0.00/0.06 YES 0.00/0.06 0.00/0.06 Problem 1: 0.00/0.06 0.00/0.06 (VAR v_NonEmpty:S a:S a_4:S l:S l':S l1:S l1_2:S l2:S l2_1:S l_3:S l_5:S x:S x_0:S y:S) 0.00/0.06 (RULES 0.00/0.06 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.06 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.06 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.06 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.06 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.06 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.06 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.06 match_4(l_5:S,Nil) -> Nil 0.00/0.06 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.06 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.06 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.06 test(x_0:S,y:S) -> False 0.00/0.06 test(x_0:S,y:S) -> True 0.00/0.06 ) 0.00/0.06 0.00/0.06 Problem 1: 0.00/0.06 0.00/0.06 Dependency Pairs Processor: 0.00/0.06 -> Pairs: 0.00/0.06 APPEND(l1_2:S,l2_1:S) -> MATCH_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.06 MATCH_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> APPEND(l:S,l2_1:S) 0.00/0.06 MATCH_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> MATCH_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.06 MATCH_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> PART(a_4:S,l':S) 0.00/0.06 MATCH_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> MATCH_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.06 MATCH_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> TEST(a_4:S,x:S) 0.00/0.06 MATCH_4(l_5:S,Cons(a:S,l':S)) -> MATCH_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.06 MATCH_4(l_5:S,Cons(a:S,l':S)) -> PART(a:S,l':S) 0.00/0.06 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> APPEND(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.06 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> QUICK(l1:S) 0.00/0.06 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> QUICK(l2:S) 0.00/0.06 PART(a_4:S,l_3:S) -> MATCH_1(a_4:S,l_3:S,l_3:S) 0.00/0.06 QUICK(l_5:S) -> MATCH_4(l_5:S,l_5:S) 0.00/0.06 -> Rules: 0.00/0.06 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.06 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.06 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.06 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.06 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.06 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.06 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.06 match_4(l_5:S,Nil) -> Nil 0.00/0.06 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.06 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.06 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.06 test(x_0:S,y:S) -> False 0.00/0.06 test(x_0:S,y:S) -> True 0.00/0.06 0.00/0.06 Problem 1: 0.00/0.06 0.00/0.06 SCC Processor: 0.00/0.06 -> Pairs: 0.00/0.06 APPEND(l1_2:S,l2_1:S) -> MATCH_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.06 MATCH_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> APPEND(l:S,l2_1:S) 0.00/0.06 MATCH_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> MATCH_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.06 MATCH_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> PART(a_4:S,l':S) 0.00/0.06 MATCH_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> MATCH_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.06 MATCH_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> TEST(a_4:S,x:S) 0.00/0.06 MATCH_4(l_5:S,Cons(a:S,l':S)) -> MATCH_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.06 MATCH_4(l_5:S,Cons(a:S,l':S)) -> PART(a:S,l':S) 0.00/0.06 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> APPEND(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.06 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> QUICK(l1:S) 0.00/0.06 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> QUICK(l2:S) 0.00/0.06 PART(a_4:S,l_3:S) -> MATCH_1(a_4:S,l_3:S,l_3:S) 0.00/0.06 QUICK(l_5:S) -> MATCH_4(l_5:S,l_5:S) 0.00/0.06 -> Rules: 0.00/0.06 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.06 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.06 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.06 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.06 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.06 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.06 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.06 match_4(l_5:S,Nil) -> Nil 0.00/0.06 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.06 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.06 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.06 test(x_0:S,y:S) -> False 0.00/0.06 test(x_0:S,y:S) -> True 0.00/0.06 ->Strongly Connected Components: 0.00/0.06 ->->Cycle: 0.00/0.06 ->->-> Pairs: 0.00/0.06 MATCH_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> PART(a_4:S,l':S) 0.00/0.06 PART(a_4:S,l_3:S) -> MATCH_1(a_4:S,l_3:S,l_3:S) 0.00/0.06 ->->-> Rules: 0.00/0.06 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.06 