/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: a__f(X) -> a__if(mark(X),c(),f(true())) a__if(true(),X,Y) -> mark(X) a__if(false(),X,Y) -> mark(Y) mark(f(X)) -> a__f(mark(X)) mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3) mark(c()) -> c() mark(true()) -> true() mark(false()) -> false() a__f(X) -> f(X) a__if(X1,X2,X3) -> if(X1,X2,X3) Proof: Matrix Interpretation Processor: dim=1 interpretation: [if](x0, x1, x2) = x0 + 4x1 + x2, [false] = 0, [a__if](x0, x1, x2) = x0 + 4x1 + 4x2, [f](x0) = 4x0 + 1, [true] = 0, [c] = 0, [mark](x0) = 4x0, [a__f](x0) = 4x0 + 4 orientation: a__f(X) = 4X + 4 >= 4X + 4 = a__if(mark(X),c(),f(true())) a__if(true(),X,Y) = 4X + 4Y >= 4X = mark(X) a__if(false(),X,Y) = 4X + 4Y >= 4Y = mark(Y) mark(f(X)) = 16X + 4 >= 16X + 4 = a__f(mark(X)) mark(if(X1,X2,X3)) = 4X1 + 16X2 + 4X3 >= 4X1 + 16X2 + 4X3 = a__if(mark(X1),mark(X2),X3) mark(c()) = 0 >= 0 = c() mark(true()) = 0 >= 0 = true() mark(false()) = 0 >= 0 = false() a__f(X) = 4X + 4 >= 4X + 1 = f(X) a__if(X1,X2,X3) = X1 + 4X2 + 4X3 >= X1 + 4X2 + X3 = if(X1,X2,X3) problem: a__f(X) -> a__if(mark(X),c(),f(true())) a__if(true(),X,Y) -> mark(X) a__if(false(),X,Y) -> mark(Y) mark(f(X)) -> a__f(mark(X)) mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3) mark(c()) -> c() mark(true()) -> true() mark(false()) -> false() a__if(X1,X2,X3) -> if(X1,X2,X3) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [1 1 0] [1 1 1] [if](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 1] [0 0 1] [0 0 0] , [1] [false] = [0] [0], [1 1 0] [1 1 1] [1 1 1] [a__if](x0, x1, x2) = [0 0 1]x0 + [0 1 1]x1 + [0 0 0]x2 [0 0 1] [0 0 1] [0 0 0] , [1 0 1] [1] [f](x0) = [0 0 0]x0 + [0] [0 1 0] [0], [0] [true] = [0] [0], [0] [c] = [0] [0], [1 0 1] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 1 1] [1] [a__f](x0) = [0 0 0]x0 + [0] [0 1 1] [0] orientation: [1 1 1] [1] [1 0 1] [1] a__f(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__if(mark(X),c(),f(true())) [0 1 1] [0] [0 0 0] [0] [1 1 1] [1 1 1] [1 0 1] a__if(true(),X,Y) = [0 1 1]X + [0 0 0]Y >= [0 0 0]X = mark(X) [0 0 1] [0 0 0] [0 0 0] [1 1 1] [1 1 1] [1] [1 0 1] a__if(false(),X,Y) = [0 1 1]X + [0 0 0]Y + [0] >= [0 0 0]Y = mark(Y) [0 0 1] [0 0 0] [0] [0 0 0] [1 1 1] [1] [1 0 1] [1] mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__f(mark(X)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1 1 1] [1 1 1] [1 0 1] [1 0 1] [1 1 1] mark(if(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = a__if(mark(X1),mark(X2),X3) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] mark(c()) = [0] >= [0] = c() [0] [0] [0] [0] mark(true()) = [0] >= [0] = true() [0] [0] [1] [1] mark(false()) = [0] >= [0] = false() [0] [0] [1 1 0] [1 1 1] [1 1 1] [1 1 0] [1 1 0] [1 1 1] a__if(X1,X2,X3) = [0 0 1]X1 + [0 1 1]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = if(X1,X2,X3) [0 0 1] [0 0 1] [0 0 0] [0 0 1] [0 0 1] [0 0 0] problem: a__f(X) -> a__if(mark(X),c(),f(true())) a__if(true(),X,Y) -> mark(X) mark(f(X)) -> a__f(mark(X)) mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3) mark(c()) -> c() mark(true()) -> true() mark(false()) -> false() a__if(X1,X2,X3) -> if(X1,X2,X3) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 1 1] [1 0 0] [0] [if](x0, x1, x2) = [0 0 0]x0 + [0 1 0]x1 + [0 0 0]x2 + [1] [0 0 1] [0 0 0] [0 0 0] [0], [1] [false] = [0] [0], [1 0 0] [1 1 1] [1 0 0] [0] [a__if](x0, x1, x2) = [0 