0.00/0.20 YES 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 (VAR v_NonEmpty:S L:S X:S X1:S X2:S XS:S Y:S YS:S) 0.00/0.20 (RULES 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ) 0.00/0.20 (STRATEGY INNERMOST) 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 Dependency Pairs Processor: 0.00/0.20 -> Pairs: 0.00/0.20 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> APP(XS:S,YS:S) 0.00/0.20 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> CONS(X:S,app(XS:S,YS:S)) 0.00/0.20 ACTIVE(app(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(app(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.20 ACTIVE(app(X1:S,X2:S)) -> APP(active(X1:S),X2:S) 0.00/0.20 ACTIVE(app(X1:S,X2:S)) -> APP(X1:S,active(X2:S)) 0.00/0.20 ACTIVE(cons(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(cons(X1:S,X2:S)) -> CONS(active(X1:S),X2:S) 0.00/0.20 ACTIVE(from(X:S)) -> ACTIVE(X:S) 0.00/0.20 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S))) 0.00/0.20 ACTIVE(from(X:S)) -> FROM(active(X:S)) 0.00/0.20 ACTIVE(from(X:S)) -> FROM(s(X:S)) 0.00/0.20 ACTIVE(from(X:S)) -> S(X:S) 0.00/0.20 ACTIVE(prefix(L:S)) -> CONS(nil,zWadr(L:S,prefix(L:S))) 0.00/0.20 ACTIVE(prefix(L:S)) -> ZWADR(L:S,prefix(L:S)) 0.00/0.20 ACTIVE(prefix(X:S)) -> ACTIVE(X:S) 0.00/0.20 ACTIVE(prefix(X:S)) -> PREFIX(active(X:S)) 0.00/0.20 ACTIVE(s(X:S)) -> ACTIVE(X:S) 0.00/0.20 ACTIVE(s(X:S)) -> S(active(X:S)) 0.00/0.20 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> APP(Y:S,cons(X:S,nil)) 0.00/0.20 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> CONS(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)) 0.00/0.20 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> CONS(X:S,nil) 0.00/0.20 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> ZWADR(XS:S,YS:S) 0.00/0.20 ACTIVE(zWadr(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(zWadr(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.20 ACTIVE(zWadr(X1:S,X2:S)) -> ZWADR(active(X1:S),X2:S) 0.00/0.20 ACTIVE(zWadr(X1:S,X2:S)) -> ZWADR(X1:S,active(X2:S)) 0.00/0.20 APP(mark(X1:S),X2:S) -> APP(X1:S,X2:S) 0.00/0.20 APP(ok(X1:S),ok(X2:S)) -> APP(X1:S,X2:S) 0.00/0.20 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S) 0.00/0.20 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 0.00/0.20 CONS(ok(X1:S),ok(X2:S)) -> CONS(X1:S,X2:S) 0.00/0.20 FROM(mark(X:S)) -> FROM(X:S) 0.00/0.20 FROM(ok(X:S)) -> FROM(X:S) 0.00/0.20 PREFIX(mark(X:S)) -> PREFIX(X:S) 0.00/0.20 PREFIX(ok(X:S)) -> PREFIX(X:S) 0.00/0.20 PROPER(app(X1:S,X2:S)) -> APP(proper(X1:S),proper(X2:S)) 0.00/0.20 PROPER(app(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(app(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(cons(X1:S,X2:S)) -> CONS(proper(X1:S),proper(X2:S)) 0.00/0.20 PROPER(cons(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(cons(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(from(X:S)) -> FROM(proper(X:S)) 0.00/0.20 PROPER(from(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(prefix(X:S)) -> PREFIX(proper(X:S)) 0.00/0.20 PROPER(prefix(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(s(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(s(X:S)) -> S(proper(X:S)) 0.00/0.20 PROPER(zWadr(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(zWadr(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(zWadr(X1:S,X2:S)) -> ZWADR(proper(X1:S),proper(X2:S)) 0.00/0.20 S(mark(X:S)) -> S(X:S) 0.00/0.20 S(ok(X:S)) -> S(X:S) 0.00/0.20 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.20 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.20 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.20 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.20 