YES(?,O(n^1)) Problem: f(x,x) -> f(a(),b()) b() -> c() Proof: RT Transformation Processor: strict: f(x,x) -> f(a(),b()) b() -> c() weak: Matrix Interpretation Processor: dimension: 1 interpretation: [c] = 0, [b] = 13, [a] = 16, [f](x0, x1) = x0 + x1 + 20 orientation: f(x,x) = 2x + 20 >= 49 = f(a(),b()) b() = 13 >= 0 = c() problem: strict: f(x,x) -> f(a(),b()) weak: b() -> c() Bounds Processor: bound: 1 enrichment: match-rt automaton: final states: {13,9,8,5} transitions: f0(13,5) -> 5* f0(8,5) -> 5* f0(13,9) -> 5* f0(8,9) -> 5* f0(13,13) -> 5* f0(8,13) -> 5* f0(9,8) -> 5* f0(5,5) -> 5* f0(5,9) -> 5* f0(5,13) -> 5* f0(13,8) -> 5* f0(8,8) -> 5* f0(9,5) -> 5* f0(9,9) -> 5* f0(9,13) -> 5* f0(5,8) -> 5* a0() -> 5* b0() -> 5* c0() -> 5* f1(8,9) -> 5* f1(8,13) -> 5* f1(7,9) -> 5* f1(7,13) -> 5* f1(8,6) -> 5* f1(7,6) -> 5* a1() -> 8*,5,7 b1() -> 9*,5,6 c1() -> 13*,5,10 10 -> 9* problem: strict: weak: f(x,x) -> f(a(),b()) b() -> c() Qed