MAYBE Problem: a(a(x1)) -> b(x1) a(a(a(x1))) -> a(b(a(x1))) a(b(a(x1))) -> b(b(b(x1))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Proof: Complexity Transformation Processor: strict: a(a(x1)) -> b(x1) a(a(a(x1))) -> a(b(a(x1))) a(b(a(x1))) -> b(b(b(x1))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) weak: Matrix Interpretation Processor: dimension: 3 max_matrix: [1 1 0] [0 0 1] [0 0 0] interpretation: [1 1 0] [b](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [0] [a](x0) = [0 0 1]x0 + [0] [0 0 0] [1] orientation: [1 1 1] [0] [1 1 0] a(a(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(x1) [0 0 0] [1] [0 0 0] [1 1 1] [1] [1 1 1] [0] a(a(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(b(a(x1))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [0] [1 1 0] a(b(a(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(b(x1))) [0 0 0] [1] [0 0 0] [1 1 1] [2] [1 1 1] [1] a(a(a(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(a(a(x1))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [0] [1 1 0] [0] a(a(b(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(b(b(a(b(x1))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] a(b(a(a(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a(b(b(a(x1))))) [0 0 0] [1] [0 0 0] [1 1 1] [0] [1 1 0] a(b(b(a(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(b(b(b(x1))))) [0 0 0] [1] [0 0 0] [1 1 1] [3] [1 1 1] [3] a(a(a(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(a(b(a(a(a(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 0] [1] a(a(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(b(a(a(b(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [0] a(a(b(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(b(a(b(a(b(a(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [0] [1 1 0] [0] a(a(b(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(b(b(b(a(b(b(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [2] [1 1 1] [2] a(b(a(a(a(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a(a(b(b(a(a(x1))))))) [0 0 0] [1] [0 0 0] [0] [1 1 1] [0] [1 1 0] a(b(a(b(a(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a(b(b(b(a(b(x1))))))) [0 0 0] [1] [0 0 0] [1 1 1] [1] [1 1 1] a(b(b(a(a(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(a(b(b(b(a(x1))))))) [0 0 0] [1] [0 0 0] [1 1 1] [0] [1 1 0] a(b(b(b(a(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(b(b(b(b(b(x1))))))) [0 0 0] [1] [0 0 0] problem: strict: a(a(x1)) -> b(x1) a(b(a(x1))) -> b(b(b(x1))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) weak: a(a(a(x1))) -> a(b(a(x1))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) Matrix Interpretation Processor: dimension: 3 max_matrix: [1 1 0] [0 0 1] [0 0 0] interpretation: [1 0 0] [b](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [0] [a](x0) = [0 0 1]x0 + [0] [0 0 0] [1] orientation: [1 1 1] [0] [1 0 0] a(a(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(x1) [0 0 0] [1] [0 0 0] [1 1 0] [0] [1 0 0] a(b(a(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(b(x1))) [0 0 0] [1] [0 0 0] [1 1 0] [0] [1 0 0] [0] a(a(b(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(b(b(a(b(x1))))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 0 0] a(b(b(a(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(b(b(b(x1))))) [0 0 0] [1] [0 0 0] [1 1 1] [3] [1 1 1] [2] a(a(a(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(a(b(a(a(a(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1] [1 0 0] [0] a(a(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(b(a(a(b(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 0 0] [0] a(a(b(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(b(b(b(a(b(b(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] a(b(a(a(a(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a(a(b(b(a(a(x1))))))) [0 0 0] [1] [0 0 0] [1 1 0] [0] [1 0 0] a(b(a(b(a(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a(b(b(b(a(b(x1))))))) [0 0 0] [1] [0 0 0] [1 1 0] [0] [1 0 0] a(b(b(b(a(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(b(b(b(b(b(x1))))))) [0 0 0] [1] [0 0 0] [1 1 1] [1] [1 1 0] [0] a(a(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(b(a(x1))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [2] [1 1 1] [0] a(a(a(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(a(a(x1))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [0] [1 1 0] a(b(a(a(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(a(b(b(a(x1))))) [0 0 0] [1] [0 0 0] [1 1 1] [0] [1 1 0] [0] a(a(b(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(b(a(b(a(b(a(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [0] [1 1 0] a(b(b(a(a(x1))))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(b(a(b(b(b(a(x1))))))) [0 0 0] [1] [0 0 0] problem: strict: a(a(x1)) -> b(x1) a(b(a(x1))) -> b(b(b(x1))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) weak: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) Matrix Interpretation Processor: dimension: 3 max_matrix: [1 1 0] [0 0 1] [0 0 0] interpretation: [1 0 0] [0] [b](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [0] [a](x0) = [0 0 1]x0 + [0] [0 0 0] [1] orientation: [1 1 1] [0] [1 0 0] [0] a(a(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = b(x1) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 0 0] [0] a(b(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = b(b(b(x1))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1] [1 0 0] [0] a(a(b(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(b(a(b(x1))))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 0 0] [0] a(b(b(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = b(b(b(b(b(x1))))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1] [1 0 0] [0] a(a(b(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(b(b(a(b(b(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 0 0] [0] a(b(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = b(a(b(b(b(a(b(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 0 0] [0] a(b(b(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = b(b(b(b(b(b(b(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [3] [1 1 1] [3] a(a(a(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(a(b(a(a(a(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [2] [1 0 0] [2] a(a(a(b(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(b(a(a(b(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [1] a(b(a(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = b(a(a(b(b(a(a(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 0] [0] a(a(a(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(a(x1))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [2] [1 1 1] [1] a(a(a(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(a(b(a(a(x1))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [0] [1 1 0] [0] a(b(a(a(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = b(a(b(b(a(x1))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 0] [0] a(a(b(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(a(b(a(b(a(x1))))))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [0] [1 1 0] [0] a(b(b(a(a(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = b(b(a(b(b(b(a(x1))))))) [0 0 0] [1] [0 0 0] [1] problem: strict: a(a(x1)) -> b(x1) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) weak: a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) Open