0.00/0.47 YES 0.00/0.47 0.00/0.47 Problem 1: 0.00/0.47 0.00/0.47 (VAR v_NonEmpty:S M:S N:S X:S X1:S X2:S) 0.00/0.47 (RULES 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ) 0.00/0.47 (STRATEGY INNERMOST) 0.00/0.47 0.00/0.47 Problem 1: 0.00/0.47 0.00/0.47 Dependency Pairs Processor: 0.00/0.47 -> Pairs: 0.00/0.47 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.47 ACTIVE(plus(N:S,s(M:S))) -> MARK(s(plus(N:S,M:S))) 0.00/0.47 ACTIVE(plus(N:S,s(M:S))) -> PLUS(N:S,M:S) 0.00/0.47 ACTIVE(plus(N:S,s(M:S))) -> S(plus(N:S,M:S)) 0.00/0.47 ACTIVE(plus(N:S,0)) -> MARK(N:S) 0.00/0.47 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.47 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.47 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.47 MARK(and(X1:S,X2:S)) -> AND(mark(X1:S),X2:S) 0.00/0.47 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> PLUS(mark(X1:S),mark(X2:S)) 0.00/0.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 0.00/0.47 MARK(s(X:S)) -> MARK(X:S) 0.00/0.47 MARK(s(X:S)) -> S(mark(X:S)) 0.00/0.47 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 S(active(X:S)) -> S(X:S) 0.00/0.47 S(mark(X:S)) -> S(X:S) 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 0.00/0.47 Problem 1: 0.00/0.47 0.00/0.47 SCC Processor: 0.00/0.47 -> Pairs: 0.00/0.47 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.47 ACTIVE(plus(N:S,s(M:S))) -> MARK(s(plus(N:S,M:S))) 0.00/0.47 ACTIVE(plus(N:S,s(M:S))) -> PLUS(N:S,M:S) 0.00/0.47 ACTIVE(plus(N:S,s(M:S))) -> S(plus(N:S,M:S)) 0.00/0.47 ACTIVE(plus(N:S,0)) -> MARK(N:S) 0.00/0.47 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.47 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.47 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.47 MARK(and(X1:S,X2:S)) -> AND(mark(X1:S),X2:S) 0.00/0.47 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> PLUS(mark(X1:S),mark(X2:S)) 0.00/0.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 0.00/0.47 MARK(s(X:S)) -> MARK(X:S) 0.00/0.47 MARK(s(X:S)) -> S(mark(X:S)) 0.00/0.47 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 S(active(X:S)) -> S(X:S) 0.00/0.47 S(mark(X:S)) -> S(X:S) 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Strongly Connected Components: 0.00/0.47 ->->Cycle: 0.00/0.47 ->->-> Pairs: 0.00/0.47 S(active(X:S)) -> S(X:S) 0.00/0.47 S(mark(X:S)) -> S(X:S) 0.00/0.47 ->->-> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->->Cycle: 0.00/0.47 ->->-> Pairs: 0.00/0.47 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 ->->-> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->->Cycle: 0.00/0.47 ->->-> Pairs: 0.00/0.47 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.47 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.47 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 ->->-> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->->Cycle: 0.00/0.47 ->->-> Pairs: 0.00/0.47 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.47 ACTIVE(plus(N:S,s(M:S))) -> MARK(s(plus(N:S,M:S))) 0.00/0.47 ACTIVE(plus(N:S,0)) -> MARK(N:S) 0.00/0.47 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.47 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 0.00/0.47 MARK(s(X:S)) -> MARK(X:S) 0.00/0.47 ->->-> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 0.00/0.47 0.00/0.47 The problem is decomposed in 4 subproblems. 