0.00/0.02 YES 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 (VAR v_NonEmpty:S fun:S x:S xs:S) 0.00/0.02 (RULES 0.00/0.02 0 -> 1 0.00/0.02 app(app(app(app(filter2,ffalse),fun:S),x:S),xs:S) -> app(app(filter,fun:S),xs:S) 0.00/0.02 app(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,fun:S),xs:S)) 0.00/0.02 app(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(fun:S,x:S)),fun:S),x:S),xs:S) 0.00/0.02 app(app(filter,fun:S),nil) -> nil 0.00/0.02 app(app(g,0),1) -> app(s,0) 0.00/0.02 app(app(map,fun:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(fun:S,x:S)),app(app(map,fun:S),xs:S)) 0.00/0.02 app(app(map,fun:S),nil) -> nil 0.00/0.02 app(f,app(s,x:S)) -> app(f,app(app(g,x:S),x:S)) 0.00/0.02 ) 0.00/0.02 (STRATEGY INNERMOST) 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 Dependency Pairs Processor: 0.00/0.02 -> Pairs: 0.00/0.02 APP(app(app(app(filter2,ffalse),fun:S),x:S),xs:S) -> APP(app(filter,fun:S),xs:S) 0.00/0.02 APP(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> APP(app(cons,x:S),app(app(filter,fun:S),xs:S)) 0.00/0.02 APP(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> APP(app(filter,fun:S),xs:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(app(app(filter2,app(fun:S,x:S)),fun:S),x:S),xs:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(app(filter2,app(fun:S,x:S)),fun:S),x:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(filter2,app(fun:S,x:S)),fun:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(filter2,app(fun:S,x:S)) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(fun:S,x:S) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(fun:S,x:S)),app(app(map,fun:S),xs:S)) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(map,fun:S),xs:S) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(cons,app(fun:S,x:S)) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(fun:S,x:S) 0.00/0.02 APP(f,app(s,x:S)) -> APP(app(g,x:S),x:S) 0.00/0.02 APP(f,app(s,x:S)) -> APP(f,app(app(g,x:S),x:S)) 0.00/0.02 -> Rules: 0.00/0.02 0 -> 1 0.00/0.02 app(app(app(app(filter2,ffalse),fun:S),x:S),xs:S) -> app(app(filter,fun:S),xs:S) 0.00/0.02 app(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,fun:S),xs:S)) 0.00/0.02 app(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(fun:S,x:S)),fun:S),x:S),xs:S) 0.00/0.02 app(app(filter,fun:S),nil) -> nil 0.00/0.02 app(app(g,0),1) -> app(s,0) 0.00/0.02 app(app(map,fun:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(fun:S,x:S)),app(app(map,fun:S),xs:S)) 0.00/0.02 app(app(map,fun:S),nil) -> nil 0.00/0.02 app(f,app(s,x:S)) -> app(f,app(app(g,x:S),x:S)) 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 SCC Processor: 0.00/0.02 -> Pairs: 0.00/0.02 APP(app(app(app(filter2,ffalse),fun:S),x:S),xs:S) -> APP(app(filter,fun:S),xs:S) 0.00/0.02 APP(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> APP(app(cons,x:S),app(app(filter,fun:S),xs:S)) 0.00/0.02 APP(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> APP(app(filter,fun:S),xs:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(app(app(filter2,app(fun:S,x:S)),fun:S),x:S),xs:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(app(filter2,app(fun:S,x:S)),fun:S),x:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(filter2,app(fun:S,x:S)),fun:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(filter2,app(fun:S,x:S)) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(fun:S,x:S) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(fun:S,x:S)),app(app(map,fun:S),xs:S)) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(map,fun:S),xs:S) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(cons,app(fun:S,x:S)) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(fun:S,x:S) 0.00/0.02 APP(f,app(s,x:S)) -> APP(app(g,x:S),x:S) 0.00/0.02 APP(f,app(s,x:S)) -> APP(f,app(app(g,x:S),x:S)) 0.00/0.02 -> Rules: 0.00/0.02 0 -> 1 0.00/0.02 app(app(app(app(filter2,ffalse),fun:S),x:S),xs:S) -> app(app(filter,fun:S),xs:S) 0.00/0.02 