ZWADR(mark(X1:S),X2:S) -> ZWADR(X1:S,X2:S) 0.00/0.20 ZWADR(ok(X1:S),ok(X2:S)) -> ZWADR(X1:S,X2:S) 0.00/0.20 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S) 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> APP(XS:S,YS:S) 0.00/0.20 ACTIVE(app(cons(X:S,XS:S),YS:S)) -> CONS(X:S,app(XS:S,YS:S)) 0.00/0.20 ACTIVE(app(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(app(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.20 ACTIVE(app(X1:S,X2:S)) -> APP(active(X1:S),X2:S) 0.00/0.20 ACTIVE(app(X1:S,X2:S)) -> APP(X1:S,active(X2:S)) 0.00/0.20 ACTIVE(cons(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(cons(X1:S,X2:S)) -> CONS(active(X1:S),X2:S) 0.00/0.20 ACTIVE(from(X:S)) -> ACTIVE(X:S) 0.00/0.20 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S))) 0.00/0.20 ACTIVE(from(X:S)) -> FROM(active(X:S)) 0.00/0.20 ACTIVE(from(X:S)) -> FROM(s(X:S)) 0.00/0.20 ACTIVE(from(X:S)) -> S(X:S) 0.00/0.20 ACTIVE(prefix(L:S)) -> CONS(nil,zWadr(L:S,prefix(L:S))) 0.00/0.20 ACTIVE(prefix(L:S)) -> ZWADR(L:S,prefix(L:S)) 0.00/0.20 ACTIVE(prefix(X:S)) -> ACTIVE(X:S) 0.00/0.20 ACTIVE(prefix(X:S)) -> PREFIX(active(X:S)) 0.00/0.20 ACTIVE(s(X:S)) -> ACTIVE(X:S) 0.00/0.20 ACTIVE(s(X:S)) -> S(active(X:S)) 0.00/0.20 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> APP(Y:S,cons(X:S,nil)) 0.00/0.20 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> CONS(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S)) 0.00/0.20 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> CONS(X:S,nil) 0.00/0.20 ACTIVE(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> ZWADR(XS:S,YS:S) 0.00/0.20 ACTIVE(zWadr(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(zWadr(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.20 ACTIVE(zWadr(X1:S,X2:S)) -> ZWADR(active(X1:S),X2:S) 0.00/0.20 ACTIVE(zWadr(X1:S,X2:S)) -> ZWADR(X1:S,active(X2:S)) 0.00/0.20 APP(mark(X1:S),X2:S) -> APP(X1:S,X2:S) 0.00/0.20 APP(ok(X1:S),ok(X2:S)) -> APP(X1:S,X2:S) 0.00/0.20 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S) 0.00/0.20 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 0.00/0.20 CONS(ok(X1:S),ok(X2:S)) -> CONS(X1:S,X2:S) 0.00/0.20 FROM(mark(X:S)) -> FROM(X:S) 0.00/0.20 FROM(ok(X:S)) -> FROM(X:S) 0.00/0.20 PREFIX(mark(X:S)) -> PREFIX(X:S) 0.00/0.20 PREFIX(ok(X:S)) -> PREFIX(X:S) 0.00/0.20 PROPER(app(X1:S,X2:S)) -> APP(proper(X1:S),proper(X2:S)) 0.00/0.20 PROPER(app(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(app(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(cons(X1:S,X2:S)) -> CONS(proper(X1:S),proper(X2:S)) 0.00/0.20 PROPER(cons(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(cons(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(from(X:S)) -> FROM(proper(X:S)) 0.00/0.20 PROPER(from(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(prefix(X:S)) -> PREFIX(proper(X:S)) 0.00/0.20 PROPER(prefix(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(s(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(s(X:S)) -> S(proper(X:S)) 0.00/0.20 PROPER(zWadr(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(zWadr(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(zWadr(X1:S,X2:S)) -> ZWADR(proper(X1:S),proper(X2:S)) 0.00/0.20 S(mark(X:S)) -> S(X:S) 0.00/0.20 S(ok(X:S)) -> S(X:S) 0.00/0.20 TOP(mark(X:S)) -> PROPER(X:S) 0.00/0.20 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.20 TOP(ok(X:S)) -> ACTIVE(X:S) 0.00/0.20 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.20 ZWADR(mark(X1:S),X2:S) -> ZWADR(X1:S,X2:S) 0.00/0.20 ZWADR(ok(X1:S),ok(X2:S)) -> ZWADR(X1:S,X2:S) 0.00/0.20 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S) 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 