0.00/0.47 0.00/0.47 Problem 1.1: 0.00/0.47 0.00/0.47 Subterm Processor: 0.00/0.47 -> Pairs: 0.00/0.47 S(active(X:S)) -> S(X:S) 0.00/0.47 S(mark(X:S)) -> S(X:S) 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Projection: 0.00/0.47 pi(S) = 1 0.00/0.47 0.00/0.47 Problem 1.1: 0.00/0.47 0.00/0.47 SCC Processor: 0.00/0.47 -> Pairs: 0.00/0.47 Empty 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Strongly Connected Components: 0.00/0.47 There is no strongly connected component 0.00/0.47 0.00/0.47 The problem is finite. 0.00/0.47 0.00/0.47 Problem 1.2: 0.00/0.47 0.00/0.47 Subterm Processor: 0.00/0.47 -> Pairs: 0.00/0.47 PLUS(active(X1:S),X2:S) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(mark(X1:S),X2:S) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Projection: 0.00/0.47 pi(PLUS) = 1 0.00/0.47 0.00/0.47 Problem 1.2: 0.00/0.47 0.00/0.47 SCC Processor: 0.00/0.47 -> Pairs: 0.00/0.47 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Strongly Connected Components: 0.00/0.47 ->->Cycle: 0.00/0.47 ->->-> Pairs: 0.00/0.47 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 ->->-> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 0.00/0.47 Problem 1.2: 0.00/0.47 0.00/0.47 Subterm Processor: 0.00/0.47 -> Pairs: 0.00/0.47 PLUS(X1:S,active(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 PLUS(X1:S,mark(X2:S)) -> PLUS(X1:S,X2:S) 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Projection: 0.00/0.47 pi(PLUS) = 2 0.00/0.47 0.00/0.47 Problem 1.2: 0.00/0.47 0.00/0.47 SCC Processor: 0.00/0.47 -> Pairs: 0.00/0.47 Empty 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Strongly Connected Components: 0.00/0.47 There is no strongly connected component 0.00/0.47 0.00/0.47 The problem is finite. 0.00/0.47 0.00/0.47 Problem 1.3: 0.00/0.47 0.00/0.47 Subterm Processor: 0.00/0.47 -> Pairs: 0.00/0.47 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.47 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S) 0.00/0.47 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Projection: 0.00/0.47 pi(AND) = 1 0.00/0.47 0.00/0.47 Problem 1.3: 0.00/0.47 0.00/0.47 SCC Processor: 0.00/0.47 -> Pairs: 0.00/0.47 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Strongly Connected Components: 0.00/0.47 ->->Cycle: 0.00/0.47 ->->-> Pairs: 0.00/0.47 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 ->->-> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 0.00/0.47 Problem 1.3: 0.00/0.47 0.00/0.47 Subterm Processor: 0.00/0.47 -> Pairs: 0.00/0.47 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S) 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Projection: 0.00/0.47 pi(AND) = 2 0.00/0.47 0.00/0.47 Problem 1.3: 0.00/0.47 0.00/0.47 SCC Processor: 0.00/0.47 -> Pairs: 0.00/0.47 Empty 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Strongly Connected Components: 0.00/0.47 There is no strongly connected component 0.00/0.47 0.00/0.47 The problem is finite. 0.00/0.47 0.00/0.47 Problem 1.4: 0.00/0.47 0.00/0.47 Reduction Pairs Processor: 0.00/0.47 -> Pairs: 0.00/0.47 ACTIVE(and(tt,X:S)) -> MARK(X:S) 0.00/0.47 ACTIVE(plus(N:S,s(M:S))) -> MARK(s(plus(N:S,M:S))) 0.00/0.47 ACTIVE(plus(N:S,0)) -> MARK(N:S) 0.00/0.47 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.47 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 0.00/0.47 MARK(s(X:S)) -> MARK(X:S) 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 -> Usable rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Interpretation type: 0.00/0.47 Linear 0.00/0.47 ->Coefficients: 0.00/0.47 Natural Numbers 0.00/0.47 ->Dimension: 