67.98/69.09 YES 67.98/69.09 67.98/69.09 Problem 1: 67.98/69.09 67.98/69.09 (VAR v_NonEmpty:S X:S X1:S X2:S Y:S Z:S) 67.98/69.09 (RULES 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 ) 67.98/69.09 (STRATEGY INNERMOST) 67.98/69.09 67.98/69.09 Problem 1: 67.98/69.09 67.98/69.09 Dependency Pairs Processor: 67.98/69.09 -> Pairs: 67.98/69.09 2ND(active(X:S)) -> 2ND(X:S) 67.98/69.09 2ND(mark(X:S)) -> 2ND(X:S) 67.98/69.09 ACTIVE(2nd(cons(X:S,X1:S))) -> 2ND(cons1(X:S,X1:S)) 67.98/69.09 ACTIVE(2nd(cons(X:S,X1:S))) -> CONS1(X:S,X1:S) 67.98/69.09 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.09 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.09 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S))) 67.98/69.09 ACTIVE(from(X:S)) -> FROM(s(X:S)) 67.98/69.09 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.09 ACTIVE(from(X:S)) -> S(X:S) 67.98/69.09 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S) 67.98/69.09 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 67.98/69.09 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.09 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.09 CONS1(active(X1:S),X2:S) -> CONS1(X1:S,X2:S) 67.98/69.09 CONS1(mark(X1:S),X2:S) -> CONS1(X1:S,X2:S) 67.98/69.09 CONS1(X1:S,active(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.09 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.09 FROM(active(X:S)) -> FROM(X:S) 67.98/69.09 FROM(mark(X:S)) -> FROM(X:S) 67.98/69.09 MARK(2nd(X:S)) -> 2ND(mark(X:S)) 67.98/69.09 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.09 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.09 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S)) 67.98/69.09 MARK(cons(X1:S,X2:S)) -> CONS(mark(X1:S),X2:S) 67.98/69.09 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.09 MARK(cons1(X1:S,X2:S)) -> ACTIVE(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 MARK(cons1(X1:S,X2:S)) -> CONS1(mark(X1:S),mark(X2:S)) 67.98/69.09 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.09 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.09 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.09 MARK(from(X:S)) -> FROM(mark(X:S)) 67.98/69.09 MARK(from(X:S)) -> MARK(X:S) 67.98/69.09 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 67.98/69.09 MARK(s(X:S)) -> MARK(X:S) 67.98/69.09 MARK(s(X:S)) -> S(mark(X:S)) 67.98/69.09 S(active(X:S)) -> S(X:S) 67.98/69.09 S(mark(X:S)) -> S(X:S) 67.98/69.09 -> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 67.98/69.09 Problem 1: 67.98/69.09 67.98/69.09 SCC Processor: 67.98/69.09 -> Pairs: 67.98/69.09 2ND(active(X:S)) -> 2ND(X:S) 67.98/69.09 2ND(mark(X:S)) -> 2ND(X:S) 67.98/69.09 ACTIVE(2nd(cons(X:S,X1:S))) -> 2ND(cons1(X:S,X1:S)) 67.98/69.09 ACTIVE(2nd(cons(X:S,X1:S))) -> CONS1(X:S,X1:S) 67.98/69.09 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.09 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.09 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S))) 67.98/69.09 ACTIVE(from(X:S)) -> FROM(s(X:S)) 67.98/69.09 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.09 ACTIVE(from(X:S)) -> S(X:S) 67.98/69.09 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S) 67.98/69.09 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 67.98/69.09 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.09 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.09 CONS1(active(X1:S),X2:S) -> CONS1(X1:S,X2:S) 67.98/69.09 CONS1(mark(X1:S),X2:S) -> CONS1(X1:S,X2:S) 67.98/69.09 CONS1(X1:S,active(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.09 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.09 FROM(active(X:S)) -> FROM(X:S) 67.98/69.09 FROM(mark(X:S)) -> FROM(X:S) 