0.00/0.01 YES 0.00/0.01 0.00/0.01 Problem 1: 0.00/0.01 0.00/0.01 (VAR v_NonEmpty:S x:S y:S) 0.00/0.01 (RULES 0.00/0.01 int(0,0) -> cons(0,nil) 0.00/0.01 int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) 0.00/0.01 int(s(x:S),0) -> nil 0.00/0.01 int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) 0.00/0.01 intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) 0.00/0.01 intlist(nil) -> nil 0.00/0.01 ) 0.00/0.01 (STRATEGY INNERMOST) 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 INT(0,s(y:S)) -> INT(s(0),s(y:S)) 0.00/0.01 INT(s(x:S),s(y:S)) -> INT(x:S,y:S) 0.00/0.01 INT(s(x:S),s(y:S)) -> INTLIST(int(x:S,y:S)) 0.00/0.01 INTLIST(cons(x:S,y:S)) -> INTLIST(y:S) 0.00/0.01 -> Rules: 0.00/0.01 int(0,0) -> cons(0,nil) 0.00/0.01 int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) 0.00/0.01 int(s(x:S),0) -> nil 0.00/0.01 int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) 0.00/0.01 intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) 0.00/0.01 intlist(nil) -> nil 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 INT(0,s(y:S)) -> INT(s(0),s(y:S)) 0.00/0.01 INT(s(x:S),s(y:S)) -> INT(x:S,y:S) 0.00/0.01 INT(s(x:S),s(y:S)) -> INTLIST(int(x:S,y:S)) 0.00/0.01 INTLIST(cons(x:S,y:S)) -> INTLIST(y:S) 0.00/0.01 -> Rules: 0.00/0.01 int(0,0) -> cons(0,nil) 0.00/0.01 int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) 0.00/0.01 int(s(x:S),0) -> nil 0.00/0.01 int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) 0.00/0.01 intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) 0.00/0.01 intlist(nil) -> nil 0.00/0.01 ->Strongly Connected Components: 0.00/0.01 ->->Cycle: 0.00/0.01 ->->-> Pairs: 0.00/0.01 INTLIST(cons(x:S,y:S)) -> INTLIST(y:S) 0.00/0.01 ->->-> Rules: 0.00/0.01 int(0,0) -> cons(0,nil) 0.00/0.01 int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) 0.00/0.01 int(s(x:S),0) -> nil 0.00/0.01 int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) 0.00/0.01 intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) 0.00/0.01 intlist(nil) -> nil 0.00/0.01 ->->Cycle: 0.00/0.01 ->->-> Pairs: 0.00/0.01 INT(0,s(y:S)) -> INT(s(0),s(y:S)) 0.00/0.01 INT(s(x:S),s(y:S)) -> INT(x:S,y:S) 0.00/0.01 ->->-> Rules: 0.00/0.01 int(0,0) -> cons(0,nil) 0.00/0.01 int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) 0.00/0.01 int(s(x:S),0) -> nil 0.00/0.01 int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) 0.00/0.01 intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) 0.00/0.01 intlist(nil) -> nil 0.00/0.01 0.00/0.01 0.00/0.01 The problem is decomposed in 2 subproblems. 0.00/0.01 0.00/0.01 Problem 1.1: 0.00/0.01 0.00/0.01 Subterm Processor: 0.00/0.01 -> Pairs: 0.00/0.01 INTLIST(cons(x:S,y:S)) -> INTLIST(y:S) 0.00/0.01 -> Rules: 0.00/0.01 int(0,0) -> cons(0,nil) 0.00/0.01 int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) 0.00/0.01 int(s(x:S),0) -> nil 0.00/0.01 int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) 0.00/0.01 intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) 0.00/0.01 intlist(nil) -> nil 0.00/0.01 ->Projection: 0.00/0.01 pi(INTLIST) = 1 0.00/0.01 0.00/0.01 Problem 1.1: 0.00/0.01 0.00/0.01 SCC Processor: 0.00/0.01 -> Pairs: 0.00/0.01 Empty 0.00/0.01 -> Rules: 0.00/0.01 int(0,0) -> cons(0,nil) 0.00/0.01 int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) 0.00/0.01 int(s(x:S),0) -> nil 0.00/0.01 int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) 0.00/0.01 intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) 0.00/0.01 intlist(nil) -> nil 0.00/0.01 ->Strongly Connected Components: 0.00/0.01 There is no strongly connected component 0.00/0.01 0.00/0.01 The problem is finite. 0.00/0.01 0.00/0.01 Problem 1.2: 0.00/0.01 0.00/0.01 Subterm Processor: 0.00/0.01 -> Pairs: 0.00/0.01 INT(0,s(y:S)) -> INT(s(0),s(y:S)) 0.00/0.01 INT(s(x:S),s(y:S)) -> INT(x:S,y:S) 0.00/0.01 -> Rules: 0.00/0.01 int(0,0) -> cons(0,nil) 0.00/0.01 int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) 0.00/0.01 int(s(x:S),0) -> nil 0.00/0.01 int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) 0.00/0.01 intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) 0.00/0.01 intlist(nil) -> nil 0.00/0.01 ->Projection: 0.00/0.01 pi(INT) = 2 0.00/0.01 0.00/0.01 Problem 1.2: 0.00/0.01 0.00/0.01 SCC Processor: 0.00/0.01 -> Pairs: 0.00/0.01 INT(0,s(y:S)) -> INT(s(0),s(y:S)) 0.00/0.01 -> Rules: 0.00/0.01 int(0,0) -> cons(0,nil) 0.00/0.01 int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) 0.00/0.01 int(s(x:S),0) -> nil 0.00/0.01 int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) 0.00/0.01 intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) 0.00/0.01 intlist(nil) -> nil 0.00/0.01 ->Strongly Connected Components: 0.00/0.01 There is no strongly connected component 0.00/0.01 0.00/0.01 The problem is finite. 0.00/0.01 EOF