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.06 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.06 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.06 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.06 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.06 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.06 match_4(l_5:S,Nil) -> Nil 0.00/0.06 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.06 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.06 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.06 test(x_0:S,y:S) -> False 0.00/0.06 test(x_0:S,y:S) -> True 0.00/0.06 ->->Cycle: 0.00/0.06 ->->-> Pairs: 0.00/0.06 APPEND(l1_2:S,l2_1:S) -> MATCH_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.06 MATCH_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> APPEND(l:S,l2_1:S) 0.00/0.06 ->->-> Rules: 0.00/0.06 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.06 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.06 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.06 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.06 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.06 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.06 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.06 match_4(l_5:S,Nil) -> Nil 0.00/0.06 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.06 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.06 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.06 test(x_0:S,y:S) -> False 0.00/0.06 test(x_0:S,y:S) -> True 0.00/0.06 ->->Cycle: 0.00/0.06 ->->-> Pairs: 0.00/0.06 MATCH_4(l_5:S,Cons(a:S,l':S)) -> MATCH_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.06 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> QUICK(l1:S) 0.00/0.06 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> QUICK(l2:S) 0.00/0.06 QUICK(l_5:S) -> MATCH_4(l_5:S,l_5:S) 0.00/0.06 ->->-> Rules: 0.00/0.06 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.06 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.06 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.06 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.06 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.06 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.06 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.06 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.06 match_4(l_5:S,Nil) -> Nil 0.00/0.06 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.06 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.06 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.06 test(x_0:S,y:S) -> False 0.00/0.06 test(x_0:S,y:S) -> True 0.00/0.06 0.00/0.06 0.00/0.06 The problem is decomposed in 3 subproblems. 0.00/0.06 0.00/0.06 Problem 1.1: 0.00/0.06 0.00/0.06 Subterm Processor: 0.00/0.06 -> Pairs: 0.00/0.06 MATCH_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> PART(a_4:S,l':S) 0.00/0.06 PART(a_4:S,l_3:S) -> MATCH_1(a_4:S,l_3:S,l_3:S) 0.00/0.06 -> Rules: 0.00/0.06 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.06 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.06 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.07 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.07 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.07 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.07 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.07 match_4(l_5:S,Nil) -> Nil 0.00/0.07 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.07 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.07 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.07 test(x_0:S,y:S) -> False 0.00/0.07 test(x_0:S,y:S) -> True 0.00/0.07 ->Projection: 0.00/0.07 pi(MATCH_1) = 3 0.00/0.07 pi(PART) = 2 0.00/0.07 0.00/0.07 Problem 1.1: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 PART(a_4:S,l_3:S) -> MATCH_1(a_4:S,l_3:S,l_3:S) 0.00/0.07 -> Rules: 0.00/0.07 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.07 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.07 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.07 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.07 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.07 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.07 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.07 match_4(l_5:S,Nil) -> Nil 0.00/0.07 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.07 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.07 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.07 test(x_0:S,y:S) -> False 0.00/0.07 test(x_0:S,y:S) -> True 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 0.00/0.07 Problem 1.2: 0.00/0.07 0.00/0.07 Subterm Processor: 0.00/0.07 -> Pairs: 0.00/0.07 APPEND(l1_2:S,l2_1:S) -> MATCH_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.07 MATCH_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> APPEND(l:S,l2_1:S) 0.00/0.07 -> Rules: 0.00/0.07 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.07 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.07 