67.98/69.09 MARK(2nd(X:S)) -> 2ND(mark(X:S)) 67.98/69.09 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.09 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.09 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S)) 67.98/69.09 MARK(cons(X1:S,X2:S)) -> CONS(mark(X1:S),X2:S) 67.98/69.09 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.09 MARK(cons1(X1:S,X2:S)) -> ACTIVE(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 MARK(cons1(X1:S,X2:S)) -> CONS1(mark(X1:S),mark(X2:S)) 67.98/69.09 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.09 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.09 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.09 MARK(from(X:S)) -> FROM(mark(X:S)) 67.98/69.09 MARK(from(X:S)) -> MARK(X:S) 67.98/69.09 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 67.98/69.09 MARK(s(X:S)) -> MARK(X:S) 67.98/69.09 MARK(s(X:S)) -> S(mark(X:S)) 67.98/69.09 S(active(X:S)) -> S(X:S) 67.98/69.09 S(mark(X:S)) -> S(X:S) 67.98/69.09 -> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 ->Strongly Connected Components: 67.98/69.09 ->->Cycle: 67.98/69.09 ->->-> Pairs: 67.98/69.09 S(active(X:S)) -> S(X:S) 67.98/69.09 S(mark(X:S)) -> S(X:S) 67.98/69.09 ->->-> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 ->->Cycle: 67.98/69.09 ->->-> Pairs: 67.98/69.09 FROM(active(X:S)) -> FROM(X:S) 67.98/69.09 FROM(mark(X:S)) -> FROM(X:S) 67.98/69.09 ->->-> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 ->->Cycle: 67.98/69.09 ->->-> Pairs: 67.98/69.09 CONS1(active(X1:S),X2:S) -> CONS1(X1:S,X2:S) 67.98/69.09 CONS1(mark(X1:S),X2:S) -> CONS1(X1:S,X2:S) 67.98/69.09 CONS1(X1:S,active(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.09 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.09 ->->-> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 ->->Cycle: 67.98/69.09 ->->-> Pairs: 67.98/69.09 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S) 67.98/69.09 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 67.98/69.09 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.09 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.09 ->->-> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 ->->Cycle: 67.98/69.09 ->->-> Pairs: 67.98/69.09 2ND(active(X:S)) -> 2ND(X:S) 67.98/69.09 2ND(mark(X:S)) -> 2ND(X:S) 67.98/69.09 ->->-> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 ->->Cycle: 67.98/69.09 ->->-> Pairs: 67.98/69.09 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.09 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.09 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.09 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.09 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.09 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S)) 67.98/69.09 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.09 MARK(cons1(X1:S,X2:S)) -> ACTIVE(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.09 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.09 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.09 MARK(from(X:S)) -> MARK(X:S) 67.98/69.09 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 67.98/69.09 MARK(s(X:S)) -> MARK(X:S) 67.98/69.09 ->->-> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 67.98/69.09 67.98/69.09 The problem is decomposed in 6 subproblems. 67.98/69.09 67.98/69.09 Problem 1.1: 67.98/69.09 67.98/69.09 Subterm Processor: 67.98/69.09 -> Pairs: 67.98/69.09 S(active(X:S)) -> S(X:S) 67.98/69.09 S(mark(X:S)) -> S(X:S) 67.98/69.09 -> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 ->Projection: 67.98/69.09 pi(S) = 1 67.98/69.09 67.98/69.09 Problem 1.1: 67.98/69.09 67.98/69.09 SCC Processor: 67.98/69.09 -> Pairs: 67.98/69.09 Empty 67.98/69.09 -> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 ->Strongly Connected Components: 67.98/69.09 There is no strongly connected component 67.98/69.09 67.98/69.09 The problem is finite. 