MAYBE Problem: f(a(),f(x,a())) -> f(a(),f(f(a(),x),f(a(),a()))) Proof: DP Processor: DPs: f#(a(),f(x,a())) -> f#(a(),a()) f#(a(),f(x,a())) -> f#(a(),x) f#(a(),f(x,a())) -> f#(f(a(),x),f(a(),a())) f#(a(),f(x,a())) -> f#(a(),f(f(a(),x),f(a(),a()))) TRS: f(a(),f(x,a())) -> f(a(),f(f(a(),x),f(a(),a()))) Restore Modifier: DPs: f#(a(),f(x,a())) -> f#(a(),a()) f#(a(),f(x,a())) -> f#(a(),x) f#(a(),f(x,a())) -> f#(f(a(),x),f(a(),a())) f#(a(),f(x,a())) -> f#(a(),f(f(a(),x),f(a(),a()))) TRS: f(a(),f(x,a())) -> f(a(),f(f(a(),x),f(a(),a()))) SCC Processor: #sccs: 1 #rules: 4 #arcs: 16/16 DPs: f#(a(),f(x,a())) -> f#(a(),a()) f#(a(),f(x,a())) -> f#(a(),x) f#(a(),f(x,a())) -> f#(f(a(),x),f(a(),a())) f#(a(),f(x,a())) -> f#(a(),f(f(a(),x),f(a(),a()))) TRS: f(a(),f(x,a())) -> f(a(),f(f(a(),x),f(a(),a()))) Matrix Interpretation Processor: dimension: 1 interpretation: [f#](x0, x1) = x0 + 1, [f](x0, x1) = 0, [a] = 1 orientation: f#(a(),f(x,a())) = 2 >= 2 = f#(a(),a()) f#(a(),f(x,a())) = 2 >= 2 = f#(a(),x) f#(a(),f(x,a())) = 2 >= 1 = f#(f(a(),x),f(a(),a())) f#(a(),f(x,a())) = 2 >= 2 = f#(a(),f(f(a(),x),f(a(),a()))) f(a(),f(x,a())) = 0 >= 0 = f(a(),f(f(a(),x),f(a(),a()))) problem: DPs: f#(a(),f(x,a())) -> f#(a(),a()) f#(a(),f(x,a())) -> f#(a(),x) f#(a(),f(x,a())) -> f#(a(),f(f(a(),x),f(a(),a()))) TRS: f(a(),f(x,a())) -> f(a(),f(f(a(),x),f(a(),a()))) Open