/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(tt(),X) -> mark(X) a__plus(N,0()) -> mark(N) a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M))) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(tt()) -> tt() mark(0()) -> 0() mark(s(X)) -> s(mark(X)) a__and(X1,X2) -> and(X1,X2) a__plus(X1,X2) -> plus(X1,X2) Proof: Matrix Interpretation Processor: dim=1 interpretation: [plus](x0, x1) = 4x0 + x1, [and](x0, x1) = 6x0 + x1, [s](x0) = x0, [a__plus](x0, x1) = 4x0 + x1, [0] = 6, [mark](x0) = x0, [a__and](x0, x1) = 6x0 + x1, [tt] = 3 orientation: a__and(tt(),X) = X + 18 >= X = mark(X) a__plus(N,0()) = 4N + 6 >= N = mark(N) a__plus(N,s(M)) = M + 4N >= M + 4N = s(a__plus(mark(N),mark(M))) mark(and(X1,X2)) = 6X1 + X2 >= 6X1 + X2 = a__and(mark(X1),X2) mark(plus(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = a__plus(mark(X1),mark(X2)) mark(tt()) = 3 >= 3 = tt() mark(0()) = 6 >= 6 = 0() mark(s(X)) = X >= X = s(mark(X)) a__and(X1,X2) = 6X1 + X2 >= 6X1 + X2 = and(X1,X2) a__plus(X1,X2) = 4X1 + X2 >= 4X1 + X2 = plus(X1,X2) problem: a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M))) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(tt()) -> tt() mark(0()) -> 0() mark(s(X)) -> s(mark(X)) a__and(X1,X2) -> and(X1,X2) a__plus(X1,X2) -> plus(X1,X2) Matrix Interpretation Processor: dim=1 interpretation: [plus](x0, x1) = 4x0 + 2x1 + 2, [and](x0, x1) = x0 + 2x1 + 4, [s](x0) = x0 + 7, [a__plus](x0, x1) = 4x0 + 2x1 + 2, [0] = 2, [mark](x0) = x0, [a__and](x0, x1) = x0 + 2x1 + 4, [tt] = 0 orientation: a__plus(N,s(M)) = 2M + 4N + 16 >= 2M + 4N + 9 = s(a__plus(mark(N),mark(M))) mark(and(X1,X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = a__and(mark(X1),X2) mark(plus(X1,X2)) = 4X1 + 2X2 + 2 >= 4X1 + 2X2 + 2 = a__plus(mark(X1),mark(X2)) mark(tt()) = 0 >= 0 = tt() mark(0()) = 2 >= 2 = 0() mark(s(X)) = X + 7 >= X + 7 = s(mark(X)) a__and(X1,X2) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = and(X1,X2) a__plus(X1,X2) = 4X1 + 2X2 + 2 >= 4X1 + 2X2 + 2 = plus(X1,X2) problem: mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(tt()) -> tt() mark(0()) -> 0() mark(s(X)) -> s(mark(X)) a__and(X1,X2) -> and(X1,X2) a__plus(X1,X2) -> plus(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [0] [plus](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 1] [1], [1 1 0] [1 0 0] [0] [and](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [0] [0 0 1] [0 0 0] [1], [1 1 0] [0] [s](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 0] [1 0 0] [0] [a__plus](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 1] [1], [0] [0] = [0] [1], [1 0 1] [0] [mark](x0) = [0 1 0]x0 + [1] [0 0 1] [0], [1 1 0] [1 0 0] [0] [a__and](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [1] [0 0 1] [0 0 0] [1], [0] [tt] = [0] [0] orientation: [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [1] mark(and(X1,X2)) = [0 0 0]X1 + [0 0 1]X2 + [1] >= [0 0 0]X1 + [0 0 1]X2 + [1] = a__and(mark(X1),X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [0] mark(plus(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = a__plus(mark(X1),mark(X2)) [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [0] [0] mark(tt()) = [1] >= [0] = tt() [0] [0] [1] [0] mark(0()) = [1] >= [0] = 0() [1] [1] [1 1 1] [1] [1 1 1] [1] mark(s(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = s(mark(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] [0] a__and(X1,X2) = [0 0 0]X1 + [0 0 1]X2 + [1] >= [0 0 0]X1 + [0 0 1]X2 + [0] = and(X1,X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] a__plus(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = plus(X1,X2) [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] problem: mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) a__and(X1,X2) -> and(X1,X2) a__plus(X1,X2) -> plus(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [plus](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1 0 0] [0] [s](x0) = [0 0 0]x0 + [1] [0 0 1] [1], [1 0 0] [1 0 0] [a__plus](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 1] [0] [mark](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [1 0 0] [1 0 0] [0] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 1] [0 0 0] [0], [0] [tt] = [1] [1] orientation: [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] 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 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1] [0] mark(tt()) = [1] >= [1] = tt() [1] [1] [1 0 1] [1] [1 0 1] [0] mark(s(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = s(mark(X)) [0 0 1] [1] [0 0 1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__plus(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = plus(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] problem: mark(and(X1,X2)) -> a__and(mark(X1),X2) a__and(X1,X2) -> and(X1,X2) a__plus(X1,X2) -> plus(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [plus](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 1] [1 0 0] [0] [and](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [1] [0 0 1] [1 0 0] [0], [1 0 0] [1 0 0] [a__plus](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 0] [mark](x0) = [0 1 1]x0 [0 0 1] , [1 0 1] [1 0 0] [0] [a__and](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [1] [0 0 1] [1 0 0] [0] orientation: [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [0] mark(and(X1,X2)) = [0 1 1]X1 + [1 0 0]X2 + [1] >= [0 1 1]X1 + [0 0 0]X2 + [1] = a__and(mark(X1),X2) [0 0 1] [1 0 0] [0] [0 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] a__and(X1,X2) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 0 1] [1 0 0] [0] [0 0 1] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__plus(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = plus(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] problem: a__and(X1,X2) -> and(X1,X2) a__plus(X1,X2) -> plus(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [plus](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [1] [a__plus](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 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] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] a__plus(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = plus(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] problem: a__and(X1,X2) -> and(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [and](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 + [0] [0 0 0] [0 0 1] [0] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 1] [0] [0 0 0] [0 0 0] problem: Qed