#](X1,X2,X3) = 0
0.00/0.30	[ACTIVE](X) = 2.X + 2
0.00/0.30	[MARK](X) = 2.X + 2
0.00/0.30	[PLUS](X1,X2) = 0
0.00/0.30	[S](X) = 0
0.00/0.30	
0.00/0.30	Problem 1.5: 
0.00/0.30	
0.00/0.30	SCC Processor:
0.00/0.30	-> Pairs:
0.00/0.30	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	->Strongly Connected Components:
0.00/0.30	->->Cycle:
0.00/0.30	->->-> Pairs:
0.00/0.30	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	->->-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	
0.00/0.30	Problem 1.5: 
0.00/0.30	
0.00/0.30	Reduction Pairs Processor:
0.00/0.30	-> Pairs:
0.00/0.30	 ACTIVE(plus(N:S,0)) -> MARK(N:S)
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	-> Usable rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	->Interpretation type:
0.00/0.30	 Linear
0.00/0.30	->Coefficients:
0.00/0.30	 Natural Numbers
0.00/0.30	->Dimension:
0.00/0.30	 1
0.00/0.30	->Bound:
0.00/0.30	 2
0.00/0.30	->Interpretation:
0.00/0.30	 
0.00/0.30	[U11](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
0.00/0.30	[U12](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
0.00/0.30	[active](X) = X
0.00/0.30	[mark](X) = X
0.00/0.30	[plus](X1,X2) = 2.X1 + 2.X2 + 2
0.00/0.30	[s](X) = X + 2
0.00/0.30	[0] = 2
0.00/0.30	[fSNonEmpty] = 0
0.00/0.30	[tt] = 2
0.00/0.30	[U11#](X1,X2,X3) = 0
0.00/0.30	[U12#](X1,X2,X3) = 0
0.00/0.30	[ACTIVE](X) = 2.X + 1
0.00/0.30	[MARK](X) = 2.X + 1
0.00/0.30	[PLUS](X1,X2) = 0
0.00/0.30	[S](X) = 0
0.00/0.30	
0.00/0.30	Problem 1.5: 
0.00/0.30	
0.00/0.30	SCC Processor:
0.00/0.30	-> Pairs:
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> ACTIVE(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> ACTIVE(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	->Strongly Connected Components:
0.00/0.30	->->Cycle:
0.00/0.30	->->-> Pairs:
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	->->-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	
0.00/0.30	Problem 1.5: 
0.00/0.30	
0.00/0.30	Subterm Processor:
0.00/0.30	-> Pairs:
0.00/0.30	 MARK(U11(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(U12(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.30	 MARK(plus(X1:S,X2:S)) -> MARK(X2:S)
0.00/0.30	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.30	-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	->Projection:
0.00/0.30	 pi(MARK) = 1
0.00/0.30	
0.00/0.30	Problem 1.5: 
0.00/0.30	
0.00/0.30	SCC Processor:
0.00/0.30	-> Pairs:
0.00/0.30	 Empty
0.00/0.30	-> Rules:
0.00/0.30	 U11(active(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(mark(X1:S),X2:S,X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,active(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,mark(X2:S),X3:S) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,active(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U11(X1:S,X2:S,mark(X3:S)) -> U11(X1:S,X2:S,X3:S)
0.00/0.30	 U12(active(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(mark(X1:S),X2:S,X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,active(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,mark(X2:S),X3:S) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,active(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 U12(X1:S,X2:S,mark(X3:S)) -> U12(X1:S,X2:S,X3:S)
0.00/0.30	 active(U11(tt,M:S,N:S)) -> mark(U12(tt,M:S,N:S))
0.00/0.30	 active(U12(tt,M:S,N:S)) -> mark(s(plus(N:S,M:S)))
0.00/0.30	 active(plus(N:S,s(M:S))) -> mark(U11(tt,M:S,N:S))
0.00/0.30	 active(plus(N:S,0)) -> mark(N:S)
0.00/0.30	 mark(U11(X1:S,X2:S,X3:S)) -> active(U11(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(U12(X1:S,X2:S,X3:S)) -> active(U12(mark(X1:S),X2:S,X3:S))
0.00/0.30	 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S)))
0.00/0.30	 mark(s(X:S)) -> active(s(mark(X:S)))
0.00/0.30	 mark(0) -> active(0)
0.00/0.30	 mark(tt) -> active(tt)
0.00/0.30	 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S)
0.00/0.30	 s(active(X:S)) -> s(X:S)
0.00/0.30	 s(mark(X:S)) -> s(X:S)
0.00/0.30	->Strongly Connected Components:
0.00/0.30	 There is no strongly connected component
0.00/0.30	
0.00/0.30	The problem is finite.
0.00/0.30	EOF