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.07 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.07 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.07 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.07 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.07 match_4(l_5:S,Nil) -> Nil 0.00/0.07 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.07 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.07 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.07 test(x_0:S,y:S) -> False 0.00/0.07 test(x_0:S,y:S) -> True 0.00/0.07 ->Projection: 0.00/0.07 pi(APPEND) = 1 0.00/0.07 pi(MATCH_0) = 3 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 APPEND(l1_2:S,l2_1:S) -> MATCH_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.07 -> Rules: 0.00/0.07 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.07 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.07 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.07 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.07 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.07 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.07 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.07 match_4(l_5:S,Nil) -> Nil 0.00/0.07 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.07 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.07 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.07 test(x_0:S,y:S) -> False 0.00/0.07 test(x_0:S,y:S) -> True 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 0.00/0.07 Problem 1.3: 0.00/0.07 0.00/0.07 Reduction Pair Processor: 0.00/0.07 -> Pairs: 0.00/0.07 MATCH_4(l_5:S,Cons(a:S,l':S)) -> MATCH_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.07 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> QUICK(l1:S) 0.00/0.07 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> QUICK(l2:S) 0.00/0.07 QUICK(l_5:S) -> MATCH_4(l_5:S,l_5:S) 0.00/0.07 -> Rules: 0.00/0.07 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.07 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.07 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.07 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.07 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.07 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.07 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.07 match_4(l_5:S,Nil) -> Nil 0.00/0.07 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.07 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.07 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.07 test(x_0:S,y:S) -> False 0.00/0.07 test(x_0:S,y:S) -> True 0.00/0.07 -> Usable rules: 0.00/0.07 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.07 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.07 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.07 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.07 test(x_0:S,y:S) -> False 0.00/0.07 test(x_0:S,y:S) -> True 0.00/0.07 ->Interpretation type: 0.00/0.07 Linear 0.00/0.07 ->Coefficients: 0.00/0.07 Natural Numbers 0.00/0.07 ->Dimension: 0.00/0.07 1 0.00/0.07 ->Bound: 0.00/0.07 2 0.00/0.07 ->Interpretation: 0.00/0.07 0.00/0.07 [match_1](X1,X2,X3) = 2.X3 + 2 0.00/0.07 [match_2](X1,X2,X3,X4,X5) = 2.X1 + 2.X5 + 2 0.00/0.07 [match_3](X1,X2,X3,X4,X5,X6,X7) = 2.X1 + 2.X2 + 2.X3 + 2.X7 + 2 0.00/0.07 [part](X1,X2) = 2.X2 + 2 0.00/0.07 [test](X1,X2) = 1 0.00/0.07 [Cons](X1,X2) = 2.X1 + 2.X2 + 2 0.00/0.07 [False] = 1 0.00/0.07 [Nil] = 0 0.00/0.07 [Pair](X1,X2) = X1 + X2 + 2 0.00/0.07 [True] = 1 0.00/0.07 [MATCH_4](X1,X2) = 2.X2 + 2 0.00/0.07 [MATCH_5](X1,X2,X3,X4) = 2.X4 + 1 0.00/0.07 [QUICK](X) = 2.X + 2 0.00/0.07 0.00/0.07 Problem 1.3: 0.00/0.07 0.00/0.07 SCC Processor: 0.00/0.07 -> Pairs: 0.00/0.07 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> QUICK(l1:S) 0.00/0.07 MATCH_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> QUICK(l2:S) 0.00/0.07 QUICK(l_5:S) -> MATCH_4(l_5:S,l_5:S) 0.00/0.07 -> Rules: 0.00/0.07 append(l1_2:S,l2_1:S) -> match_0(l1_2:S,l2_1:S,l1_2:S) 0.00/0.07 match_0(l1_2:S,l2_1:S,Cons(x:S,l:S)) -> Cons(x:S,append(l:S,l2_1:S)) 0.00/0.07 match_0(l1_2:S,l2_1:S,Nil) -> l2_1:S 0.00/0.07 match_1(a_4:S,l_3:S,Cons(x:S,l':S)) -> match_2(x:S,l':S,a_4:S,l_3:S,part(a_4:S,l':S)) 0.00/0.07 match_1(a_4:S,l_3:S,Nil) -> Pair(Nil,Nil) 0.00/0.07 match_2(x:S,l':S,a_4:S,l_3:S,Pair(l1:S,l2:S)) -> match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,test(a_4:S,x:S)) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,False) -> Pair(Cons(x:S,l1:S),l2:S) 0.00/0.07 match_3(l1:S,l2:S,x:S,l':S,a_4:S,l_3:S,True) -> Pair(l1:S,Cons(x:S,l2:S)) 0.00/0.07 match_4(l_5:S,Cons(a:S,l':S)) -> match_5(a:S,l':S,l_5:S,part(a:S,l':S)) 0.00/0.07 match_4(l_5:S,Nil) -> Nil 0.00/0.07 match_5(a:S,l':S,l_5:S,Pair(l1:S,l2:S)) -> append(quick(l1:S),Cons(a:S,quick(l2:S))) 0.00/0.07 part(a_4:S,l_3:S) -> match_1(a_4:S,l_3:S,l_3:S) 0.00/0.07 quick(l_5:S) -> match_4(l_5:S,l_5:S) 0.00/0.07 test(x_0:S,y:S) -> False 0.00/0.07 test(x_0:S,y:S) -> True 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