/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR fun x xs y z) (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),1),x) -> app(app(app(f,app(s,x)),x),x) app(app(app(f,x),y),app(s,z)) -> app(s,app(app(app(f,0),1),z)) 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(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs)) app(app(map,fun),nil) -> nil ) 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),1),x) -> APP(app(app(f,app(s,x)),x),x) APP(app(app(f,x),y),app(s,z)) -> APP(app(app(f,0),1),z) APP(app(app(f,x),y),app(s,z)) -> APP(s,app(app(app(f,0),1),z)) 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) -> 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),1),x) -> app(app(app(f,app(s,x)),x),x) app(app(app(f,x),y),app(s,z)) -> app(s,app(app(app(f,0),1),z)) 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(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs)) app(app(map,fun),nil) -> nil 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),1),x) -> APP(app(app(f,app(s,x)),x),x) APP(app(app(f,x),y),app(s,z)) -> APP(app(app(f,0),1),z) APP(app(app(f,x),y),app(s,z)) -> APP(s,app(app(app(f,0),1),z)) 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) -> 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),1),x) -> app(app(app(f,app(s,x)),x),x) app(app(app(f,x),y),app(s,z)) -> app(s,app(app(app(f,0),1),z)) 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(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs)) app(app(map,fun),nil) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(app(f,0),1),x) -> APP(app(app(f,app(s,x)),x),x) APP(app(app(f,x),y),app(s,z)) -> APP(app(app(f,0),1),z) ->->-> 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),1),x) -> app(app(app(f,app(s,x)),x),x) app(app(app(f,x),y),app(s,z)) -> app(s,app(app(app(f,0),1),z)) 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(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs)) app(app(map,fun),nil) -> nil ->->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),1),x) -> app(app(app(f,app(s,x)),x),x) app(app(app(f,x),y),app(s,z)) -> app(s,app(app(app(f,0),1),z)) 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(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs)) app(app(map,fun),nil) -> nil The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: APP(app(app(f,0),1),x) -> APP(app(app(f,app(s,x)),x),x) APP(app(app(f,x),y),app(s,z)) -> APP(app(app(f,0),1),z) -> 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),1),x) -> app(app(app(f,app(s,x)),x),x) app(app(app(f,x),y),app(s,z)) -> app(s,app(app(app(f,0),1),z)) 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(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs)) app(app(map,fun),nil) -> nil ->Projection: pi(APP) = 2 Problem 1.1: SCC Processor: -> Pairs: APP(app(app(f,0),1),x) -> APP(app(app(f,app(s,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),1),x) -> app(app(app(f,app(s,x)),x),x) app(app(app(f,x),y),app(s,z)) -> app(s,app(app(app(f,0),1),z)) 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(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs)) app(app(map,fun),nil) -> nil ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: 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),1),x) -> app(app(app(f,app(s,x)),x),x) app(app(app(f,x),y),app(s,z)) -> app(s,app(app(app(f,0),1),z)) 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(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs)) app(app(map,fun),nil) -> nil ->Projection: pi(APP) = 2 Problem 1.2: 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),1),x) -> app(app(app(f,app(s,x)),x),x) app(app(app(f,x),y),app(s,z)) -> app(s,app(app(app(f,0),1),z)) 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(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs)) app(app(map,fun),nil) -> nil ->Strongly Connected Components: There is no strongly connected component The problem is finite.