0.00/0.01 YES 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 (VAR X Y Z) 0.00/0.01 (STRATEGY CONTEXTSENSITIVE 0.00/0.01 (add 1 2) 0.00/0.01 (from 1) 0.00/0.01 (fst 1 2) 0.00/0.01 (len 1) 0.00/0.01 (0) 0.00/0.01 (cons 1) 0.00/0.01 (nil) 0.00/0.01 (s) 0.00/0.01 ) 0.00/0.01 (RULES 0.00/0.01 add(0,X) -> X 0.00/0.01 add(s(X),Y) -> s(add(X,Y)) 0.00/0.01 from(X) -> cons(X,from(s(X))) 0.00/0.01 fst(0,Z) -> nil 0.00/0.01 fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z)) 0.00/0.01 len(cons(X,Z)) -> s(len(Z)) 0.00/0.01 len(nil) -> 0 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 add(0,X) -> X 0.00/0.01 add(s(X),Y) -> s(add(X,Y)) 0.00/0.01 from(X) -> cons(X,from(s(X))) 0.00/0.01 fst(0,Z) -> nil 0.00/0.01 fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z)) 0.00/0.01 len(cons(X,Z)) -> s(len(Z)) 0.00/0.01 len(nil) -> 0 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 Empty 0.00/0.01 -> Rules: 0.00/0.01 add(0,X) -> X 0.00/0.01 add(s(X),Y) -> s(add(X,Y)) 0.00/0.01 from(X) -> cons(X,from(s(X))) 0.00/0.01 fst(0,Z) -> nil 0.00/0.01 fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z)) 0.00/0.01 len(cons(X,Z)) -> s(len(Z)) 0.00/0.01 len(nil) -> 0 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 Basic Processor: 0.00/0.01 -> Pairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 add(0,X) -> X 0.00/0.01 add(s(X),Y) -> s(add(X,Y)) 0.00/0.01 from(X) -> cons(X,from(s(X))) 0.00/0.01 fst(0,Z) -> nil 0.00/0.01 fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z)) 0.00/0.01 len(cons(X,Z)) -> s(len(Z)) 0.00/0.01 len(nil) -> 0 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