MAYBE Time: 0.102590 TRS: { f(f(f(a(), x), b()), b()) -> f(f(a(), f(f(x, b()), b())), b()), f(a(), f(a(), f(a(), f(x, b())))) -> f(f(a(), f(a(), f(a(), x))), b())} DP: DP: { f#(f(f(a(), x), b()), b()) -> f#(x, b()), f#(f(f(a(), x), b()), b()) -> f#(f(x, b()), b()), f#(f(f(a(), x), b()), b()) -> f#(f(a(), f(f(x, b()), b())), b()), f#(f(f(a(), x), b()), b()) -> f#(a(), f(f(x, b()), b())), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(f(a(), f(a(), f(a(), x))), b()), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), x), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), x)), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x)))} TRS: { f(f(f(a(), x), b()), b()) -> f(f(a(), f(f(x, b()), b())), b()), f(a(), f(a(), f(a(), f(x, b())))) -> f(f(a(), f(a(), f(a(), x))), b())} UR: { f(f(f(a(), x), b()), b()) -> f(f(a(), f(f(x, b()), b())), b()), f(a(), f(a(), f(a(), f(x, b())))) -> f(f(a(), f(a(), f(a(), x))), b())} EDG: {(f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x))), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x)))) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x))), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), x))) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x))), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), x)) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x))), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(f(a(), f(a(), f(a(), x))), b())) (f#(f(f(a(), x), b()), b()) -> f#(x, b()), f#(f(f(a(), x), b()), b()) -> f#(a(), f(f(x, b()), b()))) (f#(f(f(a(), x), b()), b()) -> f#(x, b()), f#(f(f(a(), x), b()), b()) -> f#(f(a(), f(f(x, b()), b())), b())) (f#(f(f(a(), x), b()), b()) -> f#(x, b()), f#(f(f(a(), x), b()), b()) -> f#(f(x, b()), b())) (f#(f(f(a(), x), b()), b()) -> f#(x, b()), f#(f(f(a(), x), b()), b()) -> f#(x, b())) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(f(a(), f(a(), f(a(), x))), b()), f#(f(f(a(), x), b()), b()) -> f#(x, b())) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(f(a(), f(a(), f(a(), x))), b()), f#(f(f(a(), x), b()), b()) -> f#(f(x, b()), b())) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(f(a(), f(a(), f(a(), x))), b()), f#(f(f(a(), x), b()), b()) -> f#(f(a(), f(f(x, b()), b())), b())) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(f(a(), f(a(), f(a(), x))), b()), f#(f(f(a(), x), b()), b()) -> f#(a(), f(f(x, b()), b()))) (f#(f(f(a(), x), b()), b()) -> f#(f(x, b()), b()), f#(f(f(a(), x), b()), b()) -> f#(x, b())) (f#(f(f(a(), x), b()), b()) -> f#(f(x, b()), b()), f#(f(f(a(), x), b()), b()) -> f#(f(x, b()), b())) (f#(f(f(a(), x), b()), b()) -> f#(f(x, b()), b()), f#(f(f(a(), x), b()), b()) -> f#(f(a(), f(f(x, b()), b())), b())) (f#(f(f(a(), x), b()), b()) -> f#(f(x, b()), b()), f#(f(f(a(), x), b()), b()) -> f#(a(), f(f(x, b()), b()))) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), x)), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(f(a(), f(a(), f(a(), x))), b())) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), x)), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), x)) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), x)), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), x))) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), x)), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x)))) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), x), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(f(a(), f(a(), f(a(), x))), b())) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), x), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), x)) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), x), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), x))) (f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), x), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x))))} STATUS: arrows: 0.625000 SCCS (2): Scc: {f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), x), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), x)), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x)))} Scc: {f#(f(f(a(), x), b()), b()) -> f#(x, b()), f#(f(f(a(), x), b()), b()) -> f#(f(x, b()), b())} SCC (3): Strict: {f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), x), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), x)), f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x)))} Weak: { f(f(f(a(), x), b()), b()) -> f(f(a(), f(f(x, b()), b())), b()), f(a(), f(a(), f(a(), f(x, b())))) -> f(f(a(), f(a(), f(a(), x))), b())} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [f](x0, x1) = x0 + x1, [a] = 1, [b] = 0, [f#](x0, x1) = x0 + x1 + 1 Strict: f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x))) 4 + 1x >= 4 + 1x f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), x)) 4 + 1x >= 3 + 1x f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), x) 4 + 1x >= 2 + 1x Weak: f(a(), f(a(), f(a(), f(x, b())))) -> f(f(a(), f(a(), f(a(), x))), b()) 3 + 1x >= 3 + 1x f(f(f(a(), x), b()), b()) -> f(f(a(), f(f(x, b()), b())), b()) 1 + 1x >= 1 + 1x SCCS (1): Scc: {f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x)))} SCC (1): Strict: {f#(a(), f(a(), f(a(), f(x, b())))) -> f#(a(), f(a(), f(a(), x)))} Weak: { f(f(f(a(), x), b()), b()) -> f(f(a(), f(f(x, b()), b())), b()), f(a(), f(a(), f(a(), f(x, b())))) -> f(f(a(), f(a(), f(a(), x))), b())} Fail SCC (2): Strict: {f#(f(f(a(), x), b()), b()) -> f#(x, b()), f#(f(f(a(), x), b()), b()) -> f#(f(x, b()), b())} Weak: { f(f(f(a(), x), b()), b()) -> f(f(a(), f(f(x, b()), b())), b()), f(a(), f(a(), f(a(), f(x, b())))) -> f(f(a(), f(a(), f(a(), x))), b())} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [f](x0, x1) = x0 + x1, [a] = 1, [b] = 0, [f#](x0, x1) = x0 Strict: f#(f(f(a(), x), b()), b()) -> f#(f(x, b()), b()) 1 + 1x >= 0 + 1x f#(f(f(a(), x), b()), b()) -> f#(x, b()) 1 + 1x >= 0 + 1x Weak: f(a(), f(a(), f(a(), f(x, b())))) -> f(f(a(), f(a(), f(a(), x))), b()) 3 + 1x >= 3 + 1x f(f(f(a(), x), b()), b()) -> f(f(a(), f(f(x, b()), b())), b()) 1 + 1x >= 1 + 1x Qed