0.00/0.47 1 0.00/0.47 ->Bound: 0.00/0.47 2 0.00/0.47 ->Interpretation: 0.00/0.47 0.00/0.47 [active](X) = X 0.00/0.47 [and](X1,X2) = 2.X1 + X2 + 2 0.00/0.47 [mark](X) = X 0.00/0.47 [plus](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.47 [s](X) = X + 2 0.00/0.47 [0] = 2 0.00/0.47 [fSNonEmpty] = 0 0.00/0.47 [tt] = 2 0.00/0.47 [ACTIVE](X) = 2.X + 2 0.00/0.47 [AND](X1,X2) = 0 0.00/0.47 [MARK](X) = 2.X + 2 0.00/0.47 [PLUS](X1,X2) = 0 0.00/0.47 [S](X) = 0 0.00/0.47 0.00/0.47 Problem 1.4: 0.00/0.47 0.00/0.47 SCC Processor: 0.00/0.47 -> Pairs: 0.00/0.47 ACTIVE(plus(N:S,s(M:S))) -> MARK(s(plus(N:S,M:S))) 0.00/0.47 ACTIVE(plus(N:S,0)) -> MARK(N:S) 0.00/0.47 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.47 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 0.00/0.47 MARK(s(X:S)) -> MARK(X:S) 0.00/0.47 -> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.47 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.47 active(plus(N:S,0)) -> mark(N:S) 0.00/0.47 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.47 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.47 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.47 mark(0) -> active(0) 0.00/0.47 mark(tt) -> active(tt) 0.00/0.47 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.47 s(active(X:S)) -> s(X:S) 0.00/0.47 s(mark(X:S)) -> s(X:S) 0.00/0.47 ->Strongly Connected Components: 0.00/0.47 ->->Cycle: 0.00/0.47 ->->-> Pairs: 0.00/0.47 ACTIVE(plus(N:S,s(M:S))) -> MARK(s(plus(N:S,M:S))) 0.00/0.47 ACTIVE(plus(N:S,0)) -> MARK(N:S) 0.00/0.47 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.47 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.47 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.47 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 0.00/0.47 MARK(s(X:S)) -> MARK(X:S) 0.00/0.47 ->->-> Rules: 0.00/0.47 active(and(tt,X:S)) -> mark(X:S) 0.00/0.48 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.48 active(plus(N:S,0)) -> mark(N:S) 0.00/0.48 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.48 mark(0) -> active(0) 0.00/0.48 mark(tt) -> active(tt) 0.00/0.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 s(active(X:S)) -> s(X:S) 0.00/0.48 s(mark(X:S)) -> s(X:S) 0.00/0.48 0.00/0.48 Problem 1.4: 0.00/0.48 0.00/0.48 Reduction Pairs Processor: 0.00/0.48 -> Pairs: 0.00/0.48 ACTIVE(plus(N:S,s(M:S))) -> MARK(s(plus(N:S,M:S))) 0.00/0.48 ACTIVE(plus(N:S,0)) -> MARK(N:S) 0.00/0.48 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.48 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 0.00/0.48 MARK(s(X:S)) -> MARK(X:S) 0.00/0.48 -> Rules: 0.00/0.48 active(and(tt,X:S)) -> mark(X:S) 0.00/0.48 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.48 active(plus(N:S,0)) -> mark(N:S) 0.00/0.48 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.48 mark(0) -> active(0) 0.00/0.48 mark(tt) -> active(tt) 0.00/0.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 s(active(X:S)) -> s(X:S) 0.00/0.48 s(mark(X:S)) -> s(X:S) 0.00/0.48 -> Usable rules: 0.00/0.48 active(and(tt,X:S)) -> mark(X:S) 0.00/0.48 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.48 active(plus(N:S,0)) -> mark(N:S) 0.00/0.48 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.48 mark(0) -> active(0) 0.00/0.48 mark(tt) -> active(tt) 0.00/0.