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