/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 z) (RULES app(app(app(app(f,0),1),app(app(g,x),y)),z) -> app(app(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)),app(h,x)) 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(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,0),1) -> 0 app(app(g,0),1) -> 1 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(h,app(app(g,x),y)) -> app(h,x) ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: APP(app(app(app(f,0),1),app(app(g,x),y)),z) -> APP(app(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)),app(h,x)) APP(app(app(app(f,0),1),app(app(g,x),y)),z) -> APP(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)) APP(app(app(app(f,0),1),app(app(g,x),y)),z) -> APP(app(f,app(app(g,x),y)),app(app(g,x),y)) APP(app(app(app(f,0),1),app(app(g,x),y)),z) -> APP(f,app(app(g,x),y)) APP(app(app(app(f,0),1),app(app(g,x),y)),z) -> APP(h,x) 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(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(h,app(app(g,x),y)) -> APP(h,x) -> Rules: app(app(app(app(f,0),1),app(app(g,x),y)),z) -> app(app(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)),app(h,x)) 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(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,0),1) -> 0 app(app(g,0),1) -> 1 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(h,app(app(g,x),y)) -> app(h,x) Problem 1: SCC Processor: -> Pairs: APP(app(app(app(f,0),1),app(app(g,x),y)),z) -> APP(app(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)),app(h,x)) APP(app(app(app(f,0),1),app(app(g,x),y)),z) -> APP(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)) APP(app(app(app(f,0),1),app(app(g,x),y)),z) -> APP(app(f,app(app(g,x),y)),app(app(g,x),y)) APP(app(app(app(f,0),1),app(app(g,x),y)),z) -> APP(f,app(app(g,x),y)) APP(app(app(app(f,0),1),app(app(g,x),y)),z) -> APP(h,x) 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(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(h,app(app(g,x),y)) -> APP(h,x) -> Rules: app(app(app(app(f,0),1),app(app(g,x),y)),z) -> app(app(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)),app(h,x)) 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(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,0),1) -> 0 app(app(g,0),1) -> 1 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(h,app(app(g,x),y)) -> app(h,x) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(h,app(app(g,x),y)) -> APP(h,x) ->->-> Rules: app(app(app(app(f,0),1),app(app(g,x),y)),z) -> app(app(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)),app(h,x)) 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(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,0),1) -> 0 app(app(g,0),1) -> 1 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(h,app(app(g,x),y)) -> app(h,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(f,0),1),app(app(g,x),y)),z) -> app(app(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)),app(h,x)) 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(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,0),1) -> 0 app(app(g,0),1) -> 1 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(h,app(app(g,x),y)) -> app(h,x) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: APP(h,app(app(g,x),y)) -> APP(h,x) -> Rules: app(app(app(app(f,0),1),app(app(g,x),y)),z) -> app(app(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)),app(h,x)) 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(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,0),1) -> 0 app(app(g,0),1) -> 1 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(h,app(app(g,x),y)) -> app(h,x) ->Projection: pi(APP) = 2 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: app(app(app(app(f,0),1),app(app(g,x),y)),z) -> app(app(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)),app(h,x)) 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(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,0),1) -> 0 app(app(g,0),1) -> 1 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(h,app(app(g,x),y)) -> app(h,x) ->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(f,0),1),app(app(g,x),y)),z) -> app(app(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)),app(h,x)) 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(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,0),1) -> 0 app(app(g,0),1) -> 1 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(h,app(app(g,x),y)) -> app(h,x) ->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(f,0),1),app(app(g,x),y)),z) -> app(app(app(app(f,app(app(g,x),y)),app(app(g,x),y)),app(app(g,x),y)),app(h,x)) 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(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,0),1) -> 0 app(app(g,0),1) -> 1 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(h,app(app(g,x),y)) -> app(h,x) ->Strongly Connected Components: There is no strongly connected component The problem is finite.