ZWADR(mark(X1:S),X2:S) -> ZWADR(X1:S,X2:S) 0.00/0.20 ZWADR(ok(X1:S),ok(X2:S)) -> ZWADR(X1:S,X2:S) 0.00/0.20 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 S(mark(X:S)) -> S(X:S) 0.00/0.20 S(ok(X:S)) -> S(X:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 PREFIX(mark(X:S)) -> PREFIX(X:S) 0.00/0.20 PREFIX(ok(X:S)) -> PREFIX(X:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 FROM(mark(X:S)) -> FROM(X:S) 0.00/0.20 FROM(ok(X:S)) -> FROM(X:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 0.00/0.20 CONS(ok(X1:S),ok(X2:S)) -> CONS(X1:S,X2:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 APP(mark(X1:S),X2:S) -> APP(X1:S,X2:S) 0.00/0.20 APP(ok(X1:S),ok(X2:S)) -> APP(X1:S,X2:S) 0.00/0.20 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 PROPER(app(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(app(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(cons(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(cons(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 PROPER(from(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(prefix(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(s(X:S)) -> PROPER(X:S) 0.00/0.20 PROPER(zWadr(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.20 PROPER(zWadr(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 ACTIVE(app(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(app(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.20 ACTIVE(cons(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(from(X:S)) -> ACTIVE(X:S) 0.00/0.20 ACTIVE(prefix(X:S)) -> ACTIVE(X:S) 0.00/0.20 ACTIVE(s(X:S)) -> ACTIVE(X:S) 0.00/0.20 ACTIVE(zWadr(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.20 ACTIVE(zWadr(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.20 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.20 ->->-> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 0.00/0.20 0.00/0.20 The problem is decomposed in 9 subproblems. 0.00/0.20 0.00/0.20 Problem 1.1: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 ZWADR(mark(X1:S),X2:S) -> ZWADR(X1:S,X2:S) 0.00/0.20 ZWADR(ok(X1:S),ok(X2:S)) -> ZWADR(X1:S,X2:S) 0.00/0.20 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S) 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Projection: 0.00/0.20 pi(ZWADR) = 1 0.00/0.20 0.00/0.20 Problem 1.1: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S) 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 ->->Cycle: 0.00/0.20 ->->-> Pairs: 0.00/0.20 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S) 0.00/0.20 ->->-> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 0.00/0.20 Problem 1.1: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 ZWADR(X1:S,mark(X2:S)) -> ZWADR(X1:S,X2:S) 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Projection: 0.00/0.20 pi(ZWADR) = 2 0.00/0.20 0.00/0.20 Problem 1.1: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 Empty 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 There is no strongly connected component 0.00/0.20 0.00/0.20 The problem is finite. 0.00/0.20 0.00/0.20 Problem 1.2: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 S(mark(X:S)) -> S(X:S) 0.00/0.20 S(ok(X:S)) -> S(X:S) 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Projection: 0.00/0.20 pi(S) = 1 0.00/0.20 0.00/0.20 Problem 1.2: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 Empty 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 There is no strongly connected component 0.00/0.20 0.00/0.20 The problem is finite. 