app(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,fun:S),xs:S)) 0.00/0.02 app(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(fun:S,x:S)),fun:S),x:S),xs:S) 0.00/0.02 app(app(filter,fun:S),nil) -> nil 0.00/0.02 app(app(g,0),1) -> app(s,0) 0.00/0.02 app(app(map,fun:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(fun:S,x:S)),app(app(map,fun:S),xs:S)) 0.00/0.02 app(app(map,fun:S),nil) -> nil 0.00/0.02 app(f,app(s,x:S)) -> app(f,app(app(g,x:S),x:S)) 0.00/0.02 ->Strongly Connected Components: 0.00/0.02 ->->Cycle: 0.00/0.02 ->->-> Pairs: 0.00/0.02 APP(app(app(app(filter2,ffalse),fun:S),x:S),xs:S) -> APP(app(filter,fun:S),xs:S) 0.00/0.02 APP(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> APP(app(filter,fun:S),xs:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(app(app(filter2,app(fun:S,x:S)),fun:S),x:S),xs:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(fun:S,x:S) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(map,fun:S),xs:S) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(fun:S,x:S) 0.00/0.02 ->->-> Rules: 0.00/0.02 0 -> 1 0.00/0.02 app(app(app(app(filter2,ffalse),fun:S),x:S),xs:S) -> app(app(filter,fun:S),xs:S) 0.00/0.02 app(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,fun:S),xs:S)) 0.00/0.02 app(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(fun:S,x:S)),fun:S),x:S),xs:S) 0.00/0.02 app(app(filter,fun:S),nil) -> nil 0.00/0.02 app(app(g,0),1) -> app(s,0) 0.00/0.02 app(app(map,fun:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(fun:S,x:S)),app(app(map,fun:S),xs:S)) 0.00/0.02 app(app(map,fun:S),nil) -> nil 0.00/0.02 app(f,app(s,x:S)) -> app(f,app(app(g,x:S),x:S)) 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 Subterm Processor: 0.00/0.02 -> Pairs: 0.00/0.02 APP(app(app(app(filter2,ffalse),fun:S),x:S),xs:S) -> APP(app(filter,fun:S),xs:S) 0.00/0.02 APP(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> APP(app(filter,fun:S),xs:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(app(app(filter2,app(fun:S,x:S)),fun:S),x:S),xs:S) 0.00/0.02 APP(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> APP(fun:S,x:S) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(app(map,fun:S),xs:S) 0.00/0.02 APP(app(map,fun:S),app(app(cons,x:S),xs:S)) -> APP(fun:S,x:S) 0.00/0.02 -> Rules: 0.00/0.02 0 -> 1 0.00/0.02 app(app(app(app(filter2,ffalse),fun:S),x:S),xs:S) -> app(app(filter,fun:S),xs:S) 0.00/0.02 app(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,fun:S),xs:S)) 0.00/0.02 app(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(fun:S,x:S)),fun:S),x:S),xs:S) 0.00/0.02 app(app(filter,fun:S),nil) -> nil 0.00/0.02 app(app(g,0),1) -> app(s,0) 0.00/0.02 app(app(map,fun:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(fun:S,x:S)),app(app(map,fun:S),xs:S)) 0.00/0.02 app(app(map,fun:S),nil) -> nil 0.00/0.02 app(f,app(s,x:S)) -> app(f,app(app(g,x:S),x:S)) 0.00/0.02 ->Projection: 0.00/0.02 pi(APP) = 2 0.00/0.02 0.00/0.02 Problem 1: 0.00/0.02 0.00/0.02 SCC Processor: 0.00/0.02 -> Pairs: 0.00/0.02 APP(app(app(app(filter2,ffalse),fun:S),x:S),xs:S) -> APP(app(filter,fun:S),xs:S) 0.00/0.02 APP(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> APP(app(filter,fun:S),xs:S) 0.00/0.02 -> Rules: 0.00/0.02 0 -> 1 0.00/0.02 app(app(app(app(filter2,ffalse),fun:S),x:S),xs:S) -> app(app(filter,fun:S),xs:S) 0.00/0.02 app(app(app(app(filter2,ttrue),fun:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,fun:S),xs:S)) 0.00/0.02 app(app(filter,fun:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(fun:S,x:S)),fun:S),x:S),xs:S) 0.00/0.02 app(app(filter,fun:S),nil) -> nil 0.00/0.02 app(app(g,0),1) -> app(s,0) 0.00/0.02 app(app(map,fun:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(fun:S,x:S)),app(app(map,fun:S),xs:S)) 0.00/0.02 app(app(map,fun:S),nil) -> nil 0.00/0.02 app(f,app(s,x:S)) -> app(f,app(app(g,x:S),x:S)) 0.00/0.02 ->Strongly Connected Components: 0.00/0.02 There is no strongly connected component 0.00/0.02 0.00/0.02 The problem is finite. 0.00/0.02 EOF