0 0]x0 + [0 1 0]x1 + [0 0 0]x2 + [1] [0 0 1] [0 0 0] [0 0 0] [0], [1 0 0] [0] [f](x0) = [0 0 0]x0 + [1] [0 0 1] [1], [0] [true] = [0] [0], [0] [c] = [0] [0], [1 0 1] [mark](x0) = [0 1 0]x0 [0 0 0] , [1 0 1] [1] [a__f](x0) = [0 0 0]x0 + [1] [0 0 1] [0] orientation: [1 0 1] [1] [1 0 1] [0] a__f(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__if(mark(X),c(),f(true())) [0 0 1] [0] [0 0 0] [0] [1 1 1] [1 0 0] [0] [1 0 1] a__if(true(),X,Y) = [0 1 0]X + [0 0 0]Y + [1] >= [0 1 0]X = mark(X) [0 0 0] [0 0 0] [0] [0 0 0] [1 0 1] [1] [1 0 1] [1] mark(f(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__f(mark(X)) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 1 1] [1 0 0] [0] [1 0 1] [1 1 1] [1 0 0] [0] mark(if(X1,X2,X3)) = [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 + [1] >= [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 + [1] = a__if(mark(X1),mark(X2),X3) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [0] [0] mark(c()) = [0] >= [0] = c() [0] [0] [0] [0] mark(true()) = [0] >= [0] = true() [0] [0] [1] [1] mark(false()) = [0] >= [0] = false() [0] [0] [1 0 0] [1 1 1] [1 0 0] [0] [1 0 0] [1 1 1] [1 0 0] [0] a__if(X1,X2,X3) = [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 + [1] >= [0 0 0]X1 + [0 1 0]X2 + [0 0 0]X3 + [1] = if(X1,X2,X3) [0 0 1] [0 0 0] [0 0 0] [0] [0 0 1] [0 0 0] [0 0 0] [0] problem: a__if(true(),X,Y) -> mark(X) mark(f(X)) -> a__f(mark(X)) mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3) mark(c()) -> c() mark(true()) -> true() mark(false()) -> false() a__if(X1,X2,X3) -> if(X1,X2,X3) Matrix Interpretation Processor: dim=1 interpretation: [if](x0, x1, x2) = x0 + 2x1 + 2x2 + 4, [false] = 2, [a__if](x0, x1, x2) = x0 + 2x1 + 4x2 + 4, [f](x0) = x0, [true] = 4, [c] = 0, [mark](x0) = 2x0 + 2, [a__f](x0) = x0 orientation: a__if(true(),X,Y) = 2X + 4Y + 8 >= 2X + 2 = mark(X) mark(f(X)) = 2X + 2 >= 2X + 2 = a__f(mark(X)) mark(if(X1,X2,X3)) = 2X1 + 4X2 + 4X3 + 10 >= 2X1 + 4X2 + 4X3 + 10 = a__if(mark(X1),mark(X2),X3) mark(c()) = 2 >= 0 = c() mark(true()) = 10 >= 4 = true() mark(false()) = 6 >= 2 = false() a__if(X1,X2,X3) = X1 + 2X2 + 4X3 + 4 >= X1 + 2X2 + 2X3 + 4 = if(X1,X2,X3) problem: mark(f(X)) -> a__f(mark(X)) mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3) a__if(X1,X2,X3) -> if(X1,X2,X3) Matrix Interpretation Processor: dim=1 interpretation: [if](x0, x1, x2) = 5x0 + 3x1 + 2x2 + 4, [a__if](x0, x1, x2) = 5x0 + 3x1 + 6x2 + 5, [f](x0) = 6x0 + 4, [mark](x0) = 3x0 + 1, [a__f](x0) = 6x0 + 7 orientation: mark(f(X)) = 18X + 13 >= 18X + 13 = a__f(mark(X)) mark(if(X1,X2,X3)) = 15X1 + 9X2 + 6X3 + 13 >= 15X1 + 9X2 + 6X3 + 13 = a__if(mark(X1),mark(X2),X3) a__if(X1,X2,X3) = 5X1 + 3X2 + 6X3 + 5 >= 5X1 + 3X2 + 2X3 + 4 = if(X1,X2,X3) problem: mark(f(X)) -> a__f(mark(X)) mark(if(X1,X2,X3)) -> a__if(mark(X1),mark(X2),X3) Matrix Interpretation Processor: dim=1 interpretation: [if](x0, x1, x2) = x0 + x1 + x2 + 1, [a__if](x0, x1, x2) = x0 + x1 + x2, [f](x0) = 2x0 + 2, [mark](x0) = x0, [a__f](x0) = 2x0 + 2 orientation: mark(f(X)) = 2X + 2 >= 2X + 2 = a__f(mark(X)) mark(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 = a__if(mark(X1),mark(X2),X3) problem: mark(f(X)) -> a__f(mark(X)) Matrix Interpretation Processor: dim=1 interpretation: [f](x0) = x0 + 2, [mark](x0) = x0 + 1, [a__f](x0) = x0 + 1 orientation: mark(f(X)) = X + 3 >= X + 2 = a__f(mark(X)) problem: Qed