0.00/0.04 YES 0.00/0.04 0.00/0.04 Problem 1: 0.00/0.04 0.00/0.04 (VAR v_NonEmpty:S X:S X1:S X2:S Y:S) 0.00/0.04 (RULES 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.04 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.04 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.04 mark(length(X:S)) -> a__length(X:S) 0.00/0.04 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.04 mark(nil) -> nil 0.00/0.04 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.04 ) 0.00/0.04 (STRATEGY INNERMOST) 0.00/0.04 0.00/0.04 Problem 1: 0.00/0.04 0.00/0.04 Dependency Pairs Processor: 0.00/0.04 -> Pairs: 0.00/0.04 A__FROM(X:S) -> MARK(X:S) 0.00/0.04 A__LENGTH(cons(X:S,Y:S)) -> A__LENGTH1(Y:S) 0.00/0.04 A__LENGTH1(X:S) -> A__LENGTH(X:S) 0.00/0.04 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.04 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.04 MARK(from(X:S)) -> MARK(X:S) 0.00/0.04 MARK(length(X:S)) -> A__LENGTH(X:S) 0.00/0.04 MARK(length1(X:S)) -> A__LENGTH1(X:S) 0.00/0.04 MARK(s(X:S)) -> MARK(X:S) 0.00/0.04 -> Rules: 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.04 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.04 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.04 mark(length(X:S)) -> a__length(X:S) 0.00/0.04 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.04 mark(nil) -> nil 0.00/0.04 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.04 0.00/0.04 Problem 1: 0.00/0.04 0.00/0.04 SCC Processor: 0.00/0.04 -> Pairs: 0.00/0.04 A__FROM(X:S) -> MARK(X:S) 0.00/0.04 A__LENGTH(cons(X:S,Y:S)) -> A__LENGTH1(Y:S) 0.00/0.04 A__LENGTH1(X:S) -> A__LENGTH(X:S) 0.00/0.04 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.04 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.04 MARK(from(X:S)) -> MARK(X:S) 0.00/0.04 MARK(length(X:S)) -> A__LENGTH(X:S) 0.00/0.04 MARK(length1(X:S)) -> A__LENGTH1(X:S) 0.00/0.04 MARK(s(X:S)) -> MARK(X:S) 0.00/0.04 -> Rules: 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.04 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.04 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.04 mark(length(X:S)) -> a__length(X:S) 0.00/0.04 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.04 mark(nil) -> nil 0.00/0.04 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.04 ->Strongly Connected Components: 0.00/0.04 ->->Cycle: 0.00/0.04 ->->-> Pairs: 0.00/0.04 A__LENGTH(cons(X:S,Y:S)) -> A__LENGTH1(Y:S) 0.00/0.04 A__LENGTH1(X:S) -> A__LENGTH(X:S) 0.00/0.04 ->->-> Rules: 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.04 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.04 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.04 mark(length(X:S)) -> a__length(X:S) 0.00/0.04 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.04 mark(nil) -> nil 0.00/0.04 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.04 ->->Cycle: 0.00/0.04 ->->-> Pairs: 0.00/0.04 A__FROM(X:S) -> MARK(X:S) 0.00/0.04 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.04 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.04 MARK(from(X:S)) -> MARK(X:S) 0.00/0.04 MARK(s(X:S)) -> MARK(X:S) 0.00/0.04 ->->-> Rules: 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.04 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.04 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.04 mark(length(X:S)) -> a__length(X:S) 0.00/0.04 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.04 mark(nil) -> nil 0.00/0.04 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.04 0.00/0.04 0.00/0.04 The problem is decomposed in 2 subproblems. 0.00/0.04 0.00/0.04 Problem 1.1: 0.00/0.04 0.00/0.04 Subterm Processor: 0.00/0.04 -> Pairs: 0.00/0.04 A__LENGTH(cons(X:S,Y:S)) -> A__LENGTH1(Y:S) 0.00/0.04 A__LENGTH1(X:S) -> A__LENGTH(X:S) 0.00/0.04 -> Rules: 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.04 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.04 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.04 mark(length(X:S)) -> a__length(X:S) 0.00/0.04 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.04 mark(nil) -> nil 0.00/0.04 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.04 ->Projection: 0.00/0.04 pi(A__LENGTH) = 1 0.00/0.04 pi(A__LENGTH1) = 1 0.00/0.04 0.00/0.04 Problem 1.1: 0.00/0.04 0.00/0.04 SCC Processor: 0.00/0.04 -> Pairs: 0.00/0.04 A__LENGTH1(X:S) -> A__LENGTH(X:S) 0.00/0.04 -> Rules: 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.04 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.04 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.04 mark(length(X:S)) -> a__length(X:S) 0.00/0.04 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.04 mark(nil) -> nil 0.00/0.04 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.04 ->Strongly Connected Components: 0.00/0.04 There is no strongly connected component 0.00/0.04 0.00/0.04 The problem is finite. 