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