/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /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: [if](x0, x1, x2) = x0 + 2x1 + 2x2 + 4, [and](x0, x1) = 2x0 + 3x1, [from](x0) = 4x0 + 2, [a__from](x0) = 6x0 + 3, [first](x0, x1) = x0 + x1, [cons](x0, x1) = x0 + x1 + 1, [nil] = 2, [a__first](x0, x1) = x0 + x1, [add](x0, x1) = x0 + x1, [s](x0) = x0, [a__add](x0, x1) = x0 + 2x1, [0] = 4, [a__if](x0, x1, x2) = x0 + 2x1 + 2x2 + 4, [false] = 2, [mark](x0) = 2x0, [a__and](x0, x1) = 2x0 + 3x1, [true] = 4 orientation: a__and(true(),X) = 3X + 8 >= 2X = mark(X) a__and(false(),Y) = 3Y + 4 >= 2 = false() a__if(true(),X,Y) = 2X + 2Y + 8 >= 2X = mark(X) a__if(false(),X,Y) = 2X + 2Y + 6 >= 2Y = mark(Y) a__add(0(),X) = 2X + 4 >= 2X = mark(X) a__add(s(X),Y) = X + 2Y >= X + Y = s(add(X,Y)) a__first(0(),X) = X + 4 >= 2 = nil() a__first(s(X),cons(Y,Z)) = X + Y + Z + 1 >= X + Y + Z + 1 = cons(Y,first(X,Z)) a__from(X) = 6X + 3 >= 5X + 3 = cons(X,from(s(X))) mark(and(X1,X2)) = 4X1 + 6X2 >= 4X1 + 3X2 = a__and(mark(X1),X2) mark(if(X1,X2,X3)) = 2X1 + 4X2 + 4X3 + 8 >= 2X1 + 2X2 + 2X3 + 4 = a__if(mark(X1),X2,X3) mark(add(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__add(mark(X1),X2) mark(first(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__first(mark(X1),mark(X2)) mark(from(X)) = 8X + 4 >= 6X + 3 = a__from(X) mark(true()) = 8 >= 4 = true() mark(false()) = 4 >= 2 = false() mark(0()) = 8 >= 4 = 0() mark(s(X)) = 2X >= X = s(X) mark(nil()) = 4 >= 2 = nil() mark(cons(X1,X2)) = 2X1 + 2X2 + 2 >= X1 + X2 + 1 = cons(X1,X2) a__and(X1,X2) = 2X1 + 3X2 >= 2X1 + 3X2 = and(X1,X2) a__if(X1,X2,X3) = X1 + 2X2 + 2X3 + 4 >= X1 + 2X2 + 2X3 + 4 = if(X1,X2,X3) a__add(X1,X2) = X1 + 2X2 >= X1 + X2 = add(X1,X2) a__first(X1,X2) = X1 + X2 >= X1 + X2 = first(X1,X2) a__from(X) = 6X + 3 >= 4X + 2 = from(X) problem: a__add(s(X),Y) -> s(add(X,Y)) 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(add(X1,X2)) -> a__add(mark(X1),X2) mark(first(X1,X2)) -> a__first(mark(X1),mark(X2)) mark(s(X)) -> s(X) 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=1 interpretation: [if](x0, x1, x2) = 4x0 + x1 + 4x2, [and](x0, x1) = 4x0 + x1, [from](x0) = x0, [a__from](x0) = 6x0 + 2, [first](x0, x1) = 2x0 + 2x1, [cons](x0, x1) = 2x0 + 2x1 + 2, [a__first](x0, x1) = 2x0 + 2x1, [add](x0, x1) = 4x0 + x1, [s](x0) = 2x0, [a__add](x0, x1) = 4x0 + 2x1, [a__if](x0, x1, x2) = 4x0 + x1 + 4x2, [mark](x0) = 4x0, [a__and](x0, x1) = 4x0 + x1 orientation: a__add(s(X),Y) = 8X + 2Y >= 8X + 2Y = s(add(X,Y)) a__first(s(X),cons(Y,Z)) = 4X + 4Y + 4Z + 4 >= 4X + 2Y + 4Z + 2 = cons(Y,first(X,Z)) a__from(X) = 6X + 2 >= 6X + 2 = cons(X,from(s(X))) mark(and(X1,X2)) = 16X1 + 4X2 >= 16X1 + X2 = a__and(mark(X1),X2) mark(add(X1,X2)) = 16X1 + 4X2 >= 16X1 + 2X2 = a__add(mark(X1),X2) mark(first(X1,X2)) = 8X1 + 8X2 >= 8X1 + 8X2 = a__first(mark(X1),mark(X2)) mark(s(X)) = 8X >= 2X = s(X) a__and(X1,X2) = 4X1 + X2 >= 4X1 + X2 = and(X1,X2) a__if(X1,X2,X3) = 4X1 + X2 + 4X3 >= 4X1 + X2 + 4X3 = if(X1,X2,X3) a__add(X1,X2) = 4X1 + 2X2 >= 4X1 + X2 = add(X1,X2) a__first(X1,X2) = 2X1 + 2X2 >= 2X1 + 2X2 = first(X1,X2) problem: a__add(s(X),Y) -> s(add(X,Y)) a__from(X) -> cons(X,from(s(X))) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(add(X1,X2)) -> a__add(mark(X1),X2) mark(first(X1,X2)) -> a__first(mark(X1),mark(X2)) mark(s(X)) -> s(X) 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=1 interpretation: [if](x0, x1, x2) = 4x0 + x1 + x2, [and](x0, x1) = x0 + 4x1 + 4, [from](x0) = x0, [a__from](x0) = 7x0 + 4, [first](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = 4x0 + x1, [a__first](x0, x1) = x0 + x1 + 3, [add](x0, x1) = 3x0 + x1 + 3, [s](x0) = 3x0 + 4, [a__add](x0, x1) = 3x0 + 3x1 + 4, [a__if](x0, x1, x2) = 4x0 + x1 + 4x2 + 1, [mark](x0) = 4x0 + 1, [a__and](x0, x1) = x0 + 4x1 + 7 orientation: a__add(s(X),Y) = 9X + 3Y + 16 >= 9X + 3Y + 13 = s(add(X,Y)) a__from(X) = 7X + 4 >= 7X + 4 = cons(X,from(s(X))) mark(and(X1,X2)) = 4X1 + 16X2 + 17 >= 4X1 + 4X2 + 8 = a__and(mark(X1),X2) mark(add(X1,X2)) = 12X1 + 4X2 + 13 >= 12X1 + 3X2 + 7 = a__add(mark(X1),X2) mark(first(X1,X2)) = 4X1 + 4X2 + 5 >= 4X1 + 4X2 + 5 = a__first(mark(X1),mark(X2)) mark(s(X)) = 12X + 17 >= 3X + 4 = s(X) a__and(X1,X2) = X1 + 4X2 + 7 >= X1 + 4X2 + 4 = and(X1,X2) a__if(X1,X2,X3) = 4X1 + X2 + 4X3 + 1 >= 4X1 + X2 + X3 = if(X1,X2,X3) a__add(X1,X2) = 3X1 + 3X2 + 4 >= 3X1 + X2 + 3 = add(X1,X2) a__first(X1,X2) = X1 + X2 + 3 >= X1 + X2 + 1 = first(X1,X2) problem: a__from(X) -> cons(X,from(s(X))) mark(first(X1,X2)) -> a__first(mark(X1),mark(X2)) Matrix Interpretation Processor: dim=1 interpretation: [from](x0) = x0, [a__from](x0) = 5x0 + 2, [first](x0, x1) = x0 + 4x1 + 3, [cons](x0, x1) = x0 + x1, [a__first](x0, x1) = x0 + x1 + 2, [s](x0) = 4x0, [mark](x0) = 3x0 orientation: a__from(X) = 5X + 2 >= 5X = cons(X,from(s(X))) mark(first(X1,X2)) = 3X1 + 12X2 + 9 >= 3X1 + 3X2 + 2 = a__first(mark(X1),mark(X2)) problem: Qed