0.00/0.01 YES 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 (VAR N X XS) 0.00/0.01 (STRATEGY CONTEXTSENSITIVE 0.00/0.01 (after 1 2) 0.00/0.01 (from 1) 0.00/0.01 (0) 0.00/0.01 (cons 1) 0.00/0.01 (s 1) 0.00/0.01 ) 0.00/0.01 (RULES 0.00/0.01 after(0,XS) -> XS 0.00/0.01 after(s(N),cons(X,XS)) -> after(N,XS) 0.00/0.01 from(X) -> cons(X,from(s(X))) 0.00/0.01 ) 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 Innermost Equivalent Processor: 0.00/0.01 -> Rules: 0.00/0.01 after(0,XS) -> XS 0.00/0.01 after(s(N),cons(X,XS)) -> after(N,XS) 0.00/0.01 from(X) -> cons(X,from(s(X))) 0.00/0.01 -> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination. 0.00/0.01 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 Dependency Pairs Processor: 0.00/0.01 -> Pairs: 0.00/0.01 AFTER(s(N),cons(X,XS)) -> AFTER(N,XS) 0.00/0.01 AFTER(s(N),cons(X,XS)) -> XS 0.00/0.01 -> Rules: 0.00/0.01 after(0,XS) -> XS 0.00/0.01 after(s(N),cons(X,XS)) -> after(N,XS) 0.00/0.01 from(X) -> cons(X,from(s(X))) 0.00/0.01 -> Unhiding Rules: 0.00/0.01 from(s(X)) -> FROM(s(X)) 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 SCC Processor: 0.00/0.01 -> Pairs: 0.00/0.01 AFTER(s(N),cons(X,XS)) -> AFTER(N,XS) 0.00/0.01 AFTER(s(N),cons(X,XS)) -> XS 0.00/0.01 -> Rules: 0.00/0.01 after(0,XS) -> XS 0.00/0.01 after(s(N),cons(X,XS)) -> after(N,XS) 0.00/0.01 from(X) -> cons(X,from(s(X))) 0.00/0.01 -> Unhiding rules: 0.00/0.01 from(s(X)) -> FROM(s(X)) 0.00/0.01 ->Strongly Connected Components: 0.00/0.01 ->->Cycle: 0.00/0.01 ->->-> Pairs: 0.00/0.01 AFTER(s(N),cons(X,XS)) -> AFTER(N,XS) 0.00/0.01 ->->-> Rules: 0.00/0.01 after(0,XS) -> XS 0.00/0.01 after(s(N),cons(X,XS)) -> after(N,XS) 0.00/0.01 from(X) -> cons(X,from(s(X))) 0.00/0.01 ->->-> Unhiding rules: 0.00/0.01 Empty 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 SubNColl Processor: 0.00/0.01 -> Pairs: 0.00/0.01 AFTER(s(N),cons(X,XS)) -> AFTER(N,XS) 0.00/0.01 -> Rules: 0.00/0.01 after(0,XS) -> XS 0.00/0.01 after(s(N),cons(X,XS)) -> after(N,XS) 0.00/0.01 from(X) -> cons(X,from(s(X))) 0.00/0.01 -> Unhiding rules: 0.00/0.01 Empty 0.00/0.01 ->Projection: 0.00/0.01 pi(AFTER) = 1 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 Basic Processor: 0.00/0.01 -> Pairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 after(0,XS) -> XS 0.00/0.01 after(s(N),cons(X,XS)) -> after(N,XS) 0.00/0.01 from(X) -> cons(X,from(s(X))) 0.00/0.01 -> Unhiding rules: 0.00/0.01 Empty 0.00/0.01 -> Result: 0.00/0.01 Set P is empty 0.00/0.01 0.00/0.01 The problem is finite. 0.00/0.01 EOF