0.00/0.20 0.00/0.20 Problem 1.3: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 PREFIX(mark(X:S)) -> PREFIX(X:S) 0.00/0.20 PREFIX(ok(X:S)) -> PREFIX(X:S) 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Projection: 0.00/0.20 pi(PREFIX) = 1 0.00/0.20 0.00/0.20 Problem 1.3: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 Empty 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 There is no strongly connected component 0.00/0.20 0.00/0.20 The problem is finite. 0.00/0.20 0.00/0.20 Problem 1.4: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 FROM(mark(X:S)) -> FROM(X:S) 0.00/0.20 FROM(ok(X:S)) -> FROM(X:S) 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Projection: 0.00/0.20 pi(FROM) = 1 0.00/0.20 0.00/0.20 Problem 1.4: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 Empty 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 There is no strongly connected component 0.00/0.20 0.00/0.20 The problem is finite. 0.00/0.20 0.00/0.20 Problem 1.5: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S) 0.00/0.20 CONS(ok(X1:S),ok(X2:S)) -> CONS(X1:S,X2:S) 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Projection: 0.00/0.20 pi(CONS) = 1 0.00/0.20 0.00/0.20 Problem 1.5: 0.00/0.20 0.00/0.20 SCC Processor: 0.00/0.20 -> Pairs: 0.00/0.20 Empty 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.20 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.20 active(s(X:S)) -> s(active(X:S)) 0.00/0.20 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.20 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.20 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.20 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.20 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.20 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.20 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.20 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.20 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.20 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.20 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.20 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.20 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.20 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.20 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.20 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.20 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.20 proper(nil) -> ok(nil) 0.00/0.20 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.20 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.20 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.20 top(ok(X:S)) -> top(active(X:S)) 0.00/0.20 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.20 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.20 ->Strongly Connected Components: 0.00/0.20 There is no strongly connected component 0.00/0.20 0.00/0.20 The problem is finite. 0.00/0.20 0.00/0.20 Problem 1.6: 0.00/0.20 0.00/0.20 Subterm Processor: 0.00/0.20 -> Pairs: 0.00/0.20 APP(mark(X1:S),X2:S) -> APP(X1:S,X2:S) 0.00/0.20 APP(ok(X1:S),ok(X2:S)) -> APP(X1:S,X2:S) 0.00/0.20 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S) 0.00/0.20 -> Rules: 0.00/0.20 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.20 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.20 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.20 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.20 active(from(X:S)) -> from(active(X:S)) 0.00/0.20 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.20 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Projection: 0.00/0.21 pi(APP) = 1 0.00/0.21 0.00/0.21 Problem 1.6: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S) 0.00/0.21 -> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 ->->Cycle: 0.00/0.21 ->->-> Pairs: 0.00/0.21 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S) 