67.98/69.09 67.98/69.09 Problem 1.2: 67.98/69.09 67.98/69.09 Subterm Processor: 67.98/69.09 -> Pairs: 67.98/69.09 FROM(active(X:S)) -> FROM(X:S) 67.98/69.09 FROM(mark(X:S)) -> FROM(X:S) 67.98/69.09 -> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 ->Projection: 67.98/69.09 pi(FROM) = 1 67.98/69.09 67.98/69.09 Problem 1.2: 67.98/69.09 67.98/69.09 SCC Processor: 67.98/69.09 -> Pairs: 67.98/69.09 Empty 67.98/69.09 -> Rules: 67.98/69.09 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.09 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.09 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.09 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.09 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.09 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.09 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.09 from(active(X:S)) -> from(X:S) 67.98/69.09 from(mark(X:S)) -> from(X:S) 67.98/69.09 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.09 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.09 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.09 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.09 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.09 s(active(X:S)) -> s(X:S) 67.98/69.09 s(mark(X:S)) -> s(X:S) 67.98/69.09 ->Strongly Connected Components: 67.98/69.09 There is no strongly connected component 67.98/69.09 67.98/69.09 The problem is finite. 67.98/69.09 67.98/69.09 Problem 1.3: 67.98/69.09 67.98/69.09 Subterm Processor: 67.98/69.09 -> Pairs: 67.98/69.09 CONS1(active(X1:S),X2:S) -> CONS1(X1:S,X2:S) 67.98/69.10 CONS1(mark(X1:S),X2:S) -> CONS1(X1:S,X2:S) 67.98/69.10 CONS1(X1:S,active(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.10 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Projection: 67.98/69.10 pi(CONS1) = 1 67.98/69.10 67.98/69.10 Problem 1.3: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 CONS1(X1:S,active(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.10 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 ->->Cycle: 67.98/69.10 ->->-> Pairs: 67.98/69.10 CONS1(X1:S,active(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.10 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.10 ->->-> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 67.98/69.10 Problem 1.3: 67.98/69.10 67.98/69.10 Subterm Processor: 67.98/69.10 -> Pairs: 67.98/69.10 CONS1(X1:S,active(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.10 CONS1(X1:S,mark(X2:S)) -> CONS1(X1:S,X2:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Projection: 67.98/69.10 pi(CONS1) = 2 67.98/69.10 67.98/69.10 Problem 1.3: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 Empty 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 There is no strongly connected component 67.98/69.10 67.98/69.10 The problem is finite. 67.98/69.10 67.98/69.10 Problem 1.4: 67.98/69.10 67.98/69.10 Subterm Processor: 67.98/69.10 -> Pairs: 67.98/69.10 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S) 67.98/69.10 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 67.98/69.10 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.10 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Projection: 67.98/69.10 pi(CONS) = 1 67.98/69.10 67.98/69.10 Problem 1.4: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.10 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 ->->Cycle: 67.98/69.10 ->->-> Pairs: 67.98/69.10 