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 s(active(X:S)) -> s(X:S) 0.00/0.48 s(mark(X:S)) -> s(X:S) 0.00/0.48 ->Interpretation type: 0.00/0.48 Linear 0.00/0.48 ->Coefficients: 0.00/0.48 Natural Numbers 0.00/0.48 ->Dimension: 0.00/0.48 1 0.00/0.48 ->Bound: 0.00/0.48 2 0.00/0.48 ->Interpretation: 0.00/0.48 0.00/0.48 [active](X) = X 0.00/0.48 [and](X1,X2) = X1 + 2.X2 + 2 0.00/0.48 [mark](X) = X 0.00/0.48 [plus](X1,X2) = 2.X1 + 2.X2 0.00/0.48 [s](X) = X + 1 0.00/0.48 [0] = 2 0.00/0.48 [fSNonEmpty] = 0 0.00/0.48 [tt] = 0 0.00/0.48 [ACTIVE](X) = 2.X + 2 0.00/0.48 [AND](X1,X2) = 0 0.00/0.48 [MARK](X) = 2.X + 2 0.00/0.48 [PLUS](X1,X2) = 0 0.00/0.48 [S](X) = 0 0.00/0.48 0.00/0.48 Problem 1.4: 0.00/0.48 0.00/0.48 SCC Processor: 0.00/0.48 -> Pairs: 0.00/0.48 ACTIVE(plus(N:S,0)) -> MARK(N:S) 0.00/0.48 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.48 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 0.00/0.48 MARK(s(X:S)) -> MARK(X:S) 0.00/0.48 -> Rules: 0.00/0.48 active(and(tt,X:S)) -> mark(X:S) 0.00/0.48 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.48 active(plus(N:S,0)) -> mark(N:S) 0.00/0.48 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.48 mark(0) -> active(0) 0.00/0.48 mark(tt) -> active(tt) 0.00/0.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 s(active(X:S)) -> s(X:S) 0.00/0.48 s(mark(X:S)) -> s(X:S) 0.00/0.48 ->Strongly Connected Components: 0.00/0.48 ->->Cycle: 0.00/0.48 ->->-> Pairs: 0.00/0.48 ACTIVE(plus(N:S,0)) -> MARK(N:S) 0.00/0.48 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.48 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 0.00/0.48 MARK(s(X:S)) -> MARK(X:S) 0.00/0.48 ->->-> Rules: 0.00/0.48 active(and(tt,X:S)) -> mark(X:S) 0.00/0.48 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.48 active(plus(N:S,0)) -> mark(N:S) 0.00/0.48 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.48 mark(0) -> active(0) 0.00/0.48 mark(tt) -> active(tt) 0.00/0.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 s(active(X:S)) -> s(X:S) 0.00/0.48 s(mark(X:S)) -> s(X:S) 0.00/0.48 0.00/0.48 Problem 1.4: 0.00/0.48 0.00/0.48 Reduction Pairs Processor: 0.00/0.48 -> Pairs: 0.00/0.48 ACTIVE(plus(N:S,0)) -> MARK(N:S) 0.00/0.48 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.48 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 0.00/0.48 MARK(s(X:S)) -> MARK(X:S) 0.00/0.48 -> Rules: 0.00/0.48 active(and(tt,X:S)) -> mark(X:S) 0.00/0.48 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.48 active(plus(N:S,0)) -> mark(N:S) 0.00/0.48 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.48 mark(0) -> active(0) 0.00/0.48 mark(tt) -> active(tt) 0.00/0.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 s(active(X:S)) -> s(X:S) 0.00/0.48 s(mark(X:S)) -> s(X:S) 0.00/0.48 -> Usable rules: 0.00/0.48 active(and(tt,X:S)) -> mark(X:S) 0.00/0.48 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.48 active(plus(N:S,0)) -> mark(N:S) 0.00/0.48 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.48 mark(0) -> active(0) 0.00/0.48 mark(tt) -> active(tt) 0.00/0.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 s(active(X:S)) -> s(X:S) 0.00/0.48 s(mark(X:S)) -> s(X:S) 0.00/0.48 ->Interpretation type: 0.00/0.48 Linear 0.00/0.48 ->Coefficients: 0.00/0.48 Natural Numbers 0.00/0.48 ->Dimension: 0.00/0.48 1 0.00/0.48 ->Bound: 0.00/0.48 2 0.00/0.48 ->Interpretation: 0.00/0.48 0.00/0.48 [active](X) = X 0.00/0.48 [and](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.48 [mark](X) = X 0.00/0.48 [plus](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.48 [s](X) = X 0.00/0.48 [0] = 2 