0.00/0.21 ->->-> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 0.00/0.21 Problem 1.6: 0.00/0.21 0.00/0.21 Subterm Processor: 0.00/0.21 -> Pairs: 0.00/0.21 APP(X1:S,mark(X2:S)) -> APP(X1:S,X2:S) 0.00/0.21 -> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Projection: 0.00/0.21 pi(APP) = 2 0.00/0.21 0.00/0.21 Problem 1.6: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 Empty 0.00/0.21 -> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 There is no strongly connected component 0.00/0.21 0.00/0.21 The problem is finite. 0.00/0.21 0.00/0.21 Problem 1.7: 0.00/0.21 0.00/0.21 Subterm Processor: 0.00/0.21 -> Pairs: 0.00/0.21 PROPER(app(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.21 PROPER(app(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.21 PROPER(cons(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.21 PROPER(cons(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.21 PROPER(from(X:S)) -> PROPER(X:S) 0.00/0.21 PROPER(prefix(X:S)) -> PROPER(X:S) 0.00/0.21 PROPER(s(X:S)) -> PROPER(X:S) 0.00/0.21 PROPER(zWadr(X1:S,X2:S)) -> PROPER(X1:S) 0.00/0.21 PROPER(zWadr(X1:S,X2:S)) -> PROPER(X2:S) 0.00/0.21 -> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Projection: 0.00/0.21 pi(PROPER) = 1 0.00/0.21 0.00/0.21 Problem 1.7: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 Empty 0.00/0.21 -> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 There is no strongly connected component 0.00/0.21 0.00/0.21 The problem is finite. 0.00/0.21 0.00/0.21 Problem 1.8: 0.00/0.21 0.00/0.21 Subterm Processor: 0.00/0.21 -> Pairs: 0.00/0.21 ACTIVE(app(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.21 ACTIVE(app(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.21 ACTIVE(cons(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.21 ACTIVE(from(X:S)) -> ACTIVE(X:S) 0.00/0.21 ACTIVE(prefix(X:S)) -> ACTIVE(X:S) 0.00/0.21 ACTIVE(s(X:S)) -> ACTIVE(X:S) 0.00/0.21 ACTIVE(zWadr(X1:S,X2:S)) -> ACTIVE(X1:S) 0.00/0.21 ACTIVE(zWadr(X1:S,X2:S)) -> ACTIVE(X2:S) 0.00/0.21 -> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Projection: 0.00/0.21 pi(ACTIVE) = 1 0.00/0.21 0.00/0.21 Problem 1.8: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 Empty 0.00/0.21 -> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 There is no strongly connected component 0.00/0.21 0.00/0.21 The problem is finite. 0.00/0.21 0.00/0.21 Problem 1.9: 0.00/0.21 0.00/0.21 Reduction Pairs Processor: 0.00/0.21 -> Pairs: 0.00/0.21 TOP(mark(X:S)) -> TOP(proper(X:S)) 0.00/0.21 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.21 -> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 -> Usable rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Interpretation type: 0.00/0.21 Linear 0.00/0.21 ->Coefficients: 0.00/0.21 Natural Numbers 0.00/0.21 ->Dimension: 0.00/0.21 1 0.00/0.21 ->Bound: 0.00/0.21 2 0.00/0.21 ->Interpretation: 0.00/0.21 0.00/0.21 [active](X) = X 0.00/0.21 [app](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.21 [cons](X1,X2) = X1 + 1 0.00/0.21 [from](X) = 2.X + 2 0.00/0.21 [prefix](X) = 2.X + 2 0.00/0.21 [proper](X) = X 0.00/0.21 [s](X) = X 0.00/0.21 [top](X) = 0 0.00/0.21 [zWadr](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.21 [fSNonEmpty] = 0 0.00/0.21 [mark](X) = X + 1 0.00/0.21 [nil] = 0 0.00/0.21 [ok](X) = X 0.00/0.21 [ACTIVE](X) = 0 0.00/0.21 [APP](X1,X2) = 0 0.00/0.21 [CONS](X1,X2) = 0 0.00/0.21 [FROM](X) = 0 0.00/0.21 [PREFIX](X) = 0 0.00/0.21 [PROPER](X) = 0 0.00/0.21 [S](X) = 0 0.00/0.21 [TOP](X) = 2.X 0.00/0.21 [ZWADR](X1,X2) = 0 0.00/0.21 0.00/0.21 Problem 1.9: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.21 -> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 ->->Cycle: 0.00/0.21 ->->-> Pairs: 0.00/0.21 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.21 ->->-> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 0.00/0.21 Problem 1.9: 0.00/0.21 0.00/0.21 Reduction Pairs Processor: 0.00/0.21 -> Pairs: 0.00/0.21 TOP(ok(X:S)) -> TOP(active(X:S)) 0.00/0.21 -> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 -> Usable rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Interpretation type: 0.00/0.21 Linear 0.00/0.21 ->Coefficients: 0.00/0.21 Natural Numbers 0.00/0.21 ->Dimension: 0.00/0.21 1 0.00/0.21 ->Bound: 0.00/0.21 2 0.00/0.21 ->Interpretation: 0.00/0.21 0.00/0.21 [active](X) = 2.X + 1 0.00/0.21 [app](X1,X2) = 2.X1 + X2 + 2 0.00/0.21 [cons](X1,X2) = X1 0.00/0.21 [from](X) = 2.X + 1 0.00/0.21 [prefix](X) = X 0.00/0.21 [proper](X) = 0 0.00/0.21 [s](X) = 2.X + 2 0.00/0.21 [top](X) = 0 0.00/0.21 [zWadr](X1,X2) = X1 + 2.X2 + 1 0.00/0.21 [fSNonEmpty] = 0 0.00/0.21 [mark](X) = X + 1 0.00/0.21 [nil] = 0 0.00/0.21 [ok](X) = 2.X + 2 0.00/0.21 [ACTIVE](X) = 0 0.00/0.21 [APP](X1,X2) = 0 0.00/0.21 [CONS](X1,X2) = 0 0.00/0.21 [FROM](X) = 0 0.00/0.21 [PREFIX](X) = 0 0.00/0.21 [PROPER](X) = 0 0.00/0.21 [S](X) = 0 0.00/0.21 [TOP](X) = X 0.00/0.21 [ZWADR](X1,X2) = 0 0.00/0.21 0.00/0.21 Problem 1.9: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> Pairs: 0.00/0.21 Empty 0.00/0.21 -> Rules: 0.00/0.21 active(app(cons(X:S,XS:S),YS:S)) -> mark(cons(X:S,app(XS:S,YS:S))) 0.00/0.21 active(app(nil,YS:S)) -> mark(YS:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(active(X1:S),X2:S) 0.00/0.21 active(app(X1:S,X2:S)) -> app(X1:S,active(X2:S)) 0.00/0.21 active(cons(X1:S,X2:S)) -> cons(active(X1:S),X2:S) 0.00/0.21 active(from(X:S)) -> from(active(X:S)) 0.00/0.21 active(from(X:S)) -> mark(cons(X:S,from(s(X:S)))) 0.00/0.21 active(prefix(L:S)) -> mark(cons(nil,zWadr(L:S,prefix(L:S)))) 0.00/0.21 active(prefix(X:S)) -> prefix(active(X:S)) 0.00/0.21 active(s(X:S)) -> s(active(X:S)) 0.00/0.21 active(zWadr(cons(X:S,XS:S),cons(Y:S,YS:S))) -> mark(cons(app(Y:S,cons(X:S,nil)),zWadr(XS:S,YS:S))) 0.00/0.21 active(zWadr(nil,YS:S)) -> mark(nil) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(active(X1:S),X2:S) 0.00/0.21 active(zWadr(X1:S,X2:S)) -> zWadr(X1:S,active(X2:S)) 0.00/0.21 active(zWadr(XS:S,nil)) -> mark(nil) 0.00/0.21 app(mark(X1:S),X2:S) -> mark(app(X1:S,X2:S)) 0.00/0.21 app(ok(X1:S),ok(X2:S)) -> ok(app(X1:S,X2:S)) 0.00/0.21 app(X1:S,mark(X2:S)) -> mark(app(X1:S,X2:S)) 0.00/0.21 cons(mark(X1:S),X2:S) -> mark(cons(X1:S,X2:S)) 0.00/0.21 cons(ok(X1:S),ok(X2:S)) -> ok(cons(X1:S,X2:S)) 0.00/0.21 from(mark(X:S)) -> mark(from(X:S)) 0.00/0.21 from(ok(X:S)) -> ok(from(X:S)) 0.00/0.21 prefix(mark(X:S)) -> mark(prefix(X:S)) 0.00/0.21 prefix(ok(X:S)) -> ok(prefix(X:S)) 0.00/0.21 proper(app(X1:S,X2:S)) -> app(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(cons(X1:S,X2:S)) -> cons(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(from(X:S)) -> from(proper(X:S)) 0.00/0.21 proper(prefix(X:S)) -> prefix(proper(X:S)) 0.00/0.21 proper(s(X:S)) -> s(proper(X:S)) 0.00/0.21 proper(zWadr(X1:S,X2:S)) -> zWadr(proper(X1:S),proper(X2:S)) 0.00/0.21 proper(nil) -> ok(nil) 0.00/0.21 s(mark(X:S)) -> mark(s(X:S)) 0.00/0.21 s(ok(X:S)) -> ok(s(X:S)) 0.00/0.21 top(mark(X:S)) -> top(proper(X:S)) 0.00/0.21 top(ok(X:S)) -> top(active(X:S)) 0.00/0.21 zWadr(mark(X1:S),X2:S) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(ok(X1:S),ok(X2:S)) -> ok(zWadr(X1:S,X2:S)) 0.00/0.21 zWadr(X1:S,mark(X2:S)) -> mark(zWadr(X1:S,X2:S)) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 There is no strongly connected component 0.00/0.21 0.00/0.21 The problem is finite. 0.00/0.21 EOF