0.00/0.04 0.00/0.04 Problem 1.2: 0.00/0.04 0.00/0.04 Reduction Pairs Processor: 0.00/0.04 -> Pairs: 0.00/0.04 A__FROM(X:S) -> MARK(X:S) 0.00/0.04 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.04 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.04 MARK(from(X:S)) -> MARK(X:S) 0.00/0.04 MARK(s(X:S)) -> MARK(X:S) 0.00/0.04 -> Rules: 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.04 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.04 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.04 mark(length(X:S)) -> a__length(X:S) 0.00/0.04 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.04 mark(nil) -> nil 0.00/0.04 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.04 -> Usable rules: 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.04 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.04 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.04 mark(length(X:S)) -> a__length(X:S) 0.00/0.04 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.04 mark(nil) -> nil 0.00/0.04 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.04 ->Interpretation type: 0.00/0.04 Linear 0.00/0.04 ->Coefficients: 0.00/0.04 Natural Numbers 0.00/0.04 ->Dimension: 0.00/0.04 1 0.00/0.04 ->Bound: 0.00/0.04 2 0.00/0.04 ->Interpretation: 0.00/0.04 0.00/0.04 [a__from](X) = 2.X + 2 0.00/0.04 [a__length](X) = 0 0.00/0.04 [a__length1](X) = 0 0.00/0.04 [mark](X) = 2.X 0.00/0.04 [0] = 0 0.00/0.04 [cons](X1,X2) = X1 + 2 0.00/0.04 [fSNonEmpty] = 0 0.00/0.04 [from](X) = 2.X + 2 0.00/0.04 [length](X) = 0 0.00/0.04 [length1](X) = 0 0.00/0.04 [nil] = 2 0.00/0.04 [s](X) = 2.X 0.00/0.04 [A__FROM](X) = 2.X + 2 0.00/0.04 [A__LENGTH](X) = 0 0.00/0.04 [A__LENGTH1](X) = 0 0.00/0.04 [MARK](X) = 2.X 0.00/0.04 0.00/0.04 Problem 1.2: 0.00/0.04 0.00/0.04 SCC Processor: 0.00/0.04 -> Pairs: 0.00/0.04 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.04 MARK(from(X:S)) -> A__FROM(mark(X:S)) 0.00/0.04 MARK(from(X:S)) -> MARK(X:S) 0.00/0.04 MARK(s(X:S)) -> MARK(X:S) 0.00/0.04 -> Rules: 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.04 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.04 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.04 mark(length(X:S)) -> a__length(X:S) 0.00/0.04 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.04 mark(nil) -> nil 0.00/0.04 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.04 ->Strongly Connected Components: 0.00/0.04 ->->Cycle: 0.00/0.04 ->->-> Pairs: 0.00/0.04 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.04 MARK(from(X:S)) -> MARK(X:S) 0.00/0.04 MARK(s(X:S)) -> MARK(X:S) 0.00/0.04 ->->-> Rules: 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.04 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.04 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.04 mark(length(X:S)) -> a__length(X:S) 0.00/0.04 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.04 mark(nil) -> nil 0.00/0.04 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.04 0.00/0.04 Problem 1.2: 0.00/0.04 0.00/0.04 Subterm Processor: 0.00/0.04 -> Pairs: 0.00/0.04 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.04 MARK(from(X:S)) -> MARK(X:S) 0.00/0.04 MARK(s(X:S)) -> MARK(X:S) 0.00/0.04 -> Rules: 0.00/0.04 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.04 a__from(X:S) -> from(X:S) 0.00/0.04 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.04 a__length(nil) -> 0 0.00/0.04 a__length(X:S) -> length(X:S) 0.00/0.04 a__length1(X:S) -> a__length(X:S) 0.00/0.04 a__length1(X:S) -> length1(X:S) 0.00/0.04 mark(0) -> 0 0.00/0.07 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.07 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.07 mark(length(X:S)) -> a__length(X:S) 0.00/0.07 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.07 mark(nil) -> nil 0.00/0.07 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.07 ->Projection: 0.00/0.07 pi(MARK) = 1 0.00/0.07 0.00/0.07 Problem 1.2: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 Empty 0.00/0.07 -> Rules: 0.00/0.07 a__from(X:S) -> cons(mark(X:S),from(s(X:S))) 0.00/0.07 a__from(X:S) -> from(X:S) 0.00/0.07 a__length(cons(X:S,Y:S)) -> s(a__length1(Y:S)) 0.00/0.07 a__length(nil) -> 0 0.00/0.07 a__length(X:S) -> length(X:S) 0.00/0.07 a__length1(X:S) -> a__length(X:S) 0.00/0.07 a__length1(X:S) -> length1(X:S) 0.00/0.07 mark(0) -> 0 0.00/0.07 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.00/0.07 mark(from(X:S)) -> a__from(mark(X:S)) 0.00/0.07 mark(length(X:S)) -> a__length(X:S) 0.00/0.07 mark(length1(X:S)) -> a__length1(X:S) 0.00/0.07 mark(nil) -> nil 0.00/0.07 mark(s(X:S)) -> s(mark(X:S)) 0.00/0.07 ->Strongly Connected Components: 0.00/0.07 There is no strongly connected component 0.00/0.07 0.00/0.07 The problem is finite. 0.00/0.07 EOF