/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /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: [0] = 0, [foldC](x0, x1) = x0 + 2x1, [g](x0) = x0, [C] = 4, [foldB](x0, x1) = x0 + 2x1, [triple](x0, x1, x2) = x0 + 2x1 + 2x2 + 5, [A] = 2, [f](x0, x1) = x0 + 2x1, [f''](x0) = x0, [f'](x0, x1) = x0 + 2x1, [s](x0) = x0 + 4, [B] = 4 orientation: g(A()) = 2 >= 2 = A() g(B()) = 4 >= 2 = A() g(B()) = 4 >= 4 = B() g(C()) = 4 >= 2 = A() g(C()) = 4 >= 4 = B() g(C()) = 4 >= 4 = C() foldB(t,0()) = t >= t = t foldB(t,s(n)) = 2n + t + 8 >= 2n + t + 8 = f(foldB(t,n),B()) foldC(t,0()) = t >= t = t foldC(t,s(n)) = 2n + t + 8 >= 2n + t + 8 = f(foldC(t,n),C()) f(t,x) = t + 2x >= t + 2x = f'(t,g(x)) f'(triple(a,b,c),C()) = a + 2b + 2c + 13 >= a + 2b + 2c + 13 = triple(a,b,s(c)) f'(triple(a,b,c),B()) = a + 2b + 2c + 13 >= a + 2b + 2c + 9 = f(triple(a,b,c),A()) f'(triple(a,b,c),A()) = a + 2b + 2c + 9 >= a + 2b + 2c + 9 = f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) = a + 2b + 2c + 5 >= a + 2b + 2c + 5 = foldC(triple(a,b,0()),c) problem: g(A()) -> A() g(B()) -> B() 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),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: [0] [0] = [0] [0], [1 0 1] [1 0 1] [foldC](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 1] [0 1 0] , [1 0 1] [0] [g](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [0] [C] = [1] [0], [1 0 1] [foldB](x0, x1) = x0 + [0 1 0]x1 [0 0 0] , [1 0 0] [1 1 1] [1 0 1] [0] [triple](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 + [1] [0 0 0] [0 0 0] [0 1 0] [1], [0] [A] = [1] [1], [1 0 1] [1] [f](x0, x1) = x0 + [0 0 0]x1 + [0] [1 0 1] [0], [1 1 0] [0] [f''](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [1 1 0] [f'](x0, x1) = x0 + [0 0 0]x1 [1 0 0] , [0] [s](x0) = x0 + [0] [1], [0] [B] = [0] [0] orientation: [1] [0] g(A()) = [1] >= [1] = A() [1] [1] [0] [0] g(B()) = [1] >= [0] = B() [0] [0] [0] [0] g(C()) = [1] >= [0] = B() [0] [0] [0] [0] g(C()) = [1] >= [1] = C() [0] [0] foldB(t,0()) = t >= t = t [1 0 1] [1] [1 0 1] [1] foldB(t,s(n)) = [0 1 0]n + t + [0] >= [0 1 0]n + t + [0] = f(foldB(t,n),B()) [0 0 0] [0] [0 0 0] [0] [1 0 1] foldC(t,0()) = [0 1 0]t >= t = t [0 0 1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] foldC(t,s(n)) = [0 0 0]n + [0 1 0]t + [0] >= [0 0 0]n + [0 1 0]t + [0] = f(foldC(t,n),C()) [0 1 0] [0 0 1] [0] [0 1 0] [0 0 1] [0] [1 0 1] [1] [1 0 1] [1] f(t,x) = t + [0 0 0]x + [0] >= t + [0 0 0]x + [0] = f'(t,g(x)) [1 0 1] [0] [1 0 1] [0] [1 0 0] [1 1 1] [1 0 1] [1] [1 0 0] [1 1 1] [1 0 1] [1] f'(triple(a,b,c),C()) = [0 0 0]a + [0 0 0]b + [0 0 0]c + [1] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [1] = triple(a,b,s(c)) [0 0 0] [0 0 0] [0 1 0] [1] [0 0 0] [0 0 0] [0 1 0] [1] [1 0 0] [1 1 1] [1 0 1] [1] [1 0 0] [1 1 1] [1 0 1] [1] f'(triple(a,b,c),A()) = [0 0 0]a + [0 0 0]b + [0 0 0]c + [1] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [1] = f''(foldB(triple(s(a),0(),c),b)) [0 0 0] [0 0 0] [0 1 0] [1] [0 0 0] [0 0 0] [0 1 0] [1] [1 0 0] [1 1 1] [1 0 1] [1] [1 0 0] [1 1 1] [1 0 1] [1] f''(triple(a,b,c)) = [0 0 0]a + [0 0 0]b + [0 0 0]c + [1] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [1] = foldC(triple(a,b,0()),c) [0 0 0] [0 0 0] [0 1 0] [1] [0 0 0] [0 0 0] [0 1 0] [1] problem: g(B()) -> B() 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),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: [0] = 0, [foldC](x0, x1) = x0 + x1 + 1, [g](x0) = x0, [C] = 0, [foldB](x0, x1) = x0 + x1 + 3, [triple](x0, x1, x2) = x0 + x1 + x2, [A] = 4, [f](x0, x1) = x0 + x1 + 3, [f''](x0) = x0 + 1, [f'](x0, x1) = x0 + x1 + 3, [s](x0) = x0 + 3, [B] = 0 orientation: g(B()) = 0 >= 0 = B() g(C()) = 0 >= 0 = B() g(C()) = 0 >= 0 = C() foldB(t,0()) = t + 3 >= t = t foldB(t,s(n)) = n + t + 6 >= n + t + 6 = f(foldB(t,n),B()) foldC(t,0()) = t + 1 >= t = t foldC(t,s(n)) = n + t + 4 >= n + t + 4 = f(foldC(t,n),C()) f(t,x) = t + x + 3 >= t + x + 3 = f'(t,g(x)) f'(triple(a,b,c),C()) = a + b + c + 3 >= a + b + c + 3 = triple(a,b,s(c)) f'(triple(a,b,c),A()) = a + b + c + 7 >= a + b + c + 7 = f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) = a + b + c + 1 >= a + b + c + 1 = foldC(triple(a,b,0()),c) problem: g(B()) -> B() g(C()) -> B() g(C()) -> C() foldB(t,s(n)) -> f(foldB(t,n),B()) 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),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: [0] = 0, [foldC](x0, x1) = x0 + x1, [g](x0) = x0, [C] = 0, [foldB](x0, x1) = x0 + x1 + 4, [triple](x0, x1, x2) = x0 + x1 + x2 + 2, [A] = 5, [f](x0, x1) = x0 + x1, [f''](x0) = x0 + 1, [f'](x0, x1) = x0 + x1, [s](x0) = x0, [B] = 0 orientation: g(B()) = 0 >= 0 = B() g(C()) = 0 >= 0 = B() g(C()) = 0 >= 0 = C() foldB(t,s(n)) = n + t + 4 >= n + t + 4 = f(foldB(t,n),B()) foldC(t,s(n)) = n + t >= n + t = f(foldC(t,n),C()) f(t,x) = t + x >= t + x = f'(t,g(x)) f'(triple(a,b,c),C()) = a + b + c + 2 >= a + b + c + 2 = triple(a,b,s(c)) f'(triple(a,b,c),A()) = a + b + c + 7 >= a + b + c + 7 = f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) = a + b + c + 3 >= a + b + c + 2 = foldC(triple(a,b,0()),c) problem: g(B()) -> B() g(C()) -> B() g(C()) -> C() foldB(t,s(n)) -> f(foldB(t,n),B()) 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),A()) -> f''(foldB(triple(s(a),0(),c),b)) Matrix Interpretation Processor: dim=1 interpretation: [0] = 1, [foldC](x0, x1) = x0 + 6x1 + 6, [g](x0) = x0, [C] = 4, [foldB](x0, x1) = x0 + 2x1, [triple](x0, x1, x2) = x0 + 7x1 + 2x2 + 1, [A] = 4, [f](x0, x1) = x0 + 3x1, [f''](x0) = x0 + 1, [f'](x0, x1) = x0 + 3x1, [s](x0) = x0 + 4, [B] = 0 orientation: g(B()) = 0 >= 0 = B() g(C()) = 4 >= 0 = B() g(C()) = 4 >= 4 = C() foldB(t,s(n)) = 2n + t + 8 >= 2n + t = f(foldB(t,n),B()) foldC(t,s(n)) = 6n + t + 30 >= 6n + t + 18 = f(foldC(t,n),C()) f(t,x) = t + 3x >= t + 3x = f'(t,g(x)) f'(triple(a,b,c),C()) = a + 7b + 2c + 13 >= a + 7b + 2c + 9 = triple(a,b,s(c)) f'(triple(a,b,c),A()) = a + 7b + 2c + 13 >= a + 2b + 2c + 13 = f''(foldB(triple(s(a),0(),c),b)) problem: g(B()) -> B() g(C()) -> C() f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) Matrix Interpretation Processor: dim=1 interpretation: [0] = 0, [g](x0) = x0, [C] = 0, [foldB](x0, x1) = 7x0 + x1, [triple](x0, x1, x2) = 4x0 + x1 + 2x2 + 4, [A] = 0, [f](x0, x1) = 7x0 + x1 + 1, [f''](x0) = x0, [f'](x0, x1) = 7x0 + x1, [s](x0) = x0, [B] = 0 orientation: g(B()) = 0 >= 0 = B() g(C()) = 0 >= 0 = C() f(t,x) = 7t + x + 1 >= 7t + x = f'(t,g(x)) f'(triple(a,b,c),A()) = 28a + 7b + 14c + 28 >= 28a + b + 14c + 28 = f''(foldB(triple(s(a),0(),c),b)) problem: g(B()) -> B() g(C()) -> C() f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) Matrix Interpretation Processor: dim=1 interpretation: [0] = 5, [g](x0) = x0, [C] = 0, [foldB](x0, x1) = x0 + x1, [triple](x0, x1, x2) = x0 + x1 + x2 + 7, [A] = 7, [f''](x0) = x0, [f'](x0, x1) = x0 + x1 + 3, [s](x0) = x0 + 4, [B] = 0 orientation: g(B()) = 0 >= 0 = B() g(C()) = 0 >= 0 = C() f'(triple(a,b,c),A()) = a + b + c + 17 >= a + b + c + 16 = f''(foldB(triple(s(a),0(),c),b)) problem: g(B()) -> B() g(C()) -> C() Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1] [g](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [C] = [0] [0], [0] [B] = [0] [0] orientation: [1] [0] g(B()) = [0] >= [0] = B() [0] [0] [1] [0] g(C()) = [0] >= [0] = C() [0] [0] problem: Qed