/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR f x xs y) (RULES app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: APP(app(app(app(filter2,false),f),x),xs) -> APP(app(filter,f),xs) APP(app(app(app(filter2,true),f),x),xs) -> APP(app(cons,x),app(app(filter,f),xs)) APP(app(app(app(filter2,true),f),x),xs) -> APP(app(filter,f),xs) APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(app(app(filter2,app(f,x)),f),x),xs) APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(app(filter2,app(f,x)),f),x) APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(filter2,app(f,x)),f) APP(app(filter,f),app(app(cons,x),xs)) -> APP(filter2,app(f,x)) APP(app(filter,f),app(app(cons,x),xs)) -> APP(f,x) APP(app(int,app(s,x)),app(s,y)) -> APP(app(int,x),y) APP(app(int,app(s,x)),app(s,y)) -> APP(intlist,app(app(int,x),y)) APP(app(int,0),app(s,y)) -> APP(app(cons,0),app(app(int,app(s,0)),app(s,y))) APP(app(int,0),app(s,y)) -> APP(app(int,app(s,0)),app(s,y)) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(cons,app(f,x)),app(app(map,f),xs)) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs) APP(app(map,f),app(app(cons,x),xs)) -> APP(cons,app(f,x)) APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x) APP(intlist,app(app(cons,x),y)) -> APP(app(cons,app(s,x)),app(intlist,y)) APP(intlist,app(app(cons,x),y)) -> APP(intlist,y) -> Rules: app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil Problem 1: SCC Processor: -> Pairs: APP(app(app(app(filter2,false),f),x),xs) -> APP(app(filter,f),xs) APP(app(app(app(filter2,true),f),x),xs) -> APP(app(cons,x),app(app(filter,f),xs)) APP(app(app(app(filter2,true),f),x),xs) -> APP(app(filter,f),xs) APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(app(app(filter2,app(f,x)),f),x),xs) APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(app(filter2,app(f,x)),f),x) APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(filter2,app(f,x)),f) APP(app(filter,f),app(app(cons,x),xs)) -> APP(filter2,app(f,x)) APP(app(filter,f),app(app(cons,x),xs)) -> APP(f,x) APP(app(int,app(s,x)),app(s,y)) -> APP(app(int,x),y) APP(app(int,app(s,x)),app(s,y)) -> APP(intlist,app(app(int,x),y)) APP(app(int,0),app(s,y)) -> APP(app(cons,0),app(app(int,app(s,0)),app(s,y))) APP(app(int,0),app(s,y)) -> APP(app(int,app(s,0)),app(s,y)) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(cons,app(f,x)),app(app(map,f),xs)) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs) APP(app(map,f),app(app(cons,x),xs)) -> APP(cons,app(f,x)) APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x) APP(intlist,app(app(cons,x),y)) -> APP(app(cons,app(s,x)),app(intlist,y)) APP(intlist,app(app(cons,x),y)) -> APP(intlist,y) -> Rules: app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(intlist,app(app(cons,x),y)) -> APP(intlist,y) ->->-> Rules: app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil ->->Cycle: ->->-> Pairs: APP(app(int,app(s,x)),app(s,y)) -> APP(app(int,x),y) APP(app(int,0),app(s,y)) -> APP(app(int,app(s,0)),app(s,y)) ->->-> Rules: app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil ->->Cycle: ->->-> Pairs: APP(app(app(app(filter2,false),f),x),xs) -> APP(app(filter,f),xs) APP(app(app(app(filter2,true),f),x),xs) -> APP(app(filter,f),xs) APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(app(app(filter2,app(f,x)),f),x),xs) APP(app(filter,f),app(app(cons,x),xs)) -> APP(f,x) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs) APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x) ->->-> Rules: app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil The problem is decomposed in 3 subproblems. Problem 1.1: Subterm Processor: -> Pairs: APP(intlist,app(app(cons,x),y)) -> APP(intlist,y) -> Rules: app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil ->Projection: pi(APP) = 2 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Subterm Processor: -> Pairs: APP(app(int,app(s,x)),app(s,y)) -> APP(app(int,x),y) APP(app(int,0),app(s,y)) -> APP(app(int,app(s,0)),app(s,y)) -> Rules: app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil ->Projection: pi(APP) = 2 Problem 1.2: SCC Processor: -> Pairs: APP(app(int,0),app(s,y)) -> APP(app(int,app(s,0)),app(s,y)) -> Rules: app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.3: Subterm Processor: -> Pairs: APP(app(app(app(filter2,false),f),x),xs) -> APP(app(filter,f),xs) APP(app(app(app(filter2,true),f),x),xs) -> APP(app(filter,f),xs) APP(app(filter,f),app(app(cons,x),xs)) -> APP(app(app(app(filter2,app(f,x)),f),x),xs) APP(app(filter,f),app(app(cons,x),xs)) -> APP(f,x) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs) APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x) -> Rules: app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil ->Projection: pi(APP) = 2 Problem 1.3: SCC Processor: -> Pairs: APP(app(app(app(filter2,false),f),x),xs) -> APP(app(filter,f),xs) APP(app(app(app(filter2,true),f),x),xs) -> APP(app(filter,f),xs) -> Rules: app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs) app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) app(app(filter,f),nil) -> nil app(app(int,app(s,x)),app(s,y)) -> app(intlist,app(app(int,x),y)) app(app(int,app(s,x)),0) -> nil app(app(int,0),app(s,y)) -> app(app(cons,0),app(app(int,app(s,0)),app(s,y))) app(app(int,0),0) -> app(app(cons,0),nil) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(intlist,app(app(cons,x),y)) -> app(app(cons,app(s,x)),app(intlist,y)) app(intlist,nil) -> nil ->Strongly Connected Components: There is no strongly connected component The problem is finite.