/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: a__and(true(),X) -> mark(X) a__and(false(),Y) -> false() a__if(true(),X,Y) -> mark(X) a__if(false(),X,Y) -> mark(Y) a__add(0(),X) -> mark(X) a__add(s(X),Y) -> s(add(X,Y)) a__first(0(),X) -> nil() a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z)) a__from(X) -> cons(X,from(s(X))) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3) mark(add(X1,X2)) -> a__add(mark(X1),X2) mark(first(X1,X2)) -> a__first(mark(X1),mark(X2)) mark(from(X)) -> a__from(X) mark(true()) -> true() mark(false()) -> false() mark(0()) -> 0() mark(s(X)) -> s(X) mark(nil()) -> nil() mark(cons(X1,X2)) -> cons(X1,X2) a__and(X1,X2) -> and(X1,X2) a__if(X1,X2,X3) -> if(X1,X2,X3) a__add(X1,X2) -> add(X1,X2) a__first(X1,X2) -> first(X1,X2) a__from(X) -> from(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [a__if](x0, x1, x2) = 2x0 + 2x1 + 2x2 + 1, [and](x0, x1) = 4x0 + 2x1 + 3, [add](x0, x1) = x0 + 2x1, [a__and](x0, x1) = 4x0 + 4x1 + 3, [false] = 0, [if](x0, x1, x2) = 2x0 + 2x1 + x2 + 1, [0] = 2, [nil] = 0, [true] = 7, [s](x0) = x0, [from](x0) = x0 + 6, [first](x0, x1) = x0 + x1 + 4, [cons](x0, x1) = x0 + x1, [a__first](x0, x1) = x0 + x1 + 4, [a__from](x0) = 2x0 + 7, [a__add](x0, x1) = x0 + 3x1, [mark](x0) = 2x0 + 1 orientation: a__and(true(),X) = 4X + 31 >= 2X + 1 = mark(X) a__and(false(),Y) = 4Y + 3 >= 0 = false() a__if(true(),X,Y) = 2X + 2Y + 15 >= 2X + 1 = mark(X) a__if(false(),X,Y) = 2X + 2Y + 1 >= 2Y + 1 = mark(Y) a__add(0(),X) = 3X + 2 >= 2X + 1 = mark(X) a__add(s(X),Y) = X + 3Y >= X + 2Y = s(add(X,Y)) a__first(0(),X) = X + 6 >= 0 = nil() a__first(s(X),cons(Y,Z)) = X + Y + Z + 4 >= X + Y + Z + 4 = cons(Y,first(X,Z)) a__from(X) = 2X + 7 >= 2X + 6 = cons(X,from(s(X))) mark(and(X1,X2)) = 8X1 + 4X2 + 7 >= 8X1 + 4X2 + 7 = a__and(mark(X1),X2) mark(if(X1,X2,X3)) = 4X1 + 4X2 + 2X3 + 3 >= 4X1 + 2X2 + 2X3 + 3 = a__if(mark(X1),X2,X3) mark(add(X1,X2)) = 2X1 + 4X2 + 1 >= 2X1 + 3X2 + 1 = a__add(mark(X1),X2) mark(first(X1,X2)) = 2X1 + 2X2 + 9 >= 2X1 + 2X2 + 6 = a__first(mark(X1),mark(X2)) mark(from(X)) = 2X + 13 >= 2X + 7 = a__from(X) mark(true()) = 15 >= 7 = true() mark(false()) = 1 >= 0 = false() mark(0()) = 5 >= 2 = 0() mark(s(X)) = 2X + 1 >= X = s(X) mark(nil()) = 1 >= 0 = nil() mark(cons(X1,X2)) = 2X1 + 2X2 + 1 >= X1 + X2 = cons(X1,X2) a__and(X1,X2) = 4X1 + 4X2 + 3 >= 4X1 + 2X2 + 3 = and(X1,X2) a__if(X1,X2,X3) = 2X1 + 2X2 + 2X3 + 1 >= 2X1 + 2X2 + X3 + 1 = if(X1,X2,X3) a__add(X1,X2) = X1 + 3X2 >= X1 + 2X2 = add(X1,X2) a__first(X1,X2) = X1 + X2 + 4 >= X1 + X2 + 4 = first(X1,X2) a__from(X) = 2X + 7 >= X + 6 = from(X) problem: a__if(false(),X,Y) -> mark(Y) a__add(s(X),Y) -> s(add(X,Y)) a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3) mark(add(X1,X2)) -> a__add(mark(X1),X2) a__and(X1,X2) -> and(X1,X2) a__if(X1,X2,X3) -> if(X1,X2,X3) a__add(X1,X2) -> add(X1,X2) a__first(X1,X2) -> first(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [1 0 0] [1 1 0] [a__if](x0, x1, x2) = [0 1 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 1] [0 0 0] [0 0 0] , [1 1 0] [1 0 0] [0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [add](x0, x1) = x0 + [0 0 0]x1 [0 0 0] , [1 1 0] [1 0 0] [0] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1] [false] = [1] [0], [1 0 0] [1 0 0] [1 1 0] [if](x0, x1, x2) = [0 1 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [0 0 0] , [1 0 0] [0] [s](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 0 0] [1 0 0] [0] [first](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 1 0] [0 0 0] [0], [1 0 0] [1 1 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [1] [a__first](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 1 0] [0 0 0] [0], [1 0 1] [1 0 0] [a__add](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1 1 0] [0] [mark](x0) = [0 0 0]x0 + [1] [0 0 0] [0] orientation: [1 0 0] [1 1 0] [1] [1 1 0] [0] a__if(false(),X,Y) = [0 0 0]X + [0 0 0]Y + [1] >= [0 0 0]Y + [1] = mark(Y) [0 0 0] [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] a__add(s(X),Y) = [0 1 0]X + [0 0 0]Y + [0] >= [0 1 0]X + [0 0 0]Y + [0] = s(add(X,Y)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [1 1 0] [1] [1 0 0] [1 0 0] [1 0 0] [1] a__first(s(X),cons(Y,Z)) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [1] >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [0] = cons(Y,first(X,Z)) [0 1 