/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: g(A()) -> A() g(B()) -> A() g(B()) -> B() g(C()) -> A() g(C()) -> B() g(C()) -> C() foldB(t,0()) -> t foldB(t,s(n)) -> f(foldB(t,n),B()) foldC(t,0()) -> t foldC(t,s(n)) -> f(foldC(t,n),C()) f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f'(triple(a,b,c),B()) -> f(triple(a,b,c),A()) f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Proof: Matrix Interpretation Processor: dim=1 interpretation: [f''](x0) = x0, [triple](x0, x1, x2) = x0 + 2x1 + x2, [f'](x0, x1) = x0 + x1 + 2, [foldC](x0, x1) = x0 + x1, [f](x0, x1) = x0 + 4x1 + 2, [s](x0) = x0 + 2, [foldB](x0, x1) = x0 + 2x1, [0] = 0, [C] = 0, [B] = 0, [g](x0) = 4x0, [A] = 0 orientation: g(A()) = 0 >= 0 = A() g(B()) = 0 >= 0 = A() g(B()) = 0 >= 0 = B() g(C()) = 0 >= 0 = A() g(C()) = 0 >= 0 = B() g(C()) = 0 >= 0 = C() foldB(t,0()) = t >= t = t foldB(t,s(n)) = 2n + t + 4 >= 2n + t + 2 = f(foldB(t,n),B()) foldC(t,0()) = t >= t = t foldC(t,s(n)) = n + t + 2 >= n + t + 2 = f(foldC(t,n),C()) f(t,x) = t + 4x + 2 >= t + 4x + 2 = f'(t,g(x)) f'(triple(a,b,c),C()) = a + 2b + c + 2 >= a + 2b + c + 2 = triple(a,b,s(c)) f'(triple(a,b,c),B()) = a + 2b + c + 2 >= a + 2b + c + 2 = f(triple(a,b,c),A()) f'(triple(a,b,c),A()) = a + 2b + c + 2 >= a + 2b + c + 2 = f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) = a + 2b + c >= a + 2b + c = foldC(triple(a,b,0()),c) problem: g(A()) -> A() g(B()) -> A() g(B()) -> B() g(C()) -> A() g(C()) -> B() g(C()) -> C() foldB(t,0()) -> t foldC(t,0()) -> t foldC(t,s(n)) -> f(foldC(t,n),C()) f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f'(triple(a,b,c),B()) -> f(triple(a,b,c),A()) f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [f''](x0) = [0 0 0]x0 [1 0 0] , [1 0 1] [1 0 1] [1 0 0] [triple](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [f'](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [0 0 0] , [1 0 0] [1 0 0] [foldC](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [1 0 1] [1 0 0] , [1 0 0] [1 1 0] [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [0 0 0] , [1 0 0] [s](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [foldB](x0, x1) = x0 + [0 0 0]x1 [0 0 0] , [0] [0] = [0] [0], [0] [C] = [0] [0], [0] [B] = [1] [0], [1 1 0] [0] [g](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [0] [A] = [0] [0] orientation: [0] [0] g(A()) = [1] >= [0] = A() [1] [0] [1] [0] g(B()) = [1] >= [0] = A() [1] [0] [1] [0] g(B()) = [1] >= [1] = B() [1] [0] [0] [0] g(C()) = [1] >= [0] = A() [1] [0] [0] [0] g(C()) = [1] >= [1] = B() [1] [0] [0] [0] g(C()) = [1] >= [0] = C() [1] [0] foldB(t,0()) = t >= t = t [1 0 0] foldC(t,0()) = [0 1 0]t >= t = t [1 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] foldC(t,s(n)) = [0 0 0]n + [0 1 0]t >= [0 0 0]n + [0 0 0]t = f(foldC(t,n),C()) [1 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] f(t,x) = [0 0 0]t + [0 0 0]x >= [0 0 0]t + [0 0 0]x = f'(t,g(x)) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 1] [1 0 0] f'(triple(a,b,c),C()) = [0 0 0]a + [0 0 0]b + [0 0 0]c >= [0 0 0]a + [0 0 0]b + [0 0 0]c = triple(a,b,s(c)) [1 0 1] [1 0 1] [1 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 1] [1 0 0] f'(triple(a,b,c),B()) = [0 0 0]a + [0 0 0]b + [0 0 0]c >= [0 0 0]a + [0 0 0]b + [0 0 0]c = f(triple(a,b,c),A()) [1 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] [1 0 0] f'(triple(a,b,c),A()) = [0 0 0]a + [0 0 0]b + [0 0 0]c >= [0 0 0]a + [0 0 0]b + [0 0 0]c = f''(foldB(triple(s(a),0(),c),b)) [1 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 1] [1 0 0] f''(triple(a,b,c)) = [0 0 0]a + [0 0 0]b + [0 0 0]c >= [0 0 0]a + [0 0 0]b + [0 0 0]c = foldC(triple(a,b,0()),c) [1 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 1] [1 0 0] problem: g(A()) -> A() g(C()) -> A() g(C()) -> B() g(C()) -> C() foldB(t,0()) -> t foldC(t,0()) -> t foldC(t,s(n)) -> f(foldC(t,n),C()) f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f'(triple(a,b,c),B()) -> f(triple(a,b,c),A()) f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [f''](x0) = [0 0 1]x0 [0 0 1] , [1 0 0] [1 0 1] [1 1 1] [triple](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 1] [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [f'](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1 0 0] [1 1 0] [foldC](x0, x1) = [0 1 1]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1 0 0] [1 0 1] [f](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 0 1] [0 1 0] , [1 0 0] [0] [s](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 1] [foldB](x0, x1) = x0 + [0 0 0]x1 [0 0 0] , [0] [0] = [0] [0], [1] [C] = [0] [0], [1] [B] = [0] [0], [1 0 1] [0] [g](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [A] = [0] [1] orientation: [1] [0] g(A()) = [0] >= [0] = A() [1] [1] [1] [0] g(C()) = [0] >= [0] = A() [1] [1] [1] [1] g(C()) = [0] >= [0] = B() [1] [0] [1] [1] g(C()) = [0] >= [0] = C() [1] [0] foldB(t,0()) = t >= t = t [1 0 0] foldC(t,0()) = [0 1 1]t >= t = t [0 0 1] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] foldC(t,s(n)) = [0 0 0]n + [0 1 1]t + [0] >= [0 0 0]n + [0 0 1]t + [0] = f(foldC(t,n),C()) [0 0 0] [0 0 1] [0] [0 0 0] [0 0 1] [0] [1 0 0] [1 0 1] [1 0 0] [1 0 1] f(t,x) = [0 0 1]t + [0 0 0]x >= [0 0 1]t + [0 0 0]x = f'(t,g(x)) [0 0 1] [0 1 0] [0 0 1] [0 0 0] [1 0 0] [1 0 1] [1 1 1] [1] [1 0 0] [1 0 1] [1 1 0] [1] f'(triple(a,b,c),C()) = [0 0 1]a + [0 0 0]b + [0 0 0]c + [0] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [0] = triple(a,b,s(c)) [0 0 1] [0 0 0] [0 0 0] [0] [0 0 1] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 1] [1 1 1] [1] [1 0 0] [1 0 1] [1 1 1] [1] f'(triple(a,b,c),B()) = [0 0 1]a + [0 0 0]b + [0 0 0]c + [0] >= [0 0 1]a + [0 0 0]b + [0 0 0]c + [0] = f(triple(a,b,c),A()) [0 0 1] [0 0 0] [0 0 0] [0] [0 