0.00/0.48 [fSNonEmpty] = 0 0.00/0.48 [tt] = 0 0.00/0.48 [ACTIVE](X) = 2.X + 1 0.00/0.48 [AND](X1,X2) = 0 0.00/0.48 [MARK](X) = 2.X + 2 0.00/0.48 [PLUS](X1,X2) = 0 0.00/0.48 [S](X) = 0 0.00/0.48 0.00/0.48 Problem 1.4: 0.00/0.48 0.00/0.48 SCC Processor: 0.00/0.48 -> Pairs: 0.00/0.48 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S)) 0.00/0.48 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> ACTIVE(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.48 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 0.00/0.48 MARK(s(X:S)) -> MARK(X:S) 0.00/0.48 -> Rules: 0.00/0.48 active(and(tt,X:S)) -> mark(X:S) 0.00/0.48 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.48 active(plus(N:S,0)) -> mark(N:S) 0.00/0.48 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.48 mark(0) -> active(0) 0.00/0.48 mark(tt) -> active(tt) 0.00/0.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 s(active(X:S)) -> s(X:S) 0.00/0.48 s(mark(X:S)) -> s(X:S) 0.00/0.48 ->Strongly Connected Components: 0.00/0.48 ->->Cycle: 0.00/0.48 ->->-> Pairs: 0.00/0.48 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.48 MARK(s(X:S)) -> MARK(X:S) 0.00/0.48 ->->-> Rules: 0.00/0.48 active(and(tt,X:S)) -> mark(X:S) 0.00/0.48 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.48 active(plus(N:S,0)) -> mark(N:S) 0.00/0.48 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.48 mark(0) -> active(0) 0.00/0.48 mark(tt) -> active(tt) 0.00/0.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 s(active(X:S)) -> s(X:S) 0.00/0.48 s(mark(X:S)) -> s(X:S) 0.00/0.48 0.00/0.48 Problem 1.4: 0.00/0.48 0.00/0.48 Subterm Processor: 0.00/0.48 -> Pairs: 0.00/0.48 MARK(and(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.48 MARK(plus(X1:S,X2:S)) -> MARK(X2:S) 0.00/0.48 MARK(s(X:S)) -> MARK(X:S) 0.00/0.48 -> Rules: 0.00/0.48 active(and(tt,X:S)) -> mark(X:S) 0.00/0.48 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.48 active(plus(N:S,0)) -> mark(N:S) 0.00/0.48 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.48 mark(0) -> active(0) 0.00/0.48 mark(tt) -> active(tt) 0.00/0.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 s(active(X:S)) -> s(X:S) 0.00/0.48 s(mark(X:S)) -> s(X:S) 0.00/0.48 ->Projection: 0.00/0.48 pi(MARK) = 1 0.00/0.48 0.00/0.48 Problem 1.4: 0.00/0.48 0.00/0.48 SCC Processor: 0.00/0.48 -> Pairs: 0.00/0.48 Empty 0.00/0.48 -> Rules: 0.00/0.48 active(and(tt,X:S)) -> mark(X:S) 0.00/0.48 active(plus(N:S,s(M:S))) -> mark(s(plus(N:S,M:S))) 0.00/0.48 active(plus(N:S,0)) -> mark(N:S) 0.00/0.48 and(active(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(mark(X1:S),X2:S) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,active(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S) 0.00/0.48 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S)) 0.00/0.48 mark(plus(X1:S,X2:S)) -> active(plus(mark(X1:S),mark(X2:S))) 0.00/0.48 mark(s(X:S)) -> active(s(mark(X:S))) 0.00/0.48 mark(0) -> active(0) 0.00/0.48 mark(tt) -> active(tt) 0.00/0.48 plus(active(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(mark(X1:S),X2:S) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,active(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 plus(X1:S,mark(X2:S)) -> plus(X1:S,X2:S) 0.00/0.48 s(active(X:S)) -> s(X:S) 0.00/0.48 s(mark(X:S)) -> s(X:S) 0.00/0.48 ->Strongly Connected Components: 0.00/0.48 There is no strongly connected component 0.00/0.48 0.00/0.48 The problem is finite. 0.00/0.48 EOF