MAYBE Problem: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) Proof: DP Processor: DPs: h#(x,x) -> h#(a(),b()) g#(g(x,a()),y) -> g#(a(),x) g#(g(x,a()),y) -> g#(a(),y) g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) f#(g(x,y)) -> h#(a(),a()) f#(g(x,y)) -> f#(y) f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) TDG Processor: DPs: h#(x,x) -> h#(a(),b()) g#(g(x,a()),y) -> g#(a(),x) g#(g(x,a()),y) -> g#(a(),y) g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) f#(g(x,y)) -> h#(a(),a()) f#(g(x,y)) -> f#(y) f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) graph: f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> f#(y) f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> h#(a(),a()) f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> f#(y) f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> h#(a(),a()) f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) -> g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) -> g#(g(x,a()),y) -> g#(a(),y) f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) -> g#(g(x,a()),y) -> g#(a(),x) f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) -> g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) -> g#(g(x,a()),y) -> g#(a(),y) f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) -> g#(g(x,a()),y) -> g#(a(),x) f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(z) f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(y) f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) f#(g(x,y)) -> h#(a(),a()) -> h#(x,x) -> h#(a(),b()) g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) -> g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) -> g#(g(x,a()),y) -> g#(a(),y) g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) -> g#(g(x,a()),y) -> g#(a(),x) g#(g(x,a()),y) -> g#(a(),y) -> g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) g#(g(x,a()),y) -> g#(a(),y) -> g#(g(x,a()),y) -> g#(a(),y) g#(g(x,a()),y) -> g#(a(),y) -> g#(g(x,a()),y) -> g#(a(),x) g#(g(x,a()),y) -> g#(a(),x) -> g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) g#(g(x,a()),y) -> g#(a(),x) -> g#(g(x,a()),y) -> g#(a(),y) g#(g(x,a()),y) -> g#(a(),x) -> g#(g(x,a()),y) -> g#(a(),x) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) -> f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) -> f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) -> h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) -> h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) -> h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) -> h#(h(f(f(x)),y),h(z,v)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) -> h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) -> h#(x,x) -> h#(a(),b()) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(x,x) -> h#(a(),b()) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(x,x) -> h#(a(),b()) h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(y) h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(x,x) -> h#(a(),b()) -> h#(x,x) -> h#(a(),b()) SCC Processor: #sccs: 2 #rules: 14 #arcs: 85/256 DPs: f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> h#(a(),a()) h#(x,x) -> h#(a(),b()) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> f#(y) f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) EDG Processor: DPs: f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> h#(a(),a()) h#(x,x) -> h#(a(),b()) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> f#(y) f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) graph: f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> h#(a(),a()) f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> f#(y) f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> h#(a(),a()) f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> f#(y) f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> h#(a(),a()) -> h#(x,x) -> h#(a(),b()) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) -> h#(x,x) -> h#(a(),b()) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(x,x) -> h#(a(),b()) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(x,x) -> h#(a(),b()) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) CDG Processor: DPs: f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> h#(a(),a()) h#(x,x) -> h#(a(),b()) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> f#(y) f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) graph: f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> f#(y) f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> h#(a(),a()) f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> f#(y) f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> h#(a(),a()) f#(g(x,y)) -> h#(a(),a()) -> h#(x,x) -> h#(a(),b()) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> h#(a(),a()) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) -> h#(x,x) -> h#(a(),b()) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(z) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> f#(y) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(x,x) -> h#(a(),b()) SCC Processor: #sccs: 2 #rules: 4 #arcs: 35/121 DPs: h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) Arctic Interpretation Processor: dimension: 1 interpretation: [h#](x0, x1) = x0 + x1, [f](x0) = x0, [g](x0, x1) = 0, [b] = 3, [a] = 4, [h](x0, x1) = 1x0 + 1x1 + 5 orientation: h#(h(f(f(x)),y),h(z,v)) = 1v + 1x + 1y + 1z + 5 >= 1v + 1x + 1y + 1z + 5 = h#(h(f(z),f(f(f(y)))),h(v,x)) h#(h(f(f(x)),y),h(z,v)) = 1v + 1x + 1y + 1z + 5 >= v + x = h#(v,x) h(x,x) = 1x + 5 >= 5 = h(a(),b()) g(g(x,a()),y) = 0 >= 0 = g(g(a(),y),g(a(),x)) f(g(x,y)) = 0 >= 0 = g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) = 2v + 2x + 2y + 2z + 6 >= 2v + 2x + 2y + 2z + 6 = h(h(f(z),f(f(f(y)))),h(v,x)) problem: DPs: h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) Matrix Interpretation Processor: dim=3 interpretation: [h#](x0, x1) = [1 0 0]x0 + [0 1 0]x1, [0 0 1] [0] [f](x0) = [0 0 0]x0 + [0] [1 0 1] [1], [0] [g](x0, x1) = [0] [0], [0] [b] = [0] [0], [0] [a] = [0] [0], [1 0 0] [0 1 0] [h](x0, x1) = [0 0 1]x0 + [0 0 1]x1 [0 0 0] [0 0 0] orientation: h#(h(f(f(x)),y),h(z,v)) = [0 0 1]v + [1 0 1]x + [0 1 0]y + [0 0 1]z + [1] >= [0 0 1]v + [0 0 1]x + [0 0 1]z = h#(h(f(z),f(f(f(y)))),h(v,x)) [1 1 0] [0] h(x,x) = [0 0 2]x >= [0] = h(a(),b()) [0 0 0] [0] [0] [0] g(g(x,a()),y) = [0] >= [0] = g(g(a(),y),g(a(),x)) [0] [0] [0] [0] f(g(x,y)) = [0] >= [0] = g(g(f(f(y)),h(a(),a())),x) [1] [0] [0 0 1] [1 0 1] [0 1 0] [0 0 1] [1] [0 0 1] [0 0 1] [0 0 1] h(h(f(f(x)),y),h(z,v)) = [0 0 0]v + [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]v + [0 0 0]x + [0 0 0]z = h(h(f(z),f(f(f(y)))),h(v,x)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] problem: DPs: TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) Qed DPs: f#(g(x,y)) -> f#(f(y)) f#(g(x,y)) -> f#(y) TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) Open DPs: g#(g(x,a()),y) -> g#(a(),x) g#(g(x,a()),y) -> g#(a(),y) g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) EDG Processor: DPs: g#(g(x,a()),y) -> g#(a(),x) g#(g(x,a()),y) -> g#(a(),y) g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) graph: g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) -> g#(g(x,a()),y) -> g#(a(),x) g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) -> g#(g(x,a()),y) -> g#(a(),y) g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) -> g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) CDG Processor: DPs: g#(g(x,a()),y) -> g#(a(),x) g#(g(x,a()),y) -> g#(a(),y) g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) TRS: h(x,x) -> h(a(),b()) g(g(x,a()),y) -> g(g(a(),y),g(a(),x)) f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x) h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x)) graph: Qed