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.10 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.10 ->->-> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 67.98/69.10 Problem 1.4: 67.98/69.10 67.98/69.10 Subterm Processor: 67.98/69.10 -> Pairs: 67.98/69.10 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.10 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Projection: 67.98/69.10 pi(CONS) = 2 67.98/69.10 67.98/69.10 Problem 1.4: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 Empty 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 There is no strongly connected component 67.98/69.10 67.98/69.10 The problem is finite. 67.98/69.10 67.98/69.10 Problem 1.5: 67.98/69.10 67.98/69.10 Subterm Processor: 67.98/69.10 -> Pairs: 67.98/69.10 2ND(active(X:S)) -> 2ND(X:S) 67.98/69.10 2ND(mark(X:S)) -> 2ND(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Projection: 67.98/69.10 pi(2ND) = 1 67.98/69.10 67.98/69.10 Problem 1.5: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 Empty 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 There is no strongly connected component 67.98/69.10 67.98/69.10 The problem is finite. 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 Reduction Pairs Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S)) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> ACTIVE(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 -> Usable rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Interpretation type: 67.98/69.10 Linear 67.98/69.10 ->Coefficients: 67.98/69.10 Natural Numbers 67.98/69.10 ->Dimension: 67.98/69.10 1 67.98/69.10 ->Bound: 67.98/69.10 2 67.98/69.10 ->Interpretation: 67.98/69.10 67.98/69.10 [2nd](X) = 2 67.98/69.10 [active](X) = 2 67.98/69.10 [cons](X1,X2) = 1 67.98/69.10 [cons1](X1,X2) = 1 67.98/69.10 [from](X) = 2 67.98/69.10 [mark](X) = 2 67.98/69.10 [s](X) = 2 67.98/69.10 [fSNonEmpty] = 0 67.98/69.10 [2ND](X) = 0 67.98/69.10 [ACTIVE](X) = X 67.98/69.10 [CONS](X1,X2) = 0 67.98/69.10 [CONS1](X1,X2) = 0 67.98/69.10 [FROM](X) = 0 67.98/69.10 [MARK](X) = 2 67.98/69.10 [S](X) = 0 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> ACTIVE(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 ->->Cycle: 67.98/69.10 ->->-> Pairs: 67.98/69.10 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> ACTIVE(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 ->->-> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 Reduction Pairs Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> ACTIVE(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 -> Usable rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Interpretation type: 67.98/69.10 Linear 67.98/69.10 ->Coefficients: 67.98/69.10 Natural Numbers 67.98/69.10 ->Dimension: 67.98/69.10 1 67.98/69.10 ->Bound: 67.98/69.10 2 67.98/69.10 ->Interpretation: 67.98/69.10 67.98/69.10 [2nd](X) = 1 67.98/69.10 [active](X) = 2.X 67.98/69.10 [cons](X1,X2) = 0 67.98/69.10 [cons1](X1,X2) = 0 67.98/69.10 [from](X) = 1 67.98/69.10 [mark](X) = 2 67.98/69.10 [s](X) = 0 67.98/69.10 [fSNonEmpty] = 0 67.98/69.10 [2ND](X) = 0 67.98/69.10 [ACTIVE](X) = X + 1 67.98/69.10 [CONS](X1,X2) = 0 67.98/69.10 [CONS1](X1,X2) = 0 67.98/69.10 [FROM](X) = 0 67.98/69.10 [MARK](X) = 2 67.98/69.10 [S](X) = 0 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 ->->Cycle: 67.98/69.10 ->->-> Pairs: 67.98/69.10 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 ->->-> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 Reduction Pairs Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> ACTIVE(s(mark(X:S))) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 -> Usable rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Interpretation