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = a__and(mark(X1),X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [1 1 0] [0] [1 1 0] [1 0 0] [1 1 0] [0] mark(if(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [1] = a__if(mark(X1),X2,X3) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] [0] mark(add(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = a__add(mark(X1),X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] [0] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] [1 1 0] [1 0 0] [1 0 0] [1 1 0] a__if(X1,X2,X3) = [0 1 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 1 0]X1 + [0 0 0]X2 + [0 0 0]X3 = if(X1,X2,X3) [0 0 1] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 0] a__add(X1,X2) = [0 1 0]X1 + [0 0 0]X2 >= X1 + [0 0 0]X2 = add(X1,X2) [0 0 1] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] a__first(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = first(X1,X2) [0 1 0] [0 0 0] [0] [0 1 0] [0 0 0] [0] problem: a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3) mark(add(X1,X2)) -> a__add(mark(X1),X2) a__and(X1,X2) -> and(X1,X2) a__if(X1,X2,X3) -> if(X1,X2,X3) a__add(X1,X2) -> add(X1,X2) Matrix Interpretation Processor: dim=1 interpretation: [a__if](x0, x1, x2) = 3x0 + x1 + 2x2 + 6, [and](x0, x1) = 2x0 + 2x1 + 2, [add](x0, x1) = x0 + 2x1 + 1, [a__and](x0, x1) = 2x0 + 4x1 + 3, [if](x0, x1, x2) = 3x0 + x1 + 2x2 + 5, [s](x0) = 2x0, [first](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0 + 2x1 + 4, [a__first](x0, x1) = x0 + x1 + 2, [a__add](x0, x1) = x0 + 4x1 + 1, [mark](x0) = 2x0 + 1 orientation: a__first(s(X),cons(Y,Z)) = 2X + Y + 2Z + 6 >= 2X + Y + 2Z + 6 = cons(Y,first(X,Z)) mark(and(X1,X2)) = 4X1 + 4X2 + 5 >= 4X1 + 4X2 + 5 = a__and(mark(X1),X2) mark(if(X1,X2,X3)) = 6X1 + 2X2 + 4X3 + 11 >= 6X1 + X2 + 2X3 + 9 = a__if(mark(X1),X2,X3) mark(add(X1,X2)) = 2X1 + 4X2 + 3 >= 2X1 + 4X2 + 2 = a__add(mark(X1),X2) a__and(X1,X2) = 2X1 + 4X2 + 3 >= 2X1 + 2X2 + 2 = and(X1,X2) a__if(X1,X2,X3) = 3X1 + X2 + 2X3 + 6 >= 3X1 + X2 + 2X3 + 5 = if(X1,X2,X3) a__add(X1,X2) = X1 + 4X2 + 1 >= X1 + 2X2 + 1 = add(X1,X2) problem: a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z)) mark(and(X1,X2)) -> a__and(mark(X1),X2) a__add(X1,X2) -> add(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [1] [and](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [0] [0 0 1] [0 1 0] [0], [1 0 0] [1 0 0] [add](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [1] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 1] [0 0 0] [0], [1 0 1] [0] [s](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 0] [1 0 0] [0] [first](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 1 0] [1], [1 0 0] [1 1 0] [cons](x0, x1) = [0 0 1]x0 + [0 0 1]x1 [0 0 0] [0 0 1] , [1 1 0] [1 0 0] [0] [a__first](x0, x1) = [1 0 0]x0 + [1 1 0]x1 + [1] [0 0 0] [1 1 0] [1], [1 0 0] [1 0 0] [0] [a__add](x0, x1) = [0 0 0]x0 + [1 0 1]x1 + [0] [0 0 0] [0 0 0] [1], [1 0 1] [0] [mark](x0) = [0 1 1]x0 + [1] [0 0 0] [1] orientation: [1 1 1] [1 0 0] [1 1 0] [1] [1 1 0] [1 0 0] [1 0 0] [0] a__first(s(X),cons(Y,Z)) = [1 0 1]X + [1 0 1]Y + [1 1 1]Z + [1] >= [0 0 0]X + [0 0 1]Y + [0 1 0]Z + [1] = cons(Y,first(X,Z)) [0 0 0] [1 0 1] [1 1 1] [1] [0 0 0] [0 0 0] [0 1 0] [1] [1 0 1] [1 1 0] [1] [1 0 1] [1 0 0] [1] mark(and(X1,X2)) = [0 0 1]X1 + [0 1 1]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = a__and(mark(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] a__add(X1,X2) = [0 0 0]X1 + [1 0 1]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] problem: mark(and(X1,X2)) -> a__and(mark(X1),X2) a__add(X1,X2) -> add(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [1] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 0 0] [1 0 0] [add](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [a__add](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = a__and(mark(X1),X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__add(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] problem: a__add(X1,X2) -> add(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [add](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [1] [a__add](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 1] [0] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] a__add(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 0 1] [0] [0 0 0] [0 0 0] problem: Qed