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)) ADG 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)) -> 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#(f(y)) -> f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) 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#(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)) -> f#(y) -> f#(g(x,y)) -> g#(f(f(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)) -> g#(f(f(y)),h(a(),a())) -> g#(g(x,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#(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(),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#(g(a(),y),g(a(),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#(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)) 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(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)) -> 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)) -> 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#(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)) -> g#(g(f(f(y)),h(a(),a())),x) 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#(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)) -> g#(g(f(f(y)),h(a(),a())),x) 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)) -> 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)) -> g#(g(f(f(y)),h(a(),a())),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#(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)) SCC Processor: #sccs: 3 #rules: 5 #arcs: 57/256 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)) Open 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#(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)) Open