type: 67.98/69.10 Linear 67.98/69.10 ->Coefficients: 67.98/69.10 Natural Numbers 67.98/69.10 ->Dimension: 67.98/69.10 1 67.98/69.10 ->Bound: 67.98/69.10 2 67.98/69.10 ->Interpretation: 67.98/69.10 67.98/69.10 [2nd](X) = 2 67.98/69.10 [active](X) = X 67.98/69.10 [cons](X1,X2) = 0 67.98/69.10 [cons1](X1,X2) = 2 67.98/69.10 [from](X) = 2 67.98/69.10 [mark](X) = 2 67.98/69.10 [s](X) = 0 67.98/69.10 [fSNonEmpty] = 0 67.98/69.10 [2ND](X) = 0 67.98/69.10 [ACTIVE](X) = X 67.98/69.10 [CONS](X1,X2) = 0 67.98/69.10 [CONS1](X1,X2) = 0 67.98/69.10 [FROM](X) = 0 67.98/69.10 [MARK](X) = 2 67.98/69.10 [S](X) = 0 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 ->->Cycle: 67.98/69.10 ->->-> Pairs: 67.98/69.10 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 ->->-> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 Reduction Pairs Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(2nd(cons(X:S,X1:S))) -> MARK(2nd(cons1(X:S,X1:S))) 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 -> Usable rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Interpretation type: 67.98/69.10 Linear 67.98/69.10 ->Coefficients: 67.98/69.10 Natural Numbers 67.98/69.10 ->Dimension: 67.98/69.10 2 67.98/69.10 ->Bound: 67.98/69.10 1 67.98/69.10 ->Interpretation: 67.98/69.10 67.98/69.10 [2nd](X) = [1 1;1 1].X + [1;0] 67.98/69.10 [active](X) = [1 0;0 1].X 67.98/69.10 [cons](X1,X2) = [1 1;0 0].X1 + [0 0;1 0].X2 + [0;1] 67.98/69.10 [cons1](X1,X2) = [1 1;0 0].X1 + [1 0;0 0].X2 67.98/69.10 [from](X) = [1 1;1 0].X + [0;1] 67.98/69.10 [mark](X) = [1 0;0 1].X 67.98/69.10 [s](X) = [1 0;0 0].X 67.98/69.10 [fSNonEmpty] = 0 67.98/69.10 [2ND](X) = 0 67.98/69.10 [ACTIVE](X) = [1 0;1 0].X + [1;1] 67.98/69.10 [CONS](X1,X2) = 0 67.98/69.10 [CONS1](X1,X2) = 0 67.98/69.10 [FROM](X) = 0 67.98/69.10 [MARK](X) = [1 0;1 0].X + [1;1] 67.98/69.10 [S](X) = 0 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 ->->Cycle: 67.98/69.10 ->->-> Pairs: 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 ->->-> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 Reduction Pairs Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> MARK(Y:S) 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 -> Usable rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Interpretation type: 67.98/69.10 Linear 67.98/69.10 ->Coefficients: 67.98/69.10 Natural Numbers 67.98/69.10 ->Dimension: 67.98/69.10 2 67.98/69.10 ->Bound: 67.98/69.10 1 67.98/69.10 ->Interpretation: 67.98/69.10 67.98/69.10 [2nd](X) = [1 1;1 1].X + [1;1] 67.98/69.10 [active](X) = [1 0;0 1].X 67.98/69.10 [cons](X1,X2) = [1 1;0 0].X1 + [0 0;1 0].X2 67.98/69.10 [cons1](X1,X2) = [1 1;0 0].X1 + [1 0;0 0].X2 67.98/69.10 [from](X) = [1 1;1 0].X + [0;1] 67.98/69.10 [mark](X) = [1 0;0 1].X 67.98/69.10 [s](X) = [1 0;0 0].X + [0;1] 67.98/69.10 [fSNonEmpty] = 0 67.98/69.10 [2ND](X) = 0 67.98/69.10 [ACTIVE](X) = [1 0;1 0].X + [0;1] 67.98/69.10 [CONS](X1,X2) = 0 67.98/69.10 [CONS1](X1,X2) = 0 67.98/69.10 [FROM](X) = 0 67.98/69.10 [MARK](X) = [1 0;1 0].X + [0;1] 67.98/69.10 [S](X) = 0 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 ->->Cycle: 67.98/69.10 ->->-> Pairs: 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 ->->-> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 Reduction Pairs Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> ACTIVE(2nd(mark(X:S))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 -> Usable rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Interpretation type: 67.98/69.10 Linear 67.98/69.10 ->Coefficients: 67.98/69.10 Natural Numbers 67.98/69.10 ->Dimension: 67.98/69.10 1 67.98/69.10 ->Bound: 67.98/69.10 2 67.98/69.10 ->Interpretation: 67.98/69.10 67.98/69.10 [2nd](X) = 0 67.98/69.10 [active](X) = 1 67.98/69.10 [cons](X1,X2) = 2 67.98/69.10 [cons1](X1,X2) = 0 67.98/69.10 [from](X) = 1 67.98/69.10 [mark](X) = 1 67.98/69.10 [s](X) = 0 67.98/69.10 [fSNonEmpty] = 0 67.98/69.10 [2ND](X) = 0 67.98/69.10 [ACTIVE](X) = 2.X 67.98/69.10 [CONS](X1,X2) = 0 67.98/69.10 [CONS1](X1,X2) = 0 67.98/69.10 [FROM](X) = 0 67.98/69.10 [MARK](X) = 2 67.98/69.10 [S](X) = 0 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 ->->Cycle: 67.98/69.10 ->->-> Pairs: 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 ->->-> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 Reduction Pairs Processor: 67.98/69.10 -> Pairs: 67.98/69.10 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S)))) 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 -> Usable rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Interpretation type: 67.98/69.10 Linear 67.98/69.10 ->Coefficients: 67.98/69.10 Natural Numbers 67.98/69.10 ->Dimension: 67.98/69.10 2 67.98/69.10 ->Bound: 67.98/69.10 1 67.98/69.10 ->Interpretation: 67.98/69.10 67.98/69.10 [2nd](X) = [1 1;1 1].X + [0;1] 67.98/69.10 [active](X) = [1 0;0 1].X 67.98/69.10 [cons](X1,X2) = [0 0;1 1].X1 + [0 1;0 0].X2 67.98/69.10 [cons1](X1,X2) = [0 0;1 1].X1 + [0 0;0 1].X2 67.98/69.10 [from](X) = [0 1;1 1].X + [1;1] 67.98/69.10 [mark](X) = [1 0;0 1].X 67.98/69.10 [s](X) = [0 0;0 1].X 67.98/69.10 [fSNonEmpty] = 0 67.98/69.10 [2ND](X) = 0 67.98/69.10 [ACTIVE](X) = [0 1;0 1].X + [0;1] 67.98/69.10 [CONS](X1,X2) = 0 67.98/69.10 [CONS1](X1,X2) = 0 67.98/69.10 [FROM](X) = 0 67.98/69.10 [MARK](X) = [0 1;0 1].X + [0;1] 67.98/69.10 [S](X) = 0 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> ACTIVE(from(mark(X:S))) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 ->->Cycle: 67.98/69.10 ->->-> Pairs: 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 ->->-> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 Subterm Processor: 67.98/69.10 -> Pairs: 67.98/69.10 MARK(2nd(X:S)) -> MARK(X:S) 67.98/69.10 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X1:S) 67.98/69.10 MARK(cons1(X1:S,X2:S)) -> MARK(X2:S) 67.98/69.10 MARK(from(X:S)) -> MARK(X:S) 67.98/69.10 MARK(s(X:S)) -> MARK(X:S) 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Projection: 67.98/69.10 pi(MARK) = 1 67.98/69.10 67.98/69.10 Problem 1.6: 67.98/69.10 67.98/69.10 SCC Processor: 67.98/69.10 -> Pairs: 67.98/69.10 Empty 67.98/69.10 -> Rules: 67.98/69.10 2nd(active(X:S)) -> 2nd(X:S) 67.98/69.10 2nd(mark(X:S)) -> 2nd(X:S) 67.98/69.10 active(2nd(cons(X:S,X1:S))) -> mark(2nd(cons1(X:S,X1:S))) 67.98/69.10 active(2nd(cons1(X:S,cons(Y:S,Z:S)))) -> mark(Y:S) 67.98/69.10 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 67.98/69.10 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S) 67.98/69.10 cons1(active(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(mark(X1:S),X2:S) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,active(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 cons1(X1:S,mark(X2:S)) -> cons1(X1:S,X2:S) 67.98/69.10 from(active(X:S)) -> from(X:S) 67.98/69.10 from(mark(X:S)) -> from(X:S) 67.98/69.10 mark(2nd(X:S)) -> active(2nd(mark(X:S))) 67.98/69.10 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S)) 67.98/69.10 mark(cons1(X1:S,X2:S)) -> active(cons1(mark(X1:S),mark(X2:S))) 67.98/69.10 mark(from(X:S)) -> active(from(mark(X:S))) 67.98/69.10 mark(s(X:S)) -> active(s(mark(X:S))) 67.98/69.10 s(active(X:S)) -> s(X:S) 67.98/69.10 s(mark(X:S)) -> s(X:S) 67.98/69.10 ->Strongly Connected Components: 67.98/69.10 There is no strongly connected component 67.98/69.10 67.98/69.10 The problem is finite. 67.98/69.10 EOF