0 1] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 1] [1 1 1] [1 0 0] [1 0 1] [1 1 1] f'(triple(a,b,c),A()) = [0 0 1]a + [0 0 0]b + [0 0 0]c >= [0 0 0]a + [0 0 0]b + [0 0 0]c = f''(foldB(triple(s(a),0(),c),b)) [0 0 1] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 1 1] [1 0 0] [1 0 1] [1 1 0] f''(triple(a,b,c)) = [0 0 1]a + [0 0 0]b + [0 0 0]c >= [0 0 1]a + [0 0 0]b + [0 0 0]c = foldC(triple(a,b,0()),c) [0 0 1] [0 0 0] [0 0 0] [0 0 1] [0 0 0] [0 0 0] problem: g(C()) -> B() g(C()) -> C() foldB(t,0()) -> t foldC(t,0()) -> t foldC(t,s(n)) -> f(foldC(t,n),C()) f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f'(triple(a,b,c),B()) -> f(triple(a,b,c),A()) f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Matrix Interpretation Processor: dim=1 interpretation: [f''](x0) = x0 + 7, [triple](x0, x1, x2) = 2x0 + 4x1 + 7x2 + 1, [f'](x0, x1) = x0 + 4x1 + 4, [foldC](x0, x1) = x0 + 7x1, [f](x0, x1) = x0 + 4x1 + 4, [s](x0) = x0 + 4, [foldB](x0, x1) = x0 + 4x1 + 1, [0] = 1, [C] = 6, [B] = 6, [g](x0) = x0, [A] = 5 orientation: g(C()) = 6 >= 6 = B() g(C()) = 6 >= 6 = C() foldB(t,0()) = t + 5 >= t = t foldC(t,0()) = t + 7 >= t = t foldC(t,s(n)) = 7n + t + 28 >= 7n + t + 28 = f(foldC(t,n),C()) f(t,x) = t + 4x + 4 >= t + 4x + 4 = f'(t,g(x)) f'(triple(a,b,c),C()) = 2a + 4b + 7c + 29 >= 2a + 4b + 7c + 29 = triple(a,b,s(c)) f'(triple(a,b,c),B()) = 2a + 4b + 7c + 29 >= 2a + 4b + 7c + 25 = f(triple(a,b,c),A()) f'(triple(a,b,c),A()) = 2a + 4b + 7c + 25 >= 2a + 4b + 7c + 21 = f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) = 2a + 4b + 7c + 8 >= 2a + 4b + 7c + 8 = foldC(triple(a,b,0()),c) problem: g(C()) -> B() g(C()) -> C() foldC(t,s(n)) -> f(foldC(t,n),C()) f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Matrix Interpretation Processor: dim=1 interpretation: [f''](x0) = 4x0 + 4, [triple](x0, x1, x2) = 4x0 + 2x1 + x2 + 1, [f'](x0, x1) = x0 + x1 + 4, [foldC](x0, x1) = x0 + 4x1, [f](x0, x1) = x0 + x1 + 6, [s](x0) = x0 + 4, [0] = 5, [C] = 0, [B] = 0, [g](x0) = x0 + 1 orientation: g(C()) = 1 >= 0 = B() g(C()) = 1 >= 0 = C() foldC(t,s(n)) = 4n + t + 16 >= 4n + t + 6 = f(foldC(t,n),C()) f(t,x) = t + x + 6 >= t + x + 5 = f'(t,g(x)) f'(triple(a,b,c),C()) = 4a + 2b + c + 5 >= 4a + 2b + c + 5 = triple(a,b,s(c)) f''(triple(a,b,c)) = 16a + 8b + 4c + 8 >= 4a + 2b + 4c + 6 = foldC(triple(a,b,0()),c) problem: f'(triple(a,b,c),C()) -> triple(a,b,s(c)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [1 0 0] [triple](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [0 0 0] , [1 0 0] [1 1 0] [f'](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [0] [C] = [1] [0] orientation: [1 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1 0 0] f'(triple(a,b,c),C()) = [0 0 0]a + [0 0 0]b + [0 0 0]c + [0] >= [0 0 0]a + [0 0 0]b + [0 0 0]c = triple(a,b,s(c)) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] problem: Qed