/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(.,app(app(/,y),x)),x) -> y app(app(.,e),x) -> x app(app(.,x),app(app(\,x),y)) -> y app(app(.,x),e) -> x app(app(/,app(app(.,y),x)),x) -> y app(app(/,x),app(app(\,y),x)) -> y app(app(/,x),e) -> x app(app(/,x),x) -> e app(app(\,app(app(/,x),y)),x) -> y app(app(\,e),x) -> x app(app(\,x),app(app(.,x),y)) -> y app(app(\,x),x) -> e 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(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil ) 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(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) -> 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(.,app(app(/,y),x)),x) -> y app(app(.,e),x) -> x app(app(.,x),app(app(\,x),y)) -> y app(app(.,x),e) -> x app(app(/,app(app(.,y),x)),x) -> y app(app(/,x),app(app(\,y),x)) -> y app(app(/,x),e) -> x app(app(/,x),x) -> e app(app(\,app(app(/,x),y)),x) -> y app(app(\,e),x) -> x app(app(\,x),app(app(.,x),y)) -> y app(app(\,x),x) -> e 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(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),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(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) -> 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(.,app(app(/,y),x)),x) -> y app(app(.,e),x) -> x app(app(.,x),app(app(\,x),y)) -> y app(app(.,x),e) -> x app(app(/,app(app(.,y),x)),x) -> y app(app(/,x),app(app(\,y),x)) -> y app(app(/,x),e) -> x app(app(/,x),x) -> e app(app(\,app(app(/,x),y)),x) -> y app(app(\,e),x) -> x app(app(\,x),app(app(.,x),y)) -> y app(app(\,x),x) -> e 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(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil ->Strongly Connected Components: ->->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(.,app(app(/,y),x)),x) -> y app(app(.,e),x) -> x app(app(.,x),app(app(\,x),y)) -> y app(app(.,x),e) -> x app(app(/,app(app(.,y),x)),x) -> y app(app(/,x),app(app(\,y),x)) -> y app(app(/,x),e) -> x app(app(/,x),x) -> e app(app(\,app(app(/,x),y)),x) -> y app(app(\,e),x) -> x app(app(\,x),app(app(.,x),y)) -> y app(app(\,x),x) -> e 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(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil Problem 1: 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(.,app(app(/,y),x)),x) -> y app(app(.,e),x) -> x app(app(.,x),app(app(\,x),y)) -> y app(app(.,x),e) -> x app(app(/,app(app(.,y),x)),x) -> y app(app(/,x),app(app(\,y),x)) -> y app(app(/,x),e) -> x app(app(/,x),x) -> e app(app(\,app(app(/,x),y)),x) -> y app(app(\,e),x) -> x app(app(\,x),app(app(.,x),y)) -> y app(app(\,x),x) -> e 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(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil ->Projection: pi(APP) = 2 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(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(.,app(app(/,y),x)),x) -> y app(app(.,e),x) -> x app(app(.,x),app(app(\,x),y)) -> y app(app(.,x),e) -> x app(app(/,app(app(.,y),x)),x) -> y app(app(/,x),app(app(\,y),x)) -> y app(app(/,x),e) -> x app(app(/,x),x) -> e app(app(\,app(app(/,x),y)),x) -> y app(app(\,e),x) -> x app(app(\,x),app(app(.,x),y)) -> y app(app(\,x),x) -> e 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(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil ->Strongly Connected